Near-Surface Particle-Tracking Velocimetry

Chapter 1 Near-Surface Particle Tracking Velocimetry Peter Huang, Department of Mechanical Engineering, Binghamton University Jeffrey S. Guasto, Department of Physics, Haverford College Kenneth S. Breuer, Division of Engineering, Brown University 1 2 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 1.1 Introduction The advent of microfluidics in the late 1990’s brought about a new frontier in fluid mechanics. Since the introduction of the first microfluidic device, these miniaturized fluidic manipulation systems have been regarded as one of the most promising technologies for the 21st century. In particular, investigations into its application in biotechnology has been the most intense. Examples of such applications include immunosensors [1], reagent mixing [2], content sorter [3] and drug delivery [4]. Microfluidic devices are very attractive in biotechnology over conventional technology because they require small sample volume and produce rapid results. Additionally, the use of colloids for self-assembly processes [5] and the medical application of nanoparticles have recently become of interests [6]. The idea of a lab-on-a-chip spawned an industry that strives to miniaturize and popularize the ability to detect, process and analyze biological and chemical specimens on smaller, less expensive microfluidics-based platforms. As the device dimension shrinks, bulk properties of the fluid medium become less important while a thorough understanding of interfacial and near-wall fluid-solid interactions become vital to the advancement of these technologies. Indeed, for chemical reactions which take place at solid surfaces, the high surface-area-to-volume-ratio characteristic of microfluidics offers a much higher efficiency than its large scale counterpart [7]. On the flip side, the high surface-area-to-volume-ratio also means that near-surface phenomena will have a much larger impact on the bulk of the fluid content. An example of such near-surface phenomena is the fluidic slip on the channel walls and its influence on flow pattern and velocity [8]. Thus, a strong grasp of the fluidic and colloidal dynamics near a solid boundary is critical in designing and analyzing microfluidic devices. Current fabrication technology of small scale fluidic devices and application of microscopy techniques to fluid mechanics allow us to quantitative characterize new and interesting nearsurface physical phenomena critical to micro- and nanofluidics. Under most circumstances, the solid boundary is rigid and inert such that its physical and structural changes due to fluidic forces are nonexistent. Thus the majority of important surface-induced physical phenomena occur in the near-surface region of the fluid phase and can be categorized into two groups: (1) changes of the fluid mechanical characteristics due to the presence of the solid 1.1. INTRODUCTION 3 surface; (2) interactions between the dissolved molecules, suspended particulates and the solid surface. Examples of physical phenomena in the former group include electrokinetic flow [9], slip flow [10] and surface chemistry directed flow [11, 12], while particle or cell adhesion [13] and detachment [14], increased hydrodynamic drag [15], electrostatic interactions [16] and particle depletion layers [17] are effects of the latter group. With so much interest in near-surface phenomena, researchers have developed various techniques to study them. Optical microscopy has been widely used to observe interactions in the micrometer scale. However, as fabrication technology advances, the definition of “near-surface” has also evolved from the micrometer and to the nanometer scale. Traditional optical techniques are no longer sufficient now due to the fact that the visible wavelength limits the probing resolution to ∼ 0.5 µm. A demonstrated optical technique to overcome this obstacle is evanescent wave microscopy or, when combined with fluorescence microscopy, total internal reflection fluorescence (TIRF) microscopy [18]. The principle of total internal reflection has been known for more than a thousand years, since the time of the Persian scientist Ibn Sahl [19]. It is most commonly associated with Rene Descartes and Willebrord Snellius (Snell) after whom the common law of refraction is named. The presence of the evanescent wave propagating in the less dense optical medium was first described by Isaac Newton and later formalized in Maxwell’s theory of Electromagnetic Wave propagation. However, the adoption of the evanescent wave as a means to achieve localized illumination rose to widespread use in the life-sciences and biological physics community, where researchers realized that the near-surface illumination provided by the evanescent field provided a novel method to probe cellular structure, kinetics, diffusion and dynamics with unprecedented spatial resolution. Since the 1970’s, the TIRF microscopy technique has been used to measure chemical kinetics, surface diffusion, molecular conformation of adsorbates, cell development during culturing, visualization of cell structures and dynamics, and single molecule visualization and spectroscopy [20–24]. Surprisingly, a long time had passed before physical scientists finally caught up with the merits of evanescent wave imaging. Beginning in the 1990’s, several research groups started studying near-wall colloidal dynamics by observing the light scattered by micronsized particles inside evanescent wave field. Notable achievements include successful and 4 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY accurate measurements of gravitational attraction, double layer repulsion, hindered diffusion, van der Waals forces, optical forces, depletion and steric interactions, and particle surface charges [17, 25–32]. One application of particular relevance to our discussion is that of Prieve and co-workers [30–32], who used the evanescent field as a means to measure the behavior of micron-sized, colloidal particles in close proximity to a solid surface. Although this was not strictly velocimetry, they did track the statistical motion of particles in the evanescent field in order to back out the contributions of Brownian motion, gravitational sedimentation and electrostatic surface interactions. However, evanescent wave scattering microscopy could not further advance to the nanoscale because scattering by nanometer-sized particles is weak and thus limited the minimum particle size for evanescent wave scattering microscopy to about one micron. Therefore without fluorescence, experimental investigations of near-surface phenomena would be restricted to at least one micrometer away from the solid boundary. The advantage of the TIRF microscopy technique, in contrast to evanescent wave light scattering microscopy, lies in its ability to produce extremely confined illumination and sub-micron imaging depths and resolutions at a dielectric interface by reflecting an electromagnetic wave off of the interface. An extremely high sensitivity is achieved by imaging fluorescent dyes or particles and illuminating only those fluorophores within the first few hundred nanometers of the interface (figure 1.1). Since no extraneous, out-of-focus fluorescence is excited, there is little background noise as demonstrated by the TIRF image of 200 nm diameter colloidal particles in figure 1.2. Additionally, because the illumination intensity decreases monotonically away from the interface, it is possible to infer an object’s distance from the interface through intensity. Particle-based velocimetry has long been used in flow visualization and measurement [33]. It is based on an intuitive and for most part correct assumption that the seeding tracer particles are carried by the fluid surrounding them, and therefore their translational velocities must be that of the local fluid elements. Therefore, fluid velocities can be inferred from apparent velocities of the tracer particles calculated based on displacements of the tracer particles and the time between successive particle imaging. When particle-based velocimetry methods were adopted to study microfluidics, sub-micron fluorescent tracer particles 5 1.1. INTRODUCTION liquid z ~ penetration depth θ solid Figure 1.1: A schematic of total internal reflection fluorescence (TIRF) microscopy. An illumination beam is brought to the liquid/solid interface at an incident angle, θ, is greater than the critical angle predicted by Snell’s law. As a result total internal reflection occurs at the solid/liquid interface and an evanescent field is created in the liquid phase. The evanescent energy then illuminates the encapsulated fluorophores inside a colloidal particle in the close vicinity of the interface. were used to minimize light scattering and imaging noise while attaining spatial resolutions of tens of nanometers [34]. The first concerted effort to use TIRF microscopy with particle image velocimetry was reported by Zettner and Yoda [35] who demonstrated prism-coupled TIRF to measure the motion of tracer particles within the electric double layer of an electroosmotic flow in a microchannel. Although ground-breaking, the resolution of this approach was somewhat limited by the relatively poor spatial and temporal performance of the camera system used. More recently, TIRF microscopy has been integrated with improved particle velocimetry techniques and termed Total Internal Reflection Velocimetry (TIRV) [36] and Multilayer Nano-Particle Image Velocimetry (MnPIV) [37]. These methods have been used to measure the dynamics of significantly smaller scales (10 nm to 300 nm) and applications have included the characterization of electro-osmotic flows [38], slip flows [39, 40], hindered diffusion [41, 42], near-wall shear flows [43–47] and quantum dot tracer particles [45, 48– 52]. It is believed that evanescent wave-based near-surface particle tracking velocimetry will become a workhorse in near-surface nanofluidic, colloidal and molecular dynamics investigations as technology strives further toward smaller and smaller scale systems. The last ten years have seen a number of near-surface particle tracking velocimetrybased experimental results, each with different approaches, advantages and disadvantages, 6 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY (a) (b) Figure 1.2: Sample images of (a) conventional bright field illumination versus (b) TIRF illumination for 200 nm particles. as will be discussed during the remainder of the chapter. In this chapter, we provide a thorough review of the established fundamentals and recent development of ”Near-Surface Particle Tracking Velocimetry” to the reader. We first discuss the theories, measurement designs and experimental procedures that are essential to successful near-surface particle tracking velocimetry for nanofluidics. We follow that with a discussion of experimental studies reported in the literature and state of the art development of evanescent wave-based velocimetry techniques. We then conclude with its future directions and perceived potentials of ”Near-Surface Particle Tracking Velocimetry” in nanotechnology. 7 1.2. THEORETICAL CONSIDERATIONS z Flow TIRFM Water, n 2 Penetration Depth, δ x Glass, n 1 θ>θcr Figure 1.3: A schematic of evanescent wave illumination. 1.2 Theoretical Considerations In this section we present theoretical considerations most closely relevant to conducting nearsurface particle tracking velocimetry. They include evanescent wave illumination, fluorescent particle intensity variations, hindered Brownian motion, near-wall shear effects and particle distribution. 1.2.1 Evanescent Wave Illumination When an electromagnetic plane wave (light) in a dielectric medium of refractive index, n1 , is incident upon an interface of a different dielectric material with a lower index of refraction, n2 , at an angle, θ, greater than the critical angle predicted by Snell’s law such that θ > θcr = sin−1 (n2 /n1 ), total internal reflection occurs at the interface between the two media as illustrated in figures 1.3 and 1.4. While all of the incident energy is reflected, the full solution of Maxwell’s equations predicts that in the less dense medium there exists an electromagnetic field whose intensity decays exponentially away from the two-medium interface. This electromagnetic field, termed evanescent waves or evanescent field, propagates parallel to the interface and has a decay 8 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY water glass Figure 1.4: COMSOL simulation of total internal reflection in figure 1.3. Plotted in the figure is time-averaged total electromagnetic energy density in the vicinity of the glass/water interface. Because the refractive indices of glass and water are 1.515 and 1.33 respectively, total internal reflection occurs at θ > θcr = 61.39◦ . In this figure, the incident angle of the incoming Gaussian illumination beam is θ = 64.54◦ and the illumination wavelength is 514 nm. length, δ, on the order of the wavelength of the illuminating light, λ. Furthermore, photons are not actually reflected at the interface, but rather tunnel into the low index material (a process called optical tunneling). As a result, the reflected beam of light is shifted along the interface by a small amount (∆x ≈ 2δ tan θ), which is known as the Goos-Haenchen shift [53]. The full details to this solution of Maxwell’s equations are outlined elsewhere [22]. Only the basic results relevant to evanescent wave microscopy are presented below, specifically the intensity distribution in the lower optical density material. The solution presented here assumes an infinite plane wave incident on the interface, which is a good approximation to a Gaussian laser beam typically used in practice. The intensity has the exponential form I (z) = I0 e−z/δ , (1.1) where z is the coordinate normal to the interface into the low index medium, I0 is the wall intensity and the decay length, δ, is given by δ= −1/2 λ  2 , sin θ − n2 4πn1 (1.2) 9 1.2. THEORETICAL CONSIDERATIONS 1 Simulation Theory Normalized Intensity 0.8 0.6 0.4 0.2 0 0 0.5 1 z/λ 1.5 2 Figure 1.5: The exponential intensity decay of evanescent field in figure 1.4. There exists a close agreement between the numerical solution of Maxwell’s equations (COMSOL simulation) and theoretical calculations, equations (1.1) and (1.2). and n = n2 /n1 < 1. In a typical system with a glass substrate (n1 = 1.515), water as the working fluid (n2 = 1.33) and an Argon Ion laser for illumination (λ = 514 nm), a penetration depth of about δ = 128 nm can be produced with an incident angle of θ = 64.54o (figure 1.5). The polarization of the incident beam does not affect the penetration depth, but it does affect the amplitude of the evanescent field. For plane waves incident on the interface with intensity, I1 , in the dense medium, the amplitude of the field in the less dense medium, I0 is given by k I0 =
2 sin2 θ − n2 , n cos θ + sin2 θ − n2 4 cos2 θ I0⊥ = I1⊥ , 1 − n2 2 k 4 cos θ I1 4 2 (1.3) (1.4) for incident waves parallel and perpendicular to the plane of incidence, respectively, as shown in figure 1.6. Both polarizations yield a wall intensity significantly greater than the incident radiation, with the parallel polarization being 25% greater than the perpendicular polarization. 10 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 6 Parallel Perpendicular 5 I /I 0 1 4 3 2 1 0 60 65 70 75 80 θ [degree] 85 90 Figure 1.6: Evanescent field wall intensity as a function of incident angle for both parallel and perpendicular polarizations at a typical glass-water interface. In Total Internal Reflection Fluorescence (TIRF) microscopy, many researchers have exploited the monotonic decay of the evanescent field to map the intensity of fluorescent dye molecules or particles to their distances from the fluid/solid interface [39, 41, 42, 46]. It is intuitive to assume that for a particle which has fluorophores embedded throughout its whole volume, its fluorescent intensity will be proportional to the amount of evanescent electromagnetic energy entering its spherical shape. In figure 1.7, the amounts of electromagnetic energies enclosed inside particles of various sizes in evanescent fields are found to be in close agreement with the local intensities of the illuminating evanescent waves. It can therefore be inferred that the emission intensities of fluorescent particles can be used to determine the distances between the particles and the fluid/solid interface. Still practical applications of such intensity-position correlation require additional experimental calibrations (section 1.3.3). 11 1.2. THEORETICAL CONSIDERATIONS Enclosed EM Energy (Arb. Unit) 1 d/λ = 0.39 d/λ = 6 d/λ = 12 Evanescent Field 0.8 0.6 0.4 0.2 0 0 0.5 1 h/λ 1.5 2 Figure 1.7: Enclosed electromagnetic (EM) energy inside suspended particles when illuminated by evanescent waves. The enclosed EM energies are obtained from COMSOL simulations of spherical polystyrene particles at various diameters, d, and gap sizes where h = z − d/2 is the shortest distance between the particle surface and the glass substrate (n = 1.515). A particle would be touching the substrate if h = 0. The suspending liquid of consideration is water (n = 1.33). The illumination wavelength is λ = 514 nm. The enclosed EM energies are normalized by the total enclosed EM energy inside a particle when h = 0. The evanescent field intensity decay curve is obtained from figure 1.4. 12 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 1.2.2 Fluorescent Nanoparticle Intensity Variation When applying the intensity-distance correlation described in the previous section to an ensemble of nanometer-sized particles that are typically used in fluid mechanics and colloid dynamics measurements, one must consider the polydispersity of the particles and the variation of emission intensity with particle size. All commercially available polystyrene and latex nanoparticles are manufactured with a finite size distribution where the particle radius is specified by a mean value a0 and a coefficient of variation up to 20%. Several researchers have attempted to compensate for this variation statistically, when making ensemble-averaged measurements of fluorescent nanoparticles with TIRF [39, 47]. Most manufacturers impregnate the volume of the polymer particles with fluorescent dye, and thus it is often assumed that the light intensity emitted by a particle is proportional to its volume. For instance, Huang et al. [39] proposed that the intensity of a given particle, I p , of radius a at a distance h from the interface is p I (z, a) = I0p  a a0 3   z−a , exp − δ (1.5) where I0p is the intensity of a particle with a radius a0 and δ is the penetration depth of the evanescent field. Below, we quote results from Chew (1988) [54] for dipole radiation inside dielectric spheres to support the claim that particle intensity is proportional to volume and demonstrate the limits of this assumption for larger particles. Consider a dielectric sphere of radius, a, √ permittivity, ǫ1 , permeability, µ1 , and index of refraction, n1 = µ1 ǫ1 , inside of a second, infinite dielectric medium with ǫ2 , µ2 , and n2 . The radiation from an emitting dipole with free space wavelength, λ0 , will have momentum vectors, k1,2 = 2πn1,2 /λ0 , and subsequently, ρ1,2 = k1,2 a. The power emitted by a dipole is proportional to the dipole transition rate, R⊥,k , for perpendicular and parallel polarizations. These relations are provided in Chew (1988) and are normalized by the transition rates for dipoles contained in an infinite medium 1, ⊥,k R⊥,k /R0 . For a distribution of dipoles, c (~r), located within the sphere, the volume averaged emission is * R ⊥,k ⊥,k R0 + = R  ⊥,k c (~r) d3~r R⊥,k /R0 R . c (~r) d3~r (1.6) 13 1.2. THEORETICAL CONSIDERATIONS The volume averaged emission for randomly oriented dipoles, R/R0 , with a uniform concentration distribution, c (~r) = c0 , is  R R0  1 ≡ 3 * Rk R⊥ + 2 k R0⊥ R0 +  ∞  X Jn GKn = 2H + ′ 2 , 2 |D | |Dn | n n=1 (1.7) where H = G = Kn = Jn = Dn = Dn′ =   µ1 ǫ1 ǫ2 9ǫ1 , µ2 4ρ51 µ1 µ2 , ǫ1 ǫ2  ρ31  2 jn (ρ1 ) − jn+1 (ρ1 ) jn−1 (ρ1 ) , 2 Kn−1 − nρ1 jn2 (ρ1 ) ,  ′ ′ (1) ǫ1 jn (ρ1 ) ρ2 h(1) n (ρ2 ) − ǫ2 hn (ρ2 ) [ρ1 jn (ρ1 )] ,  ′ ′ (1) µ1 jn (ρ1 ) ρ2 h(1) n (ρ2 ) − µ2 hn (ρ2 ) [ρ1 jn (ρ1 )] . r Spherical Bessel functions of the first kind are denoted by jn , and spherical Hankel functions (1) of the first kind are denoted by hn . The terms Dn and Dn′ are the same denominators of the Mie scattering coefficients [55]. In the Rayleigh limit (ka ≪ 1), the transition rates become independent of polarization and simplify greatly to  R R0  = 9 (ǫ1 /ǫ2 + 2)2 s ǫ2 µ32 . ǫ1 µ31 (1.8) Figure 1.8 shows the normalized mean emission rates (power) for both the Rayleigh limit and the full solution proposed by Chew (1988) [54] as a function of the particle radius, a, for a polystyrene particle (n1 = 1.59) immersed in water (n2 = 1.33) with an emission wavelength λ0 = 600 nm. For particles with radius a ≤ 200 nm, the Rayleigh limit is a good approximation to the full solution. The total power, Ė, emitted by a particle is the volume averaged emission rate, hR/R0 i, 14 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY Normalied Mean Rate 1 Chew (1988) Rayleigh Limit 0.8 0.6 0.4 0.2 0 0 100 200 300 Radius, a [nm] 400 500 Figure 1.8: Volume averaged emission rate for uniformly distributed, randomly oriented radiating dipoles with emission wavelength, λ0 = 600 nm, within a polystyrene sphere (n1 = 1.59) immersed in water (n2 = 1.33). scaled by the volume of a given particle 4 Ė = πa3 3  R R0  . (1.9) The total power emitted by a particle is shown in figure 1.9 normalized by the emission of a particle with radius a = 500 nm. Since all particle radii considered here are sub-wavelength (a < λ0 ), the Rayleigh limit is a descent approximation. For particles with radii a . 125 nm, the Rayleigh approximation follows the full solution quite closely as seen in the inset of figure 1.9. Thus, the total power scales with the particle volume for sub-wavelength particle at or near the Rayleigh limit, which partially vindicates the approximation made in equation (1.5). Further validation of equation (1.5) can be achieved through verification of the uniformity of excitation in both the plane wave and evanescent wave excitation cases. 15 1.2. THEORETICAL CONSIDERATIONS 1 0.03 Chew (1988) Rayleigh Limit 0.025 0.8 0.02 Total Emission 0.015 0.01 0.6 0.005 0 0 50 100 0.4 0.2 0 0 100 200 300 Radius, a [nm] 400 500 Figure 1.9: Total emission (power) for uniformly distributed, randomly oriented radiating dipoles with emission wavelength, λ0 = 600 nm, within a polystyrene sphere (n1 = 1.59) immersed in water (n2 = 1.33). For particles approaching the Rayleigh limit with radii, a ≤ 125 nm, the emitted power scales with the particle volume. 1.2.3 Hindered Brownian Motion The Brownian motion of small particles due to molecular fluctuations is generally well understood [56] and can be significant in magnitude for nanoparticles commonly used for nearsurface particle tracking velocimetry. The random, thermal forcing of the particles is damped by the hydrodynamic drag resulting from the surrounding solvent molecules, and the particle’s motion can be described as a diffusion process [57]: ∂p (~r, t) = ∇ · (D (~r) ∇p (~r, t)) , ∂t (1.10) where p is the probability of finding a particle at a given location, ~r, at time, t, and D is the diffusion coefficient. For an isolated, spherical particle that is significantly larger than the surrounding solvent molecules, the diffusion coefficient is constant and isotropic, and it is described by the Stokes-Einstein relation [58] D0 = kb T kb T = , ξ 6πµa (1.11) 16 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY where kb is Boltzmann’s constant, T is the absolute temperature, ξ is the drag coefficient, µ is the dynamic viscosity of the solvent and a is the particle radius. In this case, the solution to equation (1.10) subject to the condition p (~r, t = t0 ) = δ (~r − ~r0 ) becomes p (~r, t) = 1 8 (πD0 ∆t)3/2 " # |~r − ~r0 |2 exp − , 4D0 ∆t (1.12) where ∆t = t − t0 [59]. When an isolated particle in a quiescent fluid is in the vicinity of a solid boundary, its Brownian motion is hindered anisotropically due to an increase in hydrodynamic drag. Several theoretical studies have accurately captured this effect for various regimes of particle wall separation distance [15, 60–62]. The hindered diffusion coefficient in the wall-parallel direction, Dx , is described by  z −6 Dx 9  z −1 1  z −3 45  z −4 1  z −5 =1− + − − +O , D0 16 a 8 a 256 a 16 a a (1.13) where z is the particle center distance to the wall. This is a direct result from the drag force on a moving particle near a stationary wall in a quiescent fluid calculated by the “method of reflections,” which is accurate far from the wall, z/a > 2 [63]. A better approximation for small particle-wall separation distances results from an asymptotic solution for the drag force based on lubrication theory for z/a < 2 [61]. Under these assumptions, the corresponding, normalized diffusion coefficient is Dx = − D0 ln z a
  2 ln az − 1 − 0.9543 .
2
− 1 − 4.325 ln az − 1 + 1.591 (1.14) The relative hindered diffusion coefficient for a particle diffusing in the wall-normal direction, Dz , is described by Dz = D0 ( " ∞ X 4 n (n + 1) sinh α 3 (2n − 1) (2n + 3) n=1 #)−1 2 sinh (2n + 1) α + (2n + 1) sinh 2α
, −1 4 sinh2 n + 12 α − (2n + 1)2 sinh2 α (1.15) 17 1.2. THEORETICAL CONSIDERATIONS 1 Dx,z/D0 0.8 0.6 0.4 Dx (Method of Reflection) 0.2 D (Lubrication) x D (Brenner, 1961) z 0 1 2 3 z/a 4 5 Figure 1.10: Hindered diffusion coefficients in the wall-parallel, Dx , and wall-normal, Dz , directions for a neutrally buoyant spherical particle near a solid boundary. where α = cosh−1 (z/a). This equation results from an exact solution of the force experienced by a particle for motions perpendicular to a stationary wall in a quiescent fluid [60]. The wall-parallel and wall-normal hindered diffusivities described in equations (1.13) - (1.15) are plotted in figure 1.10. We also note that equation (1.15) has been shown to be wellapproximated by
2
6 az − 1 + 2 az − 1 Dz , =
2
D0 6 az − 1 + 9 az − 1 + 2 (1.16) which is convenient for fast computation [28]. These theoretical results have been verified over different length scales by various researchers including several evanescent wave illumination studies [28, 30, 42, 64–67]. Deviations from the bulk diffusivity become noticeable for particle-wall separation distances of order one. For instance, the wall-parallel diffusivity drops to one half of its bulk value when z/a ≈ 1.2, while the wall-normal diffusivity drops to one half at z/a ≈ 2.1. The implications of hindered Brownian motion on near-surface par- ticle tracking velocimetry have been intensely investigated recently and is further discussed in section 1.4.4. 18 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 1.2.4 Near-Wall Shear Effects The motion of an incompressible fluid obeys the continuity condition (conservation of mass) ∇ · ~u = 0, (1.17) where the velocity field, ~u, is divergence free. The Navier-Stokes equation governs the motion of a viscous fluid and in the case of an incompressible fluid is ρ  ∂~u + ~u · ∇~u ∂t  = −∇P + µ∇2~u, (1.18) where ρ is the fluid density and P is the dynamic pressure. For the small Reynolds numbers (Re ≪ 1) typical of microfluidic devices, equation 1.18 greatly reduces in complexity to Stokes’ equation [68]: ∇P = µ∇2~u. (1.19) Most microfabrication techniques produce microchannels with approximately rectangular cross-sections. Thus, a useful result from equation (1.19) is the solution for the velocity profile in a rectangular duct with height, d, and width, w, subject to the no-slip boundary condition (~u = 0) at the walls. The laminar, unidirectional flow occurs in the pressure gradient direction with velocity, ux , described below [59]: 1 ux (y, z) = 2µ m =  ∂P − ∂x " π (2n − 1) , d # ∞ n X d2 8 (−1) cos (mz) cosh (my) , − z2 + 4 d n=1 m3 cosh (mw/2) (1.20) where the pressure gradient and volumetric flow rate, Q, are related by wd3 Q= 12µ  ∂P − ∂x " # ∞ 192d X 1 1 − exp (−nπw/d) 1− 5 . π w n=1,3,5,... n5 1 + exp (−nπw/d) (1.21) It is well known that rigid particles tend to rotate in shear, and in the special case of a sphere near a planar wall, additional hydrodynamic drag slows the particle’s translational 19 1.2. THEORETICAL CONSIDERATIONS velocity below that of the local fluid velocity [15, 62]. For wide microchannels (w ≫ d) in the very near-wall region (h ≪ d), the nearly parabolic velocity profile can be approximated by a linear shear flow u ≈ zS, (1.22) where S is the shear rate. The wall-parallel drag force experienced by a neutrally buoyant, free particle with radius a and a distance z between its center and the wall in a linear shear flow results in a particle translational velocity, v, that is different from the fluid velocity at the particle center’s plane. For large z/a, the particle’s translational velocity can be estimated by the “method of reflections” [62]. This translational velocity, normalized by the local fluid velocity at the particle’s center, is 5  z −3 v ≃1− . zS 16 a (1.23) For small particle-wall separation distances (small z/a), an asymptotic solution based on lubrication theory has also been established as v 0.7431 ≃ zS 0.6376 − 0.2 ln z a
, −1 (1.24) which is also normalized by the unperturbed fluid velocity at the particle’s center [62]. The “method of reflections” solution and asymptotic lubrication solution from equations (1.23) (1.24) are shown in figure 1.11. Additionally, Pierres et al. [69] used a cubic approximation to segment the solutions for intermediate values of z/a:  z −1 i n h z v ≃ −1 exp 0.68902 + 0.54756 ln zS a a i2 i3  h z h z . −1 −1 + 0.0037644 ln +0.072332 ln a a (1.25) Particle rotation can also induces a lifting force, which tends to make the particles migrate away from the wall [70]. Obviously, such lift force can potentially lead to biased sampling of local fluid velocities by the tracer particles during near-surface particle tracking velocimetry measurements and should be cautiously treated when designing experiments and analyzing 20 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 1 0.9 v/zS 0.8 0.7 0.6 0.5 0.4 1 Method of Reflection Lubrication 1.5 2 z/a 2.5 3 Figure 1.11: Particle velocity normalized by the local fluid velocity in a near-wall shear flow given by the “method of reflection” and lubrication approximation solutions from Goldman et al., 1967b. results. The subject of lift forces acting on a small sphere in a wall-bounded linear shear flow has been thoroughly studied by Cherukat & McLaughlin [71]. Here we will present only the theory that applies to the flow and colloidal conditions commonly encountered in near-surface particle tracking velocimetry experiments. Suppose that a free-rotating rigid sphere of radius a is in a Newtonian incompressible fluid of kinematic viscosity ν and is in the vicinity of a solid wall. In the presence of a linear shear flow, this free-rotating sphere can travel at a velocity Usph that is different from the fluid velocity, UG , of the shear plane located at its center [62] due to shear-induced particle rotation described previously. We can define a characteristic Reynolds number Reα = Us a , ν (1.26) based on the velocity difference, Us = Usph − UG . A second characteristic Reynolds number based on shear rate can be defined as Reβ = Ga2 , ν (1.27) 21 1.2. THEORETICAL CONSIDERATIONS where G is the wall shear rate. In this geometry, the wall is considered as located in the ”inner region” of flow around the particle if Reα ≪ Ω and Reβ ≪ Ω2 , where Ω ≡ a/(z − a). For near-wall particle tracking velocimetry using nanoparticles, Reα ∼ Reβ . 10−4 while Ω ∼ O (1), and thus the inner region theory of lift force applies. For a flat wall located in the inner region of flow around a free-rotating particle, the lift force, FL , which is perpendicular to the wall, is scaled by [71] FL ∼ Reα · IΩ , (1.28) where IΩ is a coefficient that can be numerically estimated by   IΩ = 1.7631 + 0.3561Ω − 1.1837Ω2 + 0.845163Ω3 −    Reβ 3.21439 2 + + 2.6760 + 0.8248Ω − 0.4616Ω Ω Reα    Reβ 2  2 3 1.8081 + 0.879585Ω − 1.9009Ω + 0.98149Ω . Reα (1.29) Again for near-surface particle tracking velocimetry using nanoparticles, IΩ . O (102 ). Therefore FL ∼ Reα · IΩ . 10−4

102 ≪ 1, (1.30) and the lift force acting on near-wall particles is insignificant and can be neglected for most practical cases. 1.2.5 Near-Wall Particle Concentration Electrostatic forces arise from the Coulombic interactions between charged bodies such as polystyrene tracer particles and glass immersed in water. When immersed in an ionic solution, these forces are moderated by the formation of an ionic double layer on their surfaces, which screen the charge. The characteristic length scale of these forces is given by the Debye length, κ−1 = r ǫ f ǫ0 kb T , 2ce2 (1.31) 22 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY where ǫ0 is the permittivity of free space, ǫf is the relative permittivity of the fluid, e is the elementary charge of an electron and c is the concentration of ions in solution [72]. In the case of a plane-sphere geometry for like-charged objects (for example, a spherical polystyrene particle and a flat glass substrate), the immobile substrate can exert a repulsive force on the particle and is quantified by the potential energy of the interaction: U el (z) = Bps e−κ(z−a) . (1.32) The magnitude of the electrostatic potential is given by Bps = 4πǫf ǫ0 a  kb T e 2 ψˆp + 4γΩκa 1 + Ωκa !" 4 tanh ψ̂s 4 !# , (1.33)     where γ = tanh ψˆp /4 , Ω = ψˆp − 4γ /2γ 3 , ψˆp = ψp e/kb T and ψ̂s = ψs e/kb T [73]. ψp and ψs represent the electric potentials of the particle and the substrate, respectively. Contributions from attractive, short-ranged van der Waals forces, which originate from multipole dispersion interactions [74], should also be considered when the particle-wall separation is on the order of 10 nm. The potential due to van der Waals interactions for a plane-sphere geometry is given by U vdw    Aps a a z−a (z) = − , + + ln 6 z−a z+a z+a (1.34) where Aps is the Hamaker constant [75, 76]. The gravitational potential can also be important for large or severely density mismatched particles. The gravitational potential of a buoyant particle in a fluid is given by 4 U g (z) = πa3 (ρs − ρf ) g (z − a) , 3 (1.35) where ρs and ρf are the densities of the sphere and fluid, respectively, and g is the acceleration due to gravity. Finally, optical forces due to electric field gradients from the illuminating light can trap or push colloidal particles [77]. Below, we present an order of magnitude estimation for the 23 1.2. THEORETICAL CONSIDERATIONS potential of a dielectric particle in a weak illuminating evanescent field typically found in evanescent wave-based near-surface particle tracking velocimetry. Following Novotny and Hecht [78], the force on a dipole is given by   ~ = α∇|E| ~ 2. ~ = αE ~ ·∇ E F~ = (~µ · ∇) E (1.36) The dipole moment, ~µ, polarizability, α, and electric field magnitude are given by the following: ~ ~µ = αE, α = (1.37) n2 − n20 3 p , 4πǫ0 a0 2 np + 2n20 1 ~ 2, I (z) = I0 e−z/δ = cǫ0 n0 |E| 2 (1.38) (1.39) where n0 is the index of the surrounding medium, np is the index of the particle and c is the speed of light in a vacuum. Combining the above expressions, we can write an approximation to the potential of a particle near an interface due to an evanescent field: U opt 8πa30 n2p − n20 2 ~ I0 e−z/δ , ≈ −α|E| = − cn0 n2p + 2n20 (1.40) which is an attractive force. However, for strongly light-absorbing particles such as the semiconductor materials found in quantum dots, this optical force can be repulsive and more detailed analyses should be carefully carried out. The equilibrium distribution for an ensemble of non-interacting, suspended Brownian particles in an external potential has been shown to be given by a Boltzmann distribution [79]. For a brief discussion, we follow Doi and Edwards (1986) [79] and consider a onedimensional distribution below. Fick’s law of diffusion describes the flux, j, of material j (z, t) = −D ∂p (z, t) , ∂z (1.41) where D is the diffusion coefficient and p is the continuous probability function of finding a particle at a location, z, in the wall-normal coordinate at time, t. In the presence of an 24 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY external potential, U (z), particles experience an additional force Fz = − ∂U . ∂z (1.42) Fick’s law (equation (1.41)) is modified to reflect the additional flux induced by this force j (z, t) = −D ∂p p ∂U − , ∂z ξ ∂z (1.43) where the drag coefficient, ξ, is related to the diffusion coefficient, D = kb T /ξ. In the steady state, the net flux vanishes, j → 0, and the solution of equation (1.43) leads to the Boltzmann distribution exp [−U (z) /kb T ] = p0 e−U/kb T , exp [−U (z) /kb T ] dz z1 p (z) = R z2 (1.44) where p0 is a normalization constant [30] from all particles in the range z1 ≤ z ≤ z2 and U is the total potential energy given by the sum of all potentials experienced by the particle (electrostatic, van der Waals, etc.). An example illustrating the non-uniform particle concentrations in the near-wall region is shown in figure 1.12 for a 500 nm diameter polystyrene particle in water near a glass substrate with a 10 nm Debye length. In this case, electrostatic and van der Waals forces dominate, clearly forming a depletion layer within about 100 nm of the wall. The implications of the presence of a near-surface particle depletion layer to velocimetry accuracy has recently been investigated and reported [44, 47]. 25 1.2. THEORETICAL CONSIDERATIONS −3 4 x 10 p(z) 3 2 1 0 0 U=0 el U=U el vdw U=U +U 100 200 h=z−a [nm] 300 400 Figure 1.12: Near-wall particle concentration profiles for a 500 nm diameter polystyrene particle in water near a glass substrate with the effect of electrostatic (10 nm Debye length) and van der Waals interactions. 26 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 1.3 Experimental Procedures In this section, we discuss in details on the experimental procedures of conducting successful evanescent wave-based near-surface particle tracking velocimetry, including selection of experimental materials, sample preparation, optical and imaging setup, measurement calibration and the particle tracking algorithm. 1.3.1 Materials and Preparations As discussed before, creation of evanescent waves inside a microfluidic or nanofluidic channel requires the solid substrate or the channel wall to have higher optical density than the flowing fluid. That is, the substrate must have a higher index of refraction than the fluid does. Furthermore, the substrate must be transparent to both the illumination and the fluorescence emission wavelengths for high precision imaging. Examples of solid materials that satisfy these conditions include glass (n = 1.47 - 1.65), quartz (n = 1.55), Poly-methyl methacrylate (PMMA, n = 1.49) and other types of clear plastics. Among these, glass is the most common choice as it is chemically inert, physically robust and optically transparent to all visible light wavelengths (350 - 700 nm). Surface roughness of less than 10 nm is found to be not impeding the creation of evanescent waves. However, surface waviness presents a more critical issue as the local illumination incident angle could significantly deviate from the predicted value and thus changes the properties of the created evanescent waves. It should also be noted that thin-film chemical coatings of sub-wavelength thickness on the substrate surface does not prevent creation of evanescent waves. Demonstrated examples of coatings used in near-surface particle tracking velocimetry includes octadecyltrichorosilane (OTS) [39, 40] and P-selectin glycoprotein ligand-1 (PSGL-1) [47] self-assembled monolayers. Selection of the experimental fluid is typically based on the following criteria: (1) lower refractive index than that of the solid substrate; (2) lack of chemical reactions with the solid substrate or surface coatings; (3) availability of chemically compatible tracer particles; (4) desired physical properties such as density, viscosity and polarity. Air and various inert gases have the lowest refractive indices possible among fluids (n ≈ 1), but creating submicron-sized 1.3. EXPERIMENTAL PROCEDURES 27 aerosol tracer particles presents a difficult challenge. Water (n = 1.33) is the most common choice of fluid for its chemical stability and compatibility with biochemical reagents. Other organic and inorganic solvents such as hexane (n = 1.375) and ethanol (n = 1.36) are also potential candidates. A wide range of micron-sized and nanometer-sized tracer particles are commercially available for near-surface particle tracking velocimetry. For light scattering-based experiments, metallic, glass and quartz particles should be considered as they are stronger scatterers of evanescent waves. For fluorescence-based measurements, the list of tracer particle candidates include fluorescent polystyrene and latex particles, fluorescently tagged macromolecules such as Dextran and DNA, and semiconductor materials such as quantum dots. Tracer particle properties such as density, average size and size variations, deformation tendency, potential affinity to substrate, coagulation tendencies, chemical compatibility with fluid, and fluorescence quantum efficiency and wavelength should be carefully evaluated before and during experimentation. In general, particles that have fluorophores embedded throughout its whole volume is preferred for maximum imaging signals. Density mismatch between tracer particles and the fluid can lead to buoyancy and sedimentation that cause velocimetry measurement bias. These problems can be avoided if the chosen type of tracer particles satisfy the following condition, 4πa4 g |ρp − ρf | ≪ 1, 3kB T (1.45) where a is average particle radius, g is gravitational acceleration, ρp is particle density, ρf is fluid density, kB is Boltzmann constant and T is experimental fluid temperature. Coagulation of tracer particles also presents serious problems for particle identifications and intensitybased 3D positioning and should avoided as much as possible. Simple sonication of particle suspension is usually quite effective in breaking up particle clumps. Finally, the tracer particle seeding density of the measurement suspension should be moderately low to avoid tracking ambiguity between frames of images and assure velocimetry accuracy. A good rule of thumb is that the average spacing (in pixels) between adjacent tracer particles in the acquired images should be at least 5 times larger than the average particle size (also in pixels) of the same images. 28 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 1.3.2 Evanescent Wave Microscopy Setup The basic components of an evanescent wave imaging system include: a light source, conditioning optics, specimen or microfluidic device, fluorescence emission imaging optics and a camera. In reported experimental setups, light sources have included both continuous-wave (CW) lasers (argon-ion, helium-neon) and pulsed lasers (Nd:YAG) since they produce collimated, narrow wavelength-band illumination beams. Non-coherent sources (arc-lamps) are not common because they require band pass filters for wavelength selection and the produced light beams cannot be as perfectly collimated. However, commercial versions of lamp-based evanescent wave microscopes are available for qualitative imaging as they are more economical than laser-based systems. Conditioning optics are used to create the angle of incidence necessary for total internal reflection and are of two types: prism-based and objective-based [21]. Prism-based evanescent imaging systems are typically laboratory-built and low cost. A prism is placed in contact with the sample substrate which the illumination light beam is coupled into by inserting an immersion medium in between. The illumination beam is focused through the prism onto the substrate at an angle greater than the critical angle such that the substrate then becomes a waveguide where evanescent waves are generated along its surface (figure 1.13(a)). An air- or a water-immersion, long working-distance objective is often used for imaging to prevent decoupling of the guided wave from the substrate into the objective. Detailed prism and microscope configurations can be found in [21]. In contrast, objective-based evanescent wave imaging is used exclusively with fluorescence and requires a high numerical aperture objective (N A > 1.4) to achieve the large incident angles required for total internal reflection (figure 1.13(b)). These objectives are usually high magnification (60× ≤ M ≤ 100×) and oil-immersion. In this method, a collimated illumination light beam is focused onto the back focal plane of the objective and translated off the optical axis of the objective to create the required large incident angle. The emitted fluorescence of tracer particles is collected by the objective and recorded by a camera as in typical fluorescence microscopy. To prevent the returning excitation light from being recorded by the camera, spectral filtering with dichroic mirrors and filters is employed. Another advantage of evanescent wave imaging to note is that its imaging depth provides significantly greater imaging resolution than the diffraction-limited depth of field, DOF , of 29 1.3. EXPERIMENTAL PROCEDURES Illumination Beam Prism Fluorescent Nanoparticle Evanescent Field Waveguide Microscope Objective (a) Fluorescent Nanoparticles Evanescent Field Substrate θ Microscope Objective (b) Figure 1.13: Two types of evanescent wave illumination: (a) prism-based setup; (b) objectivebased setup. the objective under bright field illumination. The diffraction-limited DOF is calculated by DOF = n1 λn1 e, 2 + M · NA NA (1.46) where e is the smallest distance that can be resolved by the detector [80]. Even for a high magnification and large NA microscope objective the DOF is typically at least 600 nm and is thus unable to achieve sub-micron resolution. An example of an objective TIRF microscope system is shown in figure 1.14. An illumination beam produced by a laser is first regulated by a power attenuator-halfwave platepolarizing beamsplitter combination to achieve the desired power level. This step down in power is especially critical to high power laser beams produced by pulsed lasers as their high energy density can easily damage the optical components inside a microscope objective. A portion of the beam energy is diverted to an energy meter to monitor the laser stability. The beam is then ”cleaned up” by a spatial filter (concave lens-10 micron pinhole-concave lens 30 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY Microchannel 100X, NA = 1.45 Objective lens Mirror Dichroic mirror and Barrier filter Convex lens Computer ICCD Convex Lens 10 micron pinhole Convex Lens 1360 x 1036 x 12 bit Energy Meter Polarizing Beamsplitter Half-wave plate Data Acquisition Pulse generator Laser Power Attenuator Figure 1.14: A schematic of objective-based TIRF microscope setup. combination) before being directed through an NA1.45 100X oil-immersion microscope objective at an angle that creates evanescent waves inside a microchannel. Fluorescent images of near-surface tracer particles are captured by the same microscope objective and screened by a dichroic mirror and a barrier filter before being projected onto an intensified CCD camera (ICCD), capable of recording extremely low intensity events. A TTL pulse generator is used to synchronize laser firing and ICCD image acquisitions to ensure precise control imaging timing. The energy of the illuminating laser beam cam also be recorded simultaneously with each image acquisition to account for illuminating energy fluctuation, if necessary. Recent research literature has shown that objective-based TIRF microscopy systems are becoming much more common for experimental microfluidic and nanofluidic investigations. Extremely high signal-to-noise ratio images can be produced with proper alignment and conditioning of the incident beam, and good control over the fluorescence imaging. Here, we discuss general methodologies for alignment and beam conditioning as well as supply the relevant details to reconstruct a proven system with an inverted epi-fluorescent microscope. The procedure, which follows, is valid for both pulsed and continuous wave (CW) lasers. Caution should always be exercised when working with high power laser. Proper eye protec- 31 1.3. EXPERIMENTAL PROCEDURES (b) (d) (g) (f) (e) To Microscope (c) Laser (a) Figure 1.15: Schematic of the beam conditioning and manipulation optics for an objectivebased TIRF microscopy system. The components are broken down into several subsystems: (a) power control, (b) power meter, (c) spatial filter, (d) shifting prism, (e) periscope, (f) incident beam angle control and (g) reflected beam monitor. tion should be worn at all times and power should be kept to a minimum during alignment to prevent injury or damage to equipment. To begin, a Coherent Innova CW Argon Ion laser capable of several hundred milliwatts of output power in both the green (514 nm) and blue (488 nm) is used as the light source. The microscope is a Nikon TE2000-U with two epifluorescence filter turrets. The lower turret accommodates the mercury lamp, and the upper turret can be accessed from the rear of the microscope for free space optical alignment. The components of the conditioning and alignment optics are shown in figure 1.15, which are categorized in several subsystems: power control, power meter, spatial filter, shifting prism, periscope, incident beam angle control and reflected beam monitor. Not all of these systems are necessary for TIRF imaging (optional elements will be pointed out), but each system should be aligned in turn working from the laser to the microscope. We will discuss each system and its purpose. 32 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY The laser should always be operated near maximum power for the best thermal stability. As a safety mechanism and control, a mechanical beam chopper is placed directly in front of the laser aperture (figure 1.15(a)). It is used as a beam stop for warm-up and can be controlled electronically for periodic modulation of the beam if desired. Next, the already vertically polarized laser passes through a half-wave plate to rotate the polarization to an arbitrary angle. The wave plate in combination with the polarizing beam splitter that follows allows one to continuously vary the evanescent wave intensity of the TIRF microscopy system, while maintaining maximum operating power at the laser. By rotating the polarization, the vertical component is allowed to propagate along its original path through the beam splitter, while the horizontally polarized light (excess power) is dumped to a beam stop toward the interior of the optical table. Next, the useful component of the beam is split again for power measurement (figure 1.15(b)). With a fairly sensitive meter, a few hundred microwatts is sufficient for accurate measurement without being wasteful of the excitation power. Two mirrors are now used redirect the beam toward the back of the microscope and align the beam conveniently along the optical table bolt pattern using two irises (not shown). After referencing the beam to the table, a spatial filter is implemented to obtain the TEM00 mode and expand the laser beam diameter (figure 1.15(c)). The spatial filter movement containing an objective lens (f = 8 mm) and pinhole (∼20 µm) is first aligned to be colinear with the beam, as shown in figure 1.16(a). When properly aligned, the spatial filter movement should produce a diverging, concentric ring pattern that is symmetric and bright (figure 1.16(b)), while maintaining the beam propagation to the original trajectory along the optical table. To collimate and expand the beam, a lens (f ≈ 20 cm) is placed roughly one focal length away from the pinhole. The focal length of the lens and divergence angle of the expanding beam will determine the final beam diameter, which is about one centimeter in our case. Next, an adjustable iris is placed close to the collimating lens, with sufficient space in between for further adjustment of the lens (figure 1.16(a)). The iris is aligned to block all of the rings from the diverging beam by narrowing the opening of the iris to the first minimum of the concentric ring pattern. If successful, one should now be left with a very “clean” Gaussian beam spot as shown in figure 1.16(c). Finally, fine tune the position of the collimating lens such that the beam is collimated and again maintains the original trajectory along the bolt pattern of the optical table. One can determine if the beam is collimated by 33 1.3. EXPERIMENTAL PROCEDURES (a) Objective Lens (b) Pinhole Collimating Lens Iris (c) Collimating Lens Focal Length Figure 1.16: Spatial filter schematic and resulting laser beam modes: (a) spatial filter components and orientation, (b) concentric rings produced by diffraction through the spatial filter pinhole and (c) resulting Gaussian beam spot produced by clipping the concentric rings with an iris. measuring the beam diameter just after the collimating lens, and subsequently projecting the beam on a wall several meters away to ensure that the beam diameter remains the same. The shifting prism (figure 1.15(d)) is actually one of the final elements to be placed in the beam path and is optional. For now, we proceed with aligning the beam to the microscope’s optical axis. First, an epi-fluorescence filter set to be used with the TIRF system is placed in the upper turret of the microscope. Next, one should prepare the objective-housing nosepiece of the microscope to have an empty slot, a mirror fixed atop a second empty slot with the reflective side facing down into the microscope, a slot occupied by a TIRF objective (100×, 1.45 NA or 60×, 1.49 NA in our case) and a last slot occupied by a low magnification air objective (∼10×). The TIRF objective should be adjusted to the correct operating height by placing and focusing on a sample of dried particles on the microscope stage. After focusing, the sample is removing while not disturbing operating height and maintaining the same plane of focus for the rest of the alignment procedure. A target mark should be made on the ceiling directly along the optical axis of the microscope. As an alternative, a semi- 34 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY transparent optical element (diffuser glass) with a cross-hair can be fitted to the empty slot of the nosepiece. The nosepiece should now be rotated to the empty slot. Two large, five centimeter diameter periscope mirrors (figure 1.15(e)) are placed at the rear of the microscope such that the laser beam is directed into the microscope, reflected off the dichroic mirror and projected through the empty slot of the nosepiece and onto the ceiling. Large mirrors are chosen for the periscope to capture the reflected beam since the incident and reflected beams will not travel on the same axis once the system is shifted into the TIRF mode later. In the mean time, the goal of the current task is to align the laser beam to be co-linear with the microscope’s optical axis. The next step is to rotate the nosepiece to the up-side-down mirror position. At this time, one should see a reflected beam exit the rear of the microscope. By use only one of the periscope mirrors, the incident and reflected beam are to be aligned to become co-linear at the rear of the microscope. Next, the nosepiece is rotated back to the open position while the incident beam is redirected to the target mark on the ceiling using the second periscope mirror. This process should be repeated until the optical axes are co-linear and the incident beam lands on the ceiling target without any further periscope adjustments needed. The optional shifting prism (figure 1.15(d)), which is simply a rectangular solid piece of glass, can now be inserted between the collimating lens of the spatial filter and the periscope. The prism is adjusted and rotated until the incident beam hits the target mark on the ceiling and the optical axes of the incident and reflected beams are again co-linear. The incident beam angle control (figure 1.15(f)), which consists of a large, five centimeter lens (f ≈ 30 cm) on a two-axes rotational lens mount on a three-axes translational stage, should be placed between the periscope and microscope at approximately one focal distance away from the objective’s back focal plane (BFP) as shown in figure 1.17(a). Again, the large lens is used to accommodate the shifted reflection of the incident beam in the TIRF mode. By placing a closed iris adjacent to the lens, one can align the optical axis of the lens to be co-linear with the existing beam path. The iris is then opened and the rotational mount is adjusted to align the beam to the marked target on the ceiling through the open slot in the nosepiece. Subsequently, the iris is again closed and the lens is translated on the plane perpendicular to the laser beam optical axis to align the beam through the center of 35 1.3. EXPERIMENTAL PROCEDURES (b) (a) Objective Convex Lens 3D Stage Objective BFP Convex Lens Focal Length Incident Angle Adjustment Periscope Mirrors Figure 1.17: Schematic of the periscope and beam angle control lens orientation in relation to the microscope: (a) by focusing the beam onto the back focal plane (BFP) of the objective, a collimated beam emerges from the microscope objective and (b) the proper translational adjustment direction for manipulating the incident angle into TIRF mode. the closed iris (do not translate along the optical axis). This operation is repeated until no further adjustments are necessary. Upon completion of the repetitive steps, the nosepiece is rotated to the low magnification objective to repeat alignment of the focusing lens (low magnification objective alignment is optional). The nosepiece is then rotated again to the high magnification TIRF objective. At this point, one should place a clean slide with dry fluorescent particles on the microscope stage and verify that the objective is still in focus (this is extremely important). Once verified, alignment of the beam angle control lens should be done once more until the optical axes are once again co-linear. The final step is to collimate the beam emerging from the objective lens by ensuring that the focal plane of the beam angle control lens and the objective’s BFP coincide. This can be achieved by translating the beam angle control lens along the optical axis of the beam to minimize the spot projected on the ceiling. If all steps are completed perfectly, this spot will appear Gaussian and symmetric. The incident angle is controlled and calibrated by translating the beam shifting lens perpendicular to the optical axis (figure 1.17(b)) and measuring the angle of the beam emerging from the objective and extrapolating the incident angle as a function of the translation stage position through a least-squares fit [81]. Once this relationship is obtained, a sample drop 36 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY of fluid containing fluorescent tracer particles is placed on the slide and the beam angle is adjusted until evanescent waves are created in the fluid phase (again, remember to wear proper eye protection here). The experimentally determined angle should be compared with the predicted TIRF angle to verify the calibration. Last, the shifting prism can be rotated to center the evanescent waves spot in the eyepiece field of view. Although this final adjustment is optional, if it is performed the incident angle should be re-calibrated. The final and optional system for the evanescent wave microscopy system is the reflected beam monitoring system (figure 1.15(g)), which can be used to monitor changes in the total internal reflection conditions if necessary. 1.3.3 Fluorescent Particle Intensity and Particle Position As mentioned before, the monotonic decay of the evanescent field have been exploited to map the intensities of fluorescent tracer particles to their distances from the fluid-solid interface [39, 41, 42, 46]. Using this information, one can use a calibrated ratiometric fluorescence intensity to track particle motions three-dimensionally. Although this method sounds theoretically feasible, successful use of this technique in practice requires precise knowledge of the illumination beam incident angle and a solution of Maxwell’s equation for an evanescent field in a three media system (substrate, fluid and tracer particles) which can be difficult to express explicitly. However, an experimental method can be devised to obtain a ratiometric relation between particle emission intensity and its distance to the glass surface such as that shown in figure 1.4. In our TIRF calibration, we attached individual fluorescent nanoparticles to polished fine tips of graphite rods, which were translated perpendicularly through the evanescent field to the glass substrate with a 0.4-nm precision translation stage (MadCity Nano-OP25). Multiple images of the attached particles were captured at translational increments of 20 nanometers. The intensity values of the imaged particles were averaged and fitted to a two-dimensional Gaussian function to find their center intensities. The process was repeated several times with different particles. This procedure produces an intensity-distance correlation such as one shown in figure 1.18: − z−a δ I = Ae T + B, (1.47) 37 Normalized Intensity, I (Arb. Unit) 1.3. EXPERIMENTAL PROCEDURES 1 0.8 0.6 0.4 0.2 0 0 50 100 150 200 z - a (nm) Figure 1.18: Fluorescent particle intensity as a function of its distance to the glass surface. The particles used here are 100 nm in radius. The solid line is a least-square exponential fit to the data whose decay length. where z is the distance between a particle’s center to the substrate surface and a is the particle radius. δT is the TIRF decay length constant which, along with A, B, are constants determined by a least-square exponential fit. As predicted by figure 1.4 and experimentally demonstrated in figure 1.18, the particle intensity decay is very close to the decay of the evanescent wave intensity. Figure 1.4 also predicts that emission intensities of fluorophore-embedded, micron-sized particles illuminated by evanescent waves also decays exponentially as a function of distance from the substrate, even though the sizes of these particles are significantly larger than the evanescent field penetration depth. This unique characteristic exists because frustration of the evanescent field [82] by the dielectric particles can excite fluorophores well beyond the evanescent field at several microns from the interface. This effect produces radially asymmetric particle images, which also decrease in intensity with distance from the wall, as shown in figure 1.19. To quantify the fluorescence intensity of micron-sized particles as a function of distance from the interface, one can again attach individual particles to the tip of an opaque micropipette connected to a one-dimensional nano-precision stage. The particle is traversed perpendicular to the substrate through the evanescent field while multiple images 38 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY z=0 nm z=74 nm z=130 nm 0 5 10 y [µm] 10 y [µm] y [µm] 0 5 10 0 0 5 x [µm] 10 5 0 5 x [µm] 10 0 5 x [µm] 10 Figure 1.19: Characteristic images of a 6 µm particle at various distances from a glass/water interface created due to frustration of the evanescent wave by the fluorescent, dielectric particle. of the particle at each position are taken to correlate its intensity with position. Based on figure 1.4, one can predict that the form of the integrated particle intensity, I, also decays exponentially with distance from the surface and is again given by equation 1.18. A sample fit for the intensity decay of 6-µm fluorescent tracer particles is shown in figure 1.20. The yielded a decay length, δT =204 nm, is found to be nearly identical to the evanescent field penetration depth measured independently. Other similar experimental and computational investigations for the scattering intensity of similar-sized particles in an evanescent field [32, 81] also found similar intensity decaying results. 1.3.4 Particle Tracking Velocimetry With a TIRF microscopy system and an intensity-particle position correlation function in place, quantitative analysis of near-wall particle motions can be used to examine near-surface micro- and nanofluidics by using one of several velocimetry methods. Micro-PIV [83] and nPIV [35] infer the most probable displacement of a fluid element from the cross-correlation peak between two sequential image segments taken in time. There are several shortcomings to this approach in near-wall studies. First, the high velocity gradient near the wall cannot be easily resolved directly. Second, because particles in the near-wall evanescent field are brighter than the ones that are farther away, the cross-correlation method weights slower moving particles close to the wall more heavily, thus biasing the mean velocity. Third, near- 39 1.3. EXPERIMENTAL PROCEDURES Normailzed Intensity [Arb. Unit] 1.2 Data Exponential Fit 1 0.8 0.6 0.4 0.2 0 0 200 400 z - a [nm] 600 800 Figure 1.20: Mean, integrated fluorescence emission intensity of individual 6-µm particles as a function of distance from a glass/water interface. The intensity variance is due to both thermal motion of the particle and stage noise. surface microfluidic and nanofluidic investigations using particle-based velocimetry typically have low Reynolds numbers, Re, and Peclet numbers, P e, of order unity. They are defined by Re ≡ ρV a , µ (1.48) Pe ≡ Va , D0 (1.49) and where a is the particle radius, V is the mean local velocity, ρ is the fluid density and D0 is the Stokes-Einstein diffusivity defined in equation (1.11). The high levels of diffusion of small Brownian particles used in velocimetry tend to degrade the sharpness of the crosscorrelation peak and introduce additional uncertainty. Fourth, no particle depth information is provided by PIV methods since all information regarding each particle’s intensity is lost during cross-correlation analysis. Finally, the loss of particle intensity information during cross-correlation analysis means that one could not directly measure the near-wall particle concentration profile and would have to assume the concentration distribution of the tracer particles in the near-wall region, most commonly as a uniform distribution. As discussed 40 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY in section 1.2.5, such an assumption can significantly deviate from the actual concentration profile and lead to analysis bias. Due to the statistical nature of colloidal dynamics, one method to unmask the true physics hiding behind the randomness of Brownian motion is individual particle tracking [84]. As shown in section 1.3.3, the intensities of micron-sized and nanoparticles decay exponentially away from the fluid-solid interface with decay lengths similar to that of the illuminating evanescent waves [32, 39, 42, 46]. This makes it possible to discern the height of a particle from the substrate surface based on its intensity, and has been applied to track particle motions three-dimensionally [42, 47]. Although there have been some attempts to evaluate cross-correlations over multiple particle layers [37] within the evanescent field, many challenges still remain. Tracking individual particles to resolve near-surface velocities remains a much more direct method to investigate near-wall dynamics. Below we will discuss the most common algorithms for tracking near-wall particles with details to help the readers develop their own image analysis codes. In particle tracking velocimetry (PTV), bright particles with intensities above a predetermined threshold value are first identified in a series of images. To track particle motions, all particle locations from two or more successive video frames must be identified to good accuracy, most commonly through identification of the particle center positions. For micronsized particles or larger, this is typically done by finding their intensity centroids through weighted-function particle image analysis. For sub-wavelength particles, center positions are found by fitting a two dimensional Gaussian distribution to the imaged diffraction limited spots of the tracer particles [78, 85]. A two-dimensional Gaussian curve fit closely approximates the actual point-spread function of nanoparticle intensities near their peaks and allows one to locate the particle center coordinates with sub-pixel resolution. At this point, it is also critical to distinguish real particles from noise signals as noise tracking will unnecessarily corrupt the obtained motion statistics. This is typically accomplished by building an additional abnormality detection algorithm into the particle identification code. Examples include detecting the particle shapes and sizes based on their images [36]. It is important to point out that the determination of an intensity threshold during 1.3. EXPERIMENTAL PROCEDURES 41 Observation Depth Substrate Figure 1.21: Schematic of near-wall particles moving near the surface illustrating the observation depth. particle identification sets an observation depth, as illustrated in Fig. 1.21. The lower bound of the observation range is the particle radius, representing a particle in contact with the channel surface. As the particle moves farther from the wall, and hence into a region of lower evanescent wave illumination intensity, the emitted intensity also falls. Thus, the intensity threshold chosen sets an upper bound on the observation depth which is different from the decay length of the evanescent field. Next, identified particles are matched between frames to track their trajectories. In some cases (for example, in fast moving flows), only two frames (image pairs) may be available at a time for matching due to limitations in camera acquisition speed. The time duration between image acquisitions should be set such that most tracer particles translate between 5 to 10 pixels for highest velocimetry accuracy. If the tracer concentration is dilute, the nearest neighbor matching is simple and very effective [45]. The center position of an identified particle is frame 1 is first identified and noted. A search is then started in frame two, centering around the center position of the identified particle in frame one, until the nearest neighbor is found in frame 2. The two particle center positions then become a matching pair and are considered as the locations of a single tracer particle at different times. The distance between the center positions are now used to infer the displacement of the local fluid or Brownian motion of the particle between image acquisitions. Here, noise-detection algorithms can also be inserted to improve velocimetry accuracy. One can first make an educated guess of the largest distance that a tracer particle can travel between image acquisition, and use 42 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY this distance as the radial limit of nearest neighbor search. If the nearest neighbor search done in frame 2 for a particle identified in frame 1 is beyond this set limit, one can safely assume that this ”particle” is probably mis-identified and is most likely a noise rather than an actual tracer. Secondly, if more than two signals in frame 2 can be matched to a particle identified in frame 1 using the above criteria, it is advised to discard displacement information provided by this particle. This is because the probabilistic nature of Brownian motion makes it impossible to resolve this matching ambiguity with any kind of certainty. It should be noted that the image acquisitions, particle identifications and tracking processes should be repeated for a large number of times until the number of tracked trajectories becomes a statistically sample size. It is recommended that at least 1000 successful trackings should be obtained for each experimental condition. Clearly many of the tracking ambiguities and unwanted photon noises can be avoided if the tracer particle density is low. Therefore, the tracer particle density should be kept minimal while still capturing a good number of successful trackings from each image pair. For less than perfect tracer particle seeding conditions, several variations of the basic tracking algorithm have been proposed. For large Peclet numbers (less significant particle Brownian motions), a multiple matching method may be useful [86]. However, for small Peclet numbers or highly concentrated particle solutions, a statistical tracking method [49] or a neural network matching algorithm [41, 87] might be advantageous. In the case that a multiple-frame image sequence is available, there is some benefit to using window shifting and predictor corrector methods [87], but only for large Peclet number. Once the ensemble particle displacements are measured, the individual intensities of matched particles can provide information about the particle distance to the substrate surface as mentioned previously. Colloidal particles typically have a large diameter size variation (3% to 20%) that can bias the interpretation of intensity to distance. Since particle intensity can also be a function of particle size as discussed in [54, 55, 88] and in section 1.2.2, a large particle far from the wall can appear to have the same intensity as a small particle near the wall [39, 47]. Caution must be exercised when inferring a particle’s distance from the substrate from its intensity. 1.3. EXPERIMENTAL PROCEDURES 43 Figure 1.2 compares particle images of bright field illumination and TIRF illumination. A large amount of background noise is observed in the case of bright field illumination. These background noises are attributed to the fluorescent light emitting from out-of-focus tracer particles in the bulk of the fluid and can lead to difficulty in particle identification and trajectory tracking. TIRF illumination, on the other hand, eliminates much of the background noise because the evanescent wave illumination is restricted to the near-surface region only and particles in the bulk fluid are not illuminated. This characteristic allows easy detection of only particles that are close to the channel surface and thus significantly improve particle tracking velocimetry accuracies. Using the geometric scale and the applied time separation between image acquisitions, a velocity vector can be calculated from each successful particle tracking. Figure 1.22 shows an example of a collection of velocity vectors obtained for a single shear rate. The Brownian motion is particularly strong due to the particle’s small size. Alternatively, if one desires to investigate the three-dimensional translational motions of the tracer particles, once can use the calibration equation (1.47) with the fitted peak particle intensities, I, to obtain the instantaneous position of each particle relative to the substrate, z, and subsequently track the three-dimensional trajectories of these particle over time. A straight-forward two-dimensional Gaussian fit used in nanoparticle identification has been demonstrated to be very accurate and is currently the gold standard in near-surface particle tracking velocimetry. However, this method does not provide as accurate center positions for micron-sized particles, given the oddly shaped, asymmetric particle images as shown in figure 1.19. An altered version of particle identification and center positioning algorithm has been developed to improve particle tracking analysis accuracy [47]. In this method, particle locations are first coarsely identified by intensity thresholding and matched to new positions in subsequent images by a nearest neighbor search. Because of the oddly shaped, asymmetric particle images, a cross-correlation tracking algorithm was then used to refine the particle center locations [85]. In the next step, Gaussian fitting to the peak of the correlation map is performed and can now yield an accuracy of about 0.1 pixels (28.3 nm) in the wall parallel directions, x and y. After that, overall intensity of an individual particle is obtained from integration of all its local pixel intensities and normalized by the 44 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 140 Streamwise veocity (µm/sec) 120 100 80 60 40 20 0 20 40 100 50 0 50 100 Cross-stream velocity (µm/sec) Figure 1.22: Distribution of particle velocity vectors of 200-nm particles with in a near-wall shear flow of shear rate = 469 sec−1 . Gaussian shape of the illuminating beam as measured by an aqueous solution of Rhodamine B dye. Finally, the relative particle position in the wall-normal direction, z, is computed by inverting equation (1.47), where A is given by the largest intensity of a given particle along it’s trajectory (i.e. closest position to the wall). The resolution in the wall-normal direction is estimated to be on the order of 10 nm due to intensity variation resulting from particle diffusion, laser fluctuation and camera noise [47]. Additional uncertainty can result from non-uniformity in the cover slip, non-uniformity in surface coating thickness and illumination light intensity variation over the field of view. Here we present our experimental tracking results for adhesion dynamics of micron-sized particles to demonstrate the tracking algorithm’s effectiveness. P-selectin coated 6-µm fluorescent particles and PSGL-1 coated microfluidic channels are used as mechanical models for investigating adhesion characteristics of leukocytes in pressure-driven flows inside blood vessels. As is typical in flow chamber based assays, tethering adhesion can be detected by arresting events in the particles’ in-plane motion [89]. Figure 1.23(a) shows a segment of such a trajectory, where the plateaus signal that the particle is arrested. The instantaneous particle displacements (figure 1.23(b)) show much more detail of this process. There are distinctly different features amongst the various binding events as indicated by the position 45 1.3. EXPERIMENTAL PROCEDURES x [μm] 10 (a) 5 0 0 0.5 t [s] Δx [μm] 0.3 (b) 1 1.5 Displacement Resolution 0.2 0.1 0 0 0.5 t [s] 1 1.5 Figure 1.23: Time trace of the wall-parallel motion in the flow direction for a single particle, illustrating the tethering dynamics near the substrate: (a) particle trajectory and (b) particle displacement fluctuations in the plateaus. This likely indicates the strength of an arresting event due to variations in the number of tethers that combat the Brownian motion. Although we have demonstrated this technique for a single particle here, from statistical averaging of such measurements, reaction rate constants for off-times can be computed by binning the lengths of the arresting times [90]. Furthermore, a histogram of the particle displacements shows a strongly bimodal distribution (figure 1.24), where the system transitions stochastically between the free and tethered states. There is also evidence of a third, intermediate mode that may indicate a steady rolling velocity with ∆x ∼ 100 nm. Particle motion in the wall-normal direction, z, tends to be more complex than the wall parallel case as shown for a segment of a single particle trajectory in figure 1.25. Tethering events are clearly visible in the wall-normal trajectory by sharp transitions between plateau regions, especially in comparison to figure 1.23. The plateaus correspond to times when the particle is temporarily arrested by a tether. The statistical variation of the particle’s height 46 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 0.3 0.25 pdf 0.2 0.15 0.1 0.05 0 −100 0 100 ∆x [nm] 200 300 Figure 1.24: A histogram of the wall-parallel particle displacements for the trajectory of a typical particle. The bimodal nature of the histogram demonstrates the fraction of time that the particle is tethered versus free. during tethering events contains additional information about the tether stiffness, which may also be examined. We end the Experimental Procedure section with some words on system evaluation and testing. If one follows the procedures on constructing a TIRF microscope system, setting up a intensity-position calibration component using a nanometer-precision translation stage, and developing a particle tracking velocimetry software to conduct near-surface particle tracking velocimetry, it would then be necessary to test and evaluate the performance of this homemade system, both on functionality and accuracy. In our opinion, the simplest evaluation experiment that one can conduct is an experimental verification of Brownian motion. The tracer particles, in quiescent fluid, will undergo hindered Brownian motion in the vicinity of a solid substrate. Since the theory of hindered Brownian motion is quite well established (see section 1.2.3), quantitative observations of the tracer micro- or nanoparticles using nearsurface particle tracking velocimetry can be easily compared with theories to determine if the experimental setup and the analysis software is truly functioning with the expected precision and accuracy. Many of the images and results shown in this section should provide sufficient examples for one to make a proper evaluation. 47 1.3. EXPERIMENTAL PROCEDURES 100 Trajectory Max Tether z [nm] 80 60 40 20 0 0 0.5 1 1.5 t [s] Figure 1.25: Time trace of the vertical position for a single particle, where the transitions between tethered and free states are clearly detectable by jumps in the wall-normal position, z, (interpreted from the particle intensity) as compared to the horizontal displacements. The dashed line shows the typical maximum bond length of about 92 nm for the P-selectin/PSGL1 system. 48 1.4 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY Recent Developments and Applications Near-surface particle tracking has made tremendous progress over the past several years, due in large part to increased interest in nano-fluidics and a demand for higher resolution diagnostic techniques. In this section, we will discuss the advances in tracer particles, imaging systems and velocimetry algorithms that have elevated near-surface velocimetry to its current level of precision and flexibility. Additionally, we will discuss several recent applications and advantages that make this method an appealing measurement technique for micro- and nano-fluidics, soft condensed matter physics and biophysics fields. Near-surface tracking uses a wide variety of tracer particles (for both fluorescence and scattering imaging) with sizes ranging from as large as 10 µm to just a few nanometers where the choice in tracer particle is determined by the application. Advances in nano-fabrication have lead to the development of single, uniform fluorescent particles just tens of atoms in diameter. Ultra-high numerical aperture microscope objectives in combination with high-speed image intensifiers and cameras now provide unparalleled light collection and imaging speed capabilities. Micro- and nano-scale particle velocimetry algorithms have largely been adopted from their macro scale counterparts, but have evolved to address the unique challenges of near-wall physics (large velocity gradients, highly diffusive tracer particles, etc.). Several recent applications have included: electro-osmotic flows, slip flows, near-surface temperature measurement, quantum dot tracking, hindered diffusion and velocity profile measurements. 1.4.1 Tracer Particles With the many advances in micro- and nano-fabrication techniques, there is a wide variety of commercially available tracer particles for almost any application ranging in size from several microns down to several nanometers and even the molecular level. Typically, though, the size of a tracer particle is chosen for a particular application in near-wall tracking velocimetry where either the particle dynamics or the fluid dynamics are of interest. While larger particles (> 500 nm) may be imaged by scattering, fluorescence imaging is often the only way to image diffraction limited particles. Some applications require that particles be coated with 49 1.4. RECENT DEVELOPMENTS AND APPLICATIONS z Ionic + Solution, n2 2a + δ + - z J(z) J0 - θ>θcr + + + - - - - + - + - - + - κ-1 + - - - x Substrate, n1 Figure 1.26: Typical geometry of evanescent wave illumination, where a plane, monochromatic wave is incident on a dielectric interface at an angle greater than the critical angle, θ ≥ θcr . The resulting evanescent field intensity, J (z) has a decay length, δ, on the order of 100-200 nm. Ionic solutions screen the electrostatic forces between charged particles and surfaces with a length scale characterized by the Debye length, κ−1 . bio-proteins for conjugation to surfaces or other particles. Large tracer particles (> 1 µm) are often utilized to study hydrodynamic and electrostatic forces in plane-sphere geometries as shown in figure 1.26. Interesting behavior is often captured for short-ranged forces (∼ 200 nm) or when the gap between the sphere and plate is much smaller than the particle radius. Scattering imaging has been used extensively in the past, which has the advantage of avoiding photobleaching and allowing for extended observation times [30]. Fluorescence imaging of large particles has become popularized, which uses lower illumination intensity than scattering and thus avoids unwanted optical forces that can bias measurements. Here applications have included the measurement of spatially resolved, anisotropic diffusion coefficients [42]. In addition to these typical geometries, larger particles have also been used to model leukocyte adhesion dynamics where they served as surrogate white blood cells to convey bio-proteins [47]. The most common tracer particles for an array of applications in near-wall particle tracking are fluorescent polystyrene nanoparticles ranging in size from 40 to 300 nm. Such particles have served as tracers to measure slip velocities and near-wall velocity profiles [39, 46]. 50 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY Over the past five years, semiconductor nanocrystals or quantum dots (QDs) have attracted increasing attention as extremely small, bright and robust tracer particles for near-wall particle tracking. QDs are single fluorophores with reasonable quantum efficiencies and fluorescence lifetimes similar to conventional fluorophores, but with significantly higher resistance to photo-bleaching [91]. They exhibit several qualities beneficial to nano-scale velocimetry including small diameters ranging from 5 nm to 20 nm, a narrow and finely tunable emission wavelength, and even temperature sensing abilities [51]. However, single QDs have a significantly lower emission intensity as compared to much larger polystyrene particles containing several thousand fluorophores. Additionally, their emission can fluctuate randomly (figure 1.27), which is known as fluorescence intermittency or “blinking” [92]. The first practical demonstrations using QDs in aqueous solutions for velocimetry purposes used either extremely dilute solutions [48] or statistical velocimetry algorithms [49] to negotiate the necessarily long exposure times and high diffusivities. Applications include near wall velocity bias measurements, high speed imaging, and simultaneous temperature and velocity measurements. Hybrid particles consisting of 50 nm polystyrene particles conjugated with a series of quantum dots also show promise as small, yet extremely bright tracer particles [93]. 1.4.2 Imaging Systems Although the basic list of components for evanescent wave imaging systems (light source, conditioning optics, specimen or microfluidic device, fluorescence emission imaging optics and a camera) have remained unchanged for some time, vast improvements in the quality and implementation of those components have translated into marked scientific achievements. Laser sources have diminished significantly in size with increasing stability and tunability. The conditioning optics used to create the angle of incidence necessary for total internal reflection are still primarily prism-based or objective-based with widely varying components [21]. Prism-based systems are still typically home-built with no significant recent advances in technology. In contrast, objective-based imaging has benefited greatly from advances in high magnification, high numerical aperture oil immersion objectives. Most recently, extremely large numerical apertures N A > 1.49 have become commercially available to 51 1.4. RECENT DEVELOPMENTS AND APPLICATIONS 50 SNR 40 30 Blinking Threshold 20 10 0 10 20 30 40 Time (s) 50 60 70 Figure 1.27: Sample intensity time trace for single, immobilized quantum dots under continuous illumination. An intensity greater than the threshold of SNR=5 designates blinking on-times from off-times. minimize vignetting and provide for larger illumination spots and also larger incident angles, which allows for extremely small penetration depths. A wide variety of cameras are also suitable for near-wall particle tracking depending on the sensitivity and speed requirements dictated by the tracer particles and application. Sensitive, low noise charge coupled device (CCD) cameras are a typical choice for imaging small tracer particles by scattering or fluorescence. For nanometer-sized particles, intensifiers are often employed (integrated or external) to amplify light levels. This is useful not only for low intensity particles, but also for minimizing exposure times, te , to capture fast dynamics and avoid particle image streaking. CCD cameras produce low noise, high resolution images, but suffer from the disadvantage of slow frame rates (10-100 Hz) due to readout time. This problem can be circumvented somewhat by acquiring image pairs (PIV-type imaging) rather than triggering the camera at a constant rate. This method has been shown to improve velocity resolution by capturing extremely fast tracer particle velocities, but does not provide for the Lagrangian particle tracking that is truly desirable. Most recently, multi-stage, high-speed image intensifiers have been employed to amplify 52 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY Syringe Pump z Water, n 2 Flow PDMS Microchannel Glass, n1 100X 1.45 NA TIRF Penetration Depth, δ x θ>θcr Conditioning Optics Dichroic Mirror 2-stage Hi-Speed Intensifier TIRFM Flow Relay Lens System 514 nm Argon Ion Laser Computer Synchronization Hi-Speed CMOS Camera Figure 1.28: Schematic of the experimental setup and high-speed evanescent wave (TIRF) microscopy imaging system. extreme low intensity single QD images and captured by high-speed CMOS camera sensors allowing for frame rates over 5 kHz [50]. Although CMOS cameras are less sensitive with lower spatial resolution than CCD cameras, they provide desirable high frame rates. Two key intensifier features that are necessary for imaging single molecules and fluorophores at high speeds are: (1) a two-stage microchannel plate to amplify small numbers of photons to a sufficient level for detection by the CMOS sensor and (2) a fast decay phosphor screen (P24, 6 µs decay) to prevent ghost images. Multi-stage image intensifiers have an inherently low resolution due to imperfect alignment of finite-resolution microchannel plates. Although, three-stage intensifiers are available, two-stage systems produce sufficient light amplification, while maintaining the image resolution. 1.4. RECENT DEVELOPMENTS AND APPLICATIONS 1.4.3 53 Tracking Algorithms Near-wall particle velocimetry algorithms have largely been adopted from macro-scale algorithms and are of two types: (i) particle image velocimetry (PIV) methods and (ii) particle tracking velocimetry (PTV). PIV methods use cross-correlation techniques to determine the most probable displacement for a grouping of tracer particles suspended in fluid [94]. This yields an instantaneous snap-shot of the spatially resolved velocity field (Eulerian description). Conversely, PTV algorithms identify distinct, individual particles and follow their positions in time (Lagrangian description) [87]. Both techniques have been adapted to suit micro- and nano-fluidics, and here, in particular, we will discuss the various benefits and costs in relation to near-surface velocimetry. PIV Methods Micro-scale PIV (µPIV) techniques are used to measure fluid velocity fields with length scales L < 1 mm [83]. The depth of field of the imaging objective defines a measurement plane with a typical thickness of 500 nm [80]. Nano-scale PIV (nPIV) uses the same cross-correlation analysis techniques as its micro-scale counterpart, but instead uses the penetration depth of the evanescent wave intensity to define an imaging plane with 100 ≤ δ ≤ 200 nm of the surface [35]. This provides obvious advantages over µPIV including a more defined imaging plane and significantly better signal-to-noise ratio images. This method was taken one step farther by exploiting the monotonic intensity decay of the evanescent wave in the wallnormal direction. Several groups have demonstrated that the intensities of a wide range of particles diameters decay exponentially away from the fluid-solid interface with similar decay lengths to the penetration depth [32, 39, 46]. This makes it possible to segregate particles at various ranges from the surface, based on their intensity, providing a three-dimensional, two-component (3D2C) measurement of the near-surface velocity field [37, 46]. Although PIV techniques are becoming highly developed, there are several shortcomings to this approach in near-wall studies. Currently, the wall-normal resolution has only course-grained discretization. Additionally, since particles near the wall are brighter due 54 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY to the evanescent field gradient, the cross-correlation method weights slower moving particles close to the wall more heavily introducing possible measurement biases in the velocity. Small, Brownian particles in low Reynolds number flows typically have Peclet numbers of order unity. These high levels of diffusion and Brownian motion tend to degrade the sharpness of the cross-correlation peak, and consequently, several hundred images are required to sufficiently average and smooth the correlation map. This would drastically reduce PIV’s advantages in providing time-resolved measurements. In addition, PIV methods were originally developed to measure fluid velocities under the assumption that tracer particles closely follow the fluid, but as tracer particles become smaller (. 2 µm radius), this assumption starts to break down due to Brownian motion. This random motion is a direct manifestation of the thermal fluctuations in the solvent medium. Averaging over this motion masks important statistical fluctuations that can be used to measure complex physical phenomena that only occur within several nanometers of the wall (electrostatic, van der Waals, etc.). PTV Methods The statistical nature of colloidal dynamics makes particle tracking a natural fit [95] and near-surface measurements are no exception [36]. In PTV, all particle locations from two or more successive video frames can be identified to sub-pixel accuracy (typically ≥ 0.1 pixels) using their intensity centroids for large particles [85] or by fitting a two dimensional Gaussian distribution to the diffraction limited spot for sub-wavelength particles [78, 85]. Once identified, particles are matched to one another between frames to link their positions into trajectories. The specific algorithm to achieve this task depends on several factors including: tracer particle concentration, diffusivity, velocity and the number of consecutive video frames available for tracking. With sensitive but slow CCD cameras (10 Hz), image pairs or PIV-type imaging is often used to improve the range of measurable velocities and capture fast moving particles. If the tracer concentration is dilute, then nearest neighbor matching is simple and effective [45]. Also, when dealing with fast, uniform velocities, window-shifting may be employed. When the inter-particle distance is small compared to the particle displacements and Peclet number 1.4. RECENT DEVELOPMENTS AND APPLICATIONS 55 is large, a multiple matching method may be useful [86]. However, for small Peclet numbers or highly concentrated particle solutions, a statistical tracking method [49] is advantageous. Both of these methods rely on similar principles. A number of possible particle displacements between two frames are computed to yield a statistical ensemble of displacements, a fraction of which are physical, while the rest are artificial. Based on the type of flow, some assumptions can be made about the distribution of unphysical trackings, and thus, they can be statistically subtracted from the distribution. However, one significant drawback to these statistical techniques is that they do not yield any useful information about individual tracer particle tracks; only the distribution of displacements is obtained in a meaningful way. We also note that neural network matching algorithms have been used with some success for both image pair and multi-frame particle tracking [41, 87]. Several advantages are gained in the case that multiple-frame image sequences are available. Predictive methods or minimum acceleration methods [87] are useful for large Peclet number flows. The history of a given tracer particle (position, velocity and acceleration) is used to predict it’s position some time in the future. The particle in the following frame most closely matching the predicted position is then added as a link in the trajectory. If several matches are plausible, additional frames into the future may be examined to judge the validity of a possible match. When the Peclet number is small, as in the case of quantum dots, the tracer particle concentration is often reduced to avoid mis-matching particles, which again, allows for simple nearest neighbor matching. To avoid mis-matches between particles (and noise) multiple frame nearest neighbor tracking can help [48]. For extremely small Peclet numbers, there is no substitute for fast imaging frequencies. Recently, high-speed intensified imaging has been incorporated into evanescent wave microscopy systems for the purpose of velocimetry via particle tracking techniques with quantum dot tracers [50], at frame rates in excess of 5 kHz for tracking single fluorophores. The fast imaging reduces the inter-frame displacement of the tracers significantly below the interparticle distance, thus allowing a return to simple, reliable inter-frame matching techniques (i.e. nearest neighbor). Another useful feature of particle tracking is that with proper calibration, tracer particle intensity can be used to determine the particle’s distance from the surface [30, 39, 40, 46] yielding three-dimensional, three-component (3D3C) particle tracks. In some cases, this 56 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY method of tracking can provide a resolution of several nanometers. Finally, although PTV provides the statistics of particle motion more directly as compared to PIV, many problems remain to be solved especially as tracer particles continually decrease in size. Given the extremely small image plane thickness for near-surface tracking (100300 nm), highly mobile tracer particles may easily diffuse parallel to the velocity gradient and out of the imaging depth, which is a phenomenon known as drop-out. The opposite process can sporadically bring tracers into the imaging depth creating false particle tracks. Similarly, in the case of quantum dots, fluorescence intermittency or blinking can in effect cause an optical drop-out, however, this phenomenon is usually insignificant compared to the physical drop-out [83]. Large particle concentrations or mobilities can cause confusion for matching algorithms, and near-surface velocity gradients create dispersion that is only recently becoming well understood [43, 44]. In the case of three-dimensional, near-wall particle tracking, non-uniform fluorescent particle sizes and temporally fluctuating particle intensities can also bias measurements. 1.4.4 Measurement Applications and Advantages Evanescent wave microscopy and near-surface imaging has been employed by biophysics researchers since the 1970’s [22]. During the 1990’s, several groups began studying nearwall colloidal dynamics by observing the light scattered by micron-sized particles in the evanescent field [27, 30]. More recently, evanescent wave microscopy has been integrated with the well-established particle velocimetry techniques of microfluidics [35, 36]. Typically, these methods have been used to measure the dynamics of small colloidal particles (10 nm to 300 nm) and applications have included the characterization of electro-osmotic flows [38], slip flows [39, 40, 96], hindered diffusion [41, 42], near-wall shear flows [43–47] and quantum dot tracer particles [45, 48, 51, 52]. 1.4. RECENT DEVELOPMENTS AND APPLICATIONS 57 Near-surface Flows Several of the first near-surface particle tracking experiments were investigations of two well known, but poorly understood surface flows: electro-osmotic flows and slip flows. Until recently, there were no direct experimental measurements of electro-osmotic flows within the electric double layer (EDL) about 100 nm from the fluid-solid interface. nPIV techniques were used to measure two wall-parallel velocity components in EOF within 100 nm of the wall. Analytical and numerical studies suggesting uniform flow near the wall were verified using nPIV, demonstrating that the EDL is much smaller than 100 nm as predicted [38]. Also, the microscopic limits of the no-slip boundary condition between a liquid and a solid have been the source of much debate in recent years, and this assumption has been challenged by recent experimental results and molecular dynamic simulations. Experimental studies have reported a wide range of slip lengths, ranging from micrometers to tens of nanometers or smaller (including no-slip) [97–104]. Molecular dynamics simulations, on the other hand, suggest small slip lengths, mostly less than 100 nm [105–110]. Several researcher have confirmed these simulations using near-surface particle tracking [39, 40, 52, 96], and they showed that hydrophilic surfaces show minimal slip to within measurement accuracy. Hydrophobic surfaces do appear to introduce a discernible, but small slip length of about 10-50 nm [39, 40]. Temperature Measurements Simultaneous, non-invasive thermal and velocimetry diagnostic methods have many potential applications in such fields as DNA amplification (PCR) and heat transfer in microelectro-mechanical systems (MEMS) [111, 112]. Two viable methods of micro-scale, optical temperature measurement have been successfully demonstrated including: (i) laser induced fluorescence (LIF) thermometry, which exploits the change in emission intensity of laser dye with changing temperature [113, 114] and (ii) PIV thermometry that utilizes the random motion of tracer particles to estimate temperature [115]. More recently, these techniques were demonstrated using near-surface tracking of quantum dot tracer particles within about 200 nm of a liquid/solid interface [51]. Since quantum dots also exhibit temperature sensitive emission intensity (−1.1% K−1 ) [116] and increased Brownian motion with increasing 58 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY temperature, both velocity and temperature may be measured simultaneously. Nanoparticle Tracking There is a constant demand for increased resolution in micro- and nano-fluidic diagnostics, and near-surface tracking has been applied to measure nano-particle dynamics at an ever smaller scale. Recently, interest has peaked in the use of semiconductor nanocrystals or quantum dots (QDs) (3-25 nm diameter) as nano-fluidic flow tracers [45, 48, 50–52, 93, 117]. Their quantum efficiency is comparable to typical fluorescent molecules, and they are considerably more resistant to photobleaching [91]. However, their small size means that QDs are significantly less intense than tracer particles measuring several hundred nanometers in diameter containing thousands of fluorescent molecules, and their small diameters yield high diffusivity, making imaging and tracking extremely difficult. Previously, single QD dynamics were only realized in elevated viscosity solvents [117], but the high sensitivity and low noise imaging provided by evanescent wave microscopy provided the capability make measurements in aqueous solutions [48]. Since that time, QDs and near surface tracking have provided measurements of temperature [51], velocity profiles [52] and dispersion related velocity bias [45, 50]. Most recently, the integration of two-stage, high-speed intensifiers and CMOS cameras has provided frame rates of over 5 kHz and ability to measure velocities of nearly 1 cm/s within about 200 nm of the liquid/solid interface of microchannel. Three-dimensional Measurements, Velocity Profiles and Hindered Brownian Motion When attempting to measure the mean velocity or velocity profile near a solid boundary through particle-based imaging, the concentration distribution of particles in the wall-normal direction must be established to properly weight the spatially varying velocity. In many previous studies, the concentration distribution has been assumed to be uniform, which is almost never the case [35, 36]. The equilibrium concentration of colloidal particles in the 1.4. RECENT DEVELOPMENTS AND APPLICATIONS 59 wall-normal direction from a liquid-solid interface is given by the Boltzmann distribution p (z) = p0 exp [−U (z) /kb T ] , (1.50) where p0 is a normalization constant [30] and U is the total potential energy of a particle. In the absence of any forces between particles and the surface, the potential energy is zero, leading to a uniform particle concentration distribution. However, electrostatic, van der Waals, optical and gravitational forces can create non-uniform potentials between the particle and wall, thus leading to non-uniform concentration distributions as discussed in section 1.2.5. The formation of a depletion layer near the wall can thus skew the inferred mean fluid velocity to higher values [30, 44, 46, 47]. Measurements of particle distance to the wall have allowed for estimates of the wall-parallel velocity profile in Poiseuille flows within a few hundred nanometers of the liquid-solid interface [46, 52] and proper weighting of ensemble averaged near wall measurements [39, 44]. When the distance h = z −a between a spherical particle of radius a and a solid boundary becomes sufficiently small (h/a ∼ 1), hydrodynamic interactions between the particle and wall hinder the Brownian movement of the particle. Such effects are critical to fundamental near-wall measurements and the accuracy of micro-velocimetry techniques, which rely on the accurate measurement of micro- and nano-particle displacements to infer fluid velocity. Near-surface particle tracking of fluorescent particles has been used to determine the threedimensional anisotropic hindered diffusion coefficients for particle gap sizes h/a ∼ 1 with 200 nm diameter particles [41] and h/a ≪ 1 with 3 µm diameter particles [42]. Figure 1.29 shows a comparison between the experimental results of near-surface tracking by Huang and Breuer [42] and several theoretical approximations. Velocimetry Bias Recently, much interest has centered around diffusion induced velocity bias, which is a result of dispersion stemming from diffusion of tracer particles parallel to velocity gradient and a bias imposed by the presence of the wall [43, 44]. Small Brownian fluctuations in the wall-normal direction result in large stream-wise displacements. This phenomenon has been 60 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 0.7 0.5 GCB MOR Bevan D (Sim.) 0.4 D (Sim.) 0.6 D/D0 X Z D (Exp.#1) 0.3 X DZ (Exp.#1) 0.2 D (Exp.#2) X 0.1 0 0 D (Exp.#2) Z 0.05 0.1 h/a 0.15 0.2 Figure 1.29: Normalized hindered diffusion coefficients for the wall-parallel, Dx /D0 , and wall-normal directions, Dz /D0 , near a fluid-solid interface as a function of non-dimensional gap size. “GCB”, “MOR” and “Bevan” represent asymptotic solution of Goldman et al. [61], “Method of Reflection” solution [63] and the Bevan approximation [28], respectively. “Exp.” represents experimental data while “Sim.” means data obtained from Brownian dynamics simulation. Each error bar represents the 95% confidence interval of measurement. predicted by both Langevin simulation [44] and integration of the Fokker-Plank equation [43, 118]. Experimental verification has come by way of near-surface particle tracking using nano-particles [44] and quantum dots [45, 50]. Figure 1.30 demonstrates the effects of this phenomenon on ensemble averaged tracer velocities as a function of interframe time, where the error can vary by as much as ±20%. Figure 1.31 further reveals that the presence of the wall and the associated hindered particle mobility can induce assymetric particle velocity distribution, in violation of an assumption commonly made in particle-based velocimetry analysis and thus lead to measurement bias [39, 44, 81]. Some of the reported studies in diffusion and shear induced velocimetry bias have offered analytical formula and protocols for retrieving the physically accurate flow velocities from flawed near-surface particle tracking velocimetry data [43, 44]. 61 1.4. RECENT DEVELOPMENTS AND APPLICATIONS W=2.0 (Sim) W=3.0 (Sim) W=4.0 (Sim) W=5.0 (Sim) W=3.5 (200nm) W=29.4 (QD) 1.3 〈u〉/〈up〉 1.2 1.1 1 0.9 0.8 −3 10 −2 10 −1 10 2 ∆T/W 0 10 Figure 1.30: The ensemble averaged stream-wise velocity, hui, for a Langevin simulation, 200 nm nano-particles and QD tracers within a non-dimensional observation depth, W , which varies with non-dimensional inter-frame time, ∆T , as predicted by the results from a Langevin simulation of Brownian tracer particles in a near-wall shear flow. The variation is due to dispersion effects and described as diffusion-induced velocity bias in the context of velocimetry. The velocity is scaled by the ensemble-averaged velocity of non-Brownian tracer particles, hup i, and the inter-frame time is appropriately scaled by the observation depth. 62 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY 0.05 1<Z<2 2<Z<3 0.04 3<Z<4 4<Z<5 PDF 0.03 5<Z<6 0.02 0.01 0 0 50 100 150 Vp Figure 1.31: Apparent velocity (Vp ) probability density function (PDF) of particles at various depths of observation. Z = z/a where z is the distance between particle center and the wall and a is the particle radius. All apparent velocity distributions are obtained at Peclet number P e = 10. Particles that start off farther away from the surface move faster because they are carried by fluids at higher velocity planes, and their distributions are more symmetric due to less influence of the wall and hindered Brownian motion. 1.5. CONCLUSION 1.5 63 Conclusion In this chapter, we have tried not only to outline the basic concepts and underlying physics associated with near wall particle tracking velocimetry using total internal reflection flourescence (TIRF) microscopy, but also to highlight the practical issues associated with the design, assembly and operation of a TIRF velocimetry system for micro- and nano-scale fluid measurements. As is often the case with new diagnostic methods, the first few experiments reported are exciting, but often only suggestive - they reveal the promise of a new technique, but expose more questions than they provide answers. This pattern has certainly been true in the history of near wall velocimetry. However, in the past decade the technique has matured considerably and many, certainly not all, of these questions have been identified and in some cases answered. As of today, many of the issues associated with the operation of a TIRF velocimetry system and the analysis of the resultant data have been optimized, algorithms have been developed to track particles, and many of the issues that make interpretation difficult have been identified and explained, so as to make TIRF microscopy a useful and quantitative approach for practical microfluidic measurements. To be sure, many challenges still remain to be addressed. Accurate determination of the wall-normal position of tracer particles remains difficult, and is hindered by the difficulty in discriminating between particle size variations and the position of the particle in the evanescent field. This will improve as particle manufacturing techniques improve, and with the adoption of even more advanced optical methods that employ, for example, interferometry, or other phase- and polarization sensitive methods. Another challenge is the ability to identify and track ensembles of particles whose thermal motions may be orders of magnitude larger than the local fluid velocity. This will become easier as imaging systems continue to improve, and with the further development of statistical methods for extracting particle displacements. Lastly, the physics of near-wall flows, and of the motion of particles in proximity to the liquid-solid interface are extraordinarily subtle, and these complexities continue to generate results that are often unexpected and require explanation. These explanations will take time as we continue to sort out the relative roles of each force and phenomenon before we arrive at a unified understanding of near wall fluidic flows. 64 CHAPTER 1. NEAR-SURFACE PARTICLE TRACKING VELOCIMETRY Bibliography [1] Adam Bange, H. Brian Halsall, and William R. Heineman. Microfluidic immunosensor systems. Biosensors and Bioelectronics, 20:2488–2503, 2005. [2] Samuel K. Sia and George M. 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