Recent analytical developments on triple-flame lift-off devoted to the derivation of a stabilizat... more Recent analytical developments on triple-flame lift-off devoted to the derivation of a stabilization diagram [1] are used to compare lift-off height prediction against experimental results [2]. To study lift-off properties with an approximate analytical solution, the mixing upstream of the flame base was estimated using a cold flow solution, while the speed of the flame front was obtained from recent derivation of triple flame speed including heat release effects [3]. The comparison between the approximate lift-off height solution and the measurements suggests that some of the specific features of laminar flame lift-off are not included in the cold flow mixing analysis. To understand the observed discrepancies between theory and measurement, numerical simulations of lifted laminar jet diffusion flames including heat release effects are performed. We compare the simulated lift-off height and blow-out position with their approximations provided by the analytical solution. As with the ...
Screened repulsion between uniformly charged plates with an intervening electrolyte is analyzed f... more Screened repulsion between uniformly charged plates with an intervening electrolyte is analyzed for strongly overlapped electrical double layers (EDL), accounting for the steric effect of ions and their expulsion from EDL edges into the surrounding solution. As a generalization of a study by Philipse et. al. which does not account for these effects, an analytical expression is derived for the repulsion pressure in the limit of infinitely long plates with a zero-field assumption, which agrees closely with the corresponding numerical solution
Molecular dynamics simulation is utilized to investigate the ionic transport of NaCl in solution ... more Molecular dynamics simulation is utilized to investigate the ionic transport of NaCl in solution through a graphene nanopore under an applied electric field. Results show the formation of concentration polarization layers in the vicinity of the graphene sheet. The non-uniformity of the ion distribution gives rise to an electric pressure which drives vortical motions in the fluid if the electric field is sufficiently strong to overcome the influence of viscosity and thermal fluctuations. The relative importance of hydrodynamic transport and thermal fluctuations in determining the pore conductivity is investigated. A second important effect that is observed is the mass transport of water through the nanopore, with an average velocity proportional to the applied voltage and independent of the pore diameter. The flux arises as a consequence of the asymmetry in the ion distribution with respect to reflection about the plane of the graphene sheet. The accumulation of liquid molecules in t...
A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nan... more A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nanopore is presented. It is assumed that the speed is determined by a balance of electrical and viscous forces arising from within the pore and that classical continuum electrostatics and hydrodynamics may be considered applicable. An explicit formula for the translocation speed as a function of the pore geometry and other physical parameters is obtained and is shown to be consistent with experimental measurements on DNA translocation through nanopores in silicon membranes. Experiments also show a weak dependence of the translocation speed on polymer length that is not accounted for by the present model. It is hypothesized that this is due to secondary effects that are neglected here.
The screened Coulomb interaction between uniformly charged flat plates is considered at very smal... more The screened Coulomb interaction between uniformly charged flat plates is considered at very small plate separations for which the Debye layers are strongly overlapped, in the limit of small electrical potentials. If the plates are of infinite length, the disjoining pressure between the plates decays as an inverse power of the plate separation. If the plates are of finite length, we show that screening Debye layer charges close to the edge of the plates are no longer constrained to stay between the plates, but instead spill out into the surrounding electrolyte. The resulting reduction in the disjoining pressure is calculated analytically. A similar reduction of disjoining pressure due to loss of lateral confinement of the Debye layer charges should occur whenever the sizes of the interacting charged objects become small enough to approach the Debye scale. We investigate the effect here in the context of a two dimensional model problem that is sufficiently simple to yield analytical ...
In capillary electrophoresis, sample ions migrate along a micro-capillary filled with a backgroun... more In capillary electrophoresis, sample ions migrate along a micro-capillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background.Under such conditions, the local migration velocity of sample ions becomes concentration dependent resulting in a nonlinear wave that exhibits shock like features. If the nonlinearity is weak, the sample concentration profile, under certain simplifying assumptions, can be shown to obey Burgers' equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which has an exact analytical solution for arbitrary initial condition.In this paper, we use a numerical method to study the problem in the more general case where the sample concentration is not small in comparison to the concentration of background ions. In the case of low concentrations, the numerical results agree...
Single molecule experiments on bacteriophages show an exponential scaling for the dependence of m... more Single molecule experiments on bacteriophages show an exponential scaling for the dependence of mobility on the length of DNA within the capsid. It has been suggested that this could be due to the "capstan mechanism" -- the exponential amplification of friction forces that result when a rope is wound around a cylinder as in a ship's capstan. Here we describe a desktop experiment that illustrates the effect. Though our model phage is a million times larger, it exhibits the same scaling observed in single molecule experiments.
In capillary electrophoresis (CE), analytes are separated along the axis of a single microcapilla... more In capillary electrophoresis (CE), analytes are separated along the axis of a single microcapillary by virtue of their differential migration in an applied electric field. CE can also be performed in channels etched on solid substrates such as glass or PDMS and can be integrated into a microfluidic chip with a complex network of electric and fluidic circuits. The measure of quality of a CE instrument is resolution which is limited fundamentally by mixing due to various physical processes. The theoretical limit on the best separation that can be achieved is set by molecular diffusion, which is inevitable. The goal is to eliminate or minimize the other sources of dispersion by design. This chapter provides an overview of the various mechanisms of band broadening and the mathematical results that make it possible to estimate their relative contributions.
The charge selective properties of a long planar nanochannel with an embedded finite uniformly ch... more The charge selective properties of a long planar nanochannel with an embedded finite uniformly charged section in the middle are studied. The probability flux of a single test ion initially confined to the inlet reservoir is determined by integrating the Smoluchowski equation using a previously published series solution for the Debye-Hückel potential in this geometry. The charge selective properties are characterized by a dimensionless quantity that we call the "fractional blockage". We study how the fractional blockage depends on the dimensionless parameters that characterize the charge state and channel geometry. In the limit of strongly overlapped wall Debye layers, analytical expressions for the fractional blockage are presented that are found to be in good agreement with numerically computed values in the appropriate asymptotic regimes. These results may be helpful in the design of nanofluidic devices that have a variety of applications.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2017
The screened Coulomb interaction between a pair of infinite parallel planes with spatially varyin... more The screened Coulomb interaction between a pair of infinite parallel planes with spatially varying surface charge is considered in the limit of small electrical potentials for arbitrary Debye lengths. A simple expression for the disjoining pressure is derived in terms of a two dimensional integral in Fourier space. The integral is evaluated for periodic and random charge distributions and the disjoining pressure is expressed as a sum over Fourier-Bloch reciprocal lattice vectors or in terms of an integral involving the autocorrelation function respectively. The force between planes with a finite area of uniform charge, a model for the DLVO interaction between finite surfaces, is also calculated. It is shown that the overspill of the charge cloud beyond the region immediately between the charged areas results in a reduction of the disjoining pressure, as reported by us recently in the long Debye length limit for planes of finite width.
... Contents 1 Microfluidic Transport and Micro-scale Flow Physics: An Overview 1 Debapriya Chakra... more ... Contents 1 Microfluidic Transport and Micro-scale Flow Physics: An Overview 1 Debapriya Chakraborty and Suman Chakraborty 1.1 Introduction..... ... 181 R. Martinez-Duarte, G. Turon Teixidor, PP Mukherjee, Q. Kang, and MJ Madou 5.1 Introduction..... ...
Center for Turbulence Research, NASA Ames/Stanford University, 2003
ANNUAL RESEARCH BRIEFS 2004. Preface Energy conservation in collocated discretization schemes on ... more ANNUAL RESEARCH BRIEFS 2004. Preface Energy conservation in collocated discretization schemes on unstructured meshes F. Ham and G. Iaccarino. On mass conservation and desingularization of the Level Set/Vortex Sheet method M. Herrmann. Accurate and efficient immersed-boundary interpolations for viscous flows S. Kang, G. Iaccarino and P. Moin. A computational and experimental investigation of flow inside branched coral colony S. Chang, G. Iaccarino, C. Elkins, J. Eaton and S. Monismith. ...
BOOK CHAPTER: Applications of Induced-Charge Electrokinetic in Microfluidics, 2014
CEK Microvalve The main function of a microvalve is switching the direction of the flow at the de... more CEK Microvalve The main function of a microvalve is switching the direction of the flow at the desired time to control and regulate the fluid stream. Microvalves are one of the most important components of integrated lab-on-a-chip (LOC) devices. Using microvalves with high performance, the sequential loading and washing processes could be performed accurately and fast. However, the existing microvalves have lots of serious problems which are unsolved. Thus, a new design is highly required to develop practical and efficient microvalves and overcome the current problems. Such a microvalve could be a great step toward developing integrated LOC devices. In this entry a new ICEK microvalve using a heterogeneous particle is introduced. This ICEK microvalve is easily controlled by applying two perpendicular electric fields, stable and fast, has small dead volume and short response time, has no leakage, and is easy ...
Diffusion of colored dye on water saturated paper substrates has been traditionally exploited wit... more Diffusion of colored dye on water saturated paper substrates has been traditionally exploited with great skill by renowned water color artists. The same physics finds more recent practical applications in paper based diagnostic devices deploying chemicals that react with a bodily fluid yielding colorimetric signals for disease detection. During spontaneous imbibition through the tortuous pathways of a porous electrolyte saturated paper matrix, a dye molecule undergoes diffusion in a complex network of pores. The advancing front forms a strongly correlated interface that propagates diffusively but with an enhanced effective diffusivity. We measure this effective diffusivity and show that it is several orders of magnitude greater than the free solution diffusivity and has a significant dependence on the solution pH and salt concentration in the background electrolyte. We attribute this to electrically mediated interfacial interactions between the ionic species in the liquid dye and spontaneous surface charges developed at porous interfaces, and introduce a simple theory to explain this phenomenon.
Single molecule experiments on bacteriophages show an exponential scaling for the dependence of m... more Single molecule experiments on bacteriophages show an exponential scaling for the dependence of mobility on the length of DNA within the capsid. It has been suggested that this could be due to the "capstan mechanism" -the exponential amplification of friction forces that result when a rope is wound around a cylinder as in a ship's capstan. Here we describe a desktop experiment that illustrates the effect. Though our model phage is a million times larger, it exhibits the same scaling observed in single molecule experiments.
In nanopore sensing, changes in ionic current are used to analyse single molecules in solution. T... more In nanopore sensing, changes in ionic current are used to analyse single molecules in solution. The translocation dynamics of polyelectrolytes is of particular interest given potential applications such as DNA sequencing. In this paper, we determine how the dynamics of voltage driven DNA translocation can be affected by the nanopore geometry and hence the available configurational space for the DNA. Using the inherent geometrical asymmetry of a conically shaped nanopore, we examine how DNA dynamics depends on the directionality of transport. The total translocation time of DNA when exiting the extended conical confinement is significantly larger compared to the configuration where the DNA enters the pore from the open reservoir. By using specially designed DNA molecules with positional markers, we demonstrate that the translocation velocity progressively increases as the DNA exits from confinement. We show that a hydrodynamic model can account for these observations.
Recent analytical developments on triple-flame lift-off devoted to the derivation of a stabilizat... more Recent analytical developments on triple-flame lift-off devoted to the derivation of a stabilization diagram [1] are used to compare lift-off height prediction against experimental results [2]. To study lift-off properties with an approximate analytical solution, the mixing upstream of the flame base was estimated using a cold flow solution, while the speed of the flame front was obtained from recent derivation of triple flame speed including heat release effects [3]. The comparison between the approximate lift-off height solution and the measurements suggests that some of the specific features of laminar flame lift-off are not included in the cold flow mixing analysis. To understand the observed discrepancies between theory and measurement, numerical simulations of lifted laminar jet diffusion flames including heat release effects are performed. We compare the simulated lift-off height and blow-out position with their approximations provided by the analytical solution. As with the ...
Screened repulsion between uniformly charged plates with an intervening electrolyte is analyzed f... more Screened repulsion between uniformly charged plates with an intervening electrolyte is analyzed for strongly overlapped electrical double layers (EDL), accounting for the steric effect of ions and their expulsion from EDL edges into the surrounding solution. As a generalization of a study by Philipse et. al. which does not account for these effects, an analytical expression is derived for the repulsion pressure in the limit of infinitely long plates with a zero-field assumption, which agrees closely with the corresponding numerical solution
Molecular dynamics simulation is utilized to investigate the ionic transport of NaCl in solution ... more Molecular dynamics simulation is utilized to investigate the ionic transport of NaCl in solution through a graphene nanopore under an applied electric field. Results show the formation of concentration polarization layers in the vicinity of the graphene sheet. The non-uniformity of the ion distribution gives rise to an electric pressure which drives vortical motions in the fluid if the electric field is sufficiently strong to overcome the influence of viscosity and thermal fluctuations. The relative importance of hydrodynamic transport and thermal fluctuations in determining the pore conductivity is investigated. A second important effect that is observed is the mass transport of water through the nanopore, with an average velocity proportional to the applied voltage and independent of the pore diameter. The flux arises as a consequence of the asymmetry in the ion distribution with respect to reflection about the plane of the graphene sheet. The accumulation of liquid molecules in t...
A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nan... more A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nanopore is presented. It is assumed that the speed is determined by a balance of electrical and viscous forces arising from within the pore and that classical continuum electrostatics and hydrodynamics may be considered applicable. An explicit formula for the translocation speed as a function of the pore geometry and other physical parameters is obtained and is shown to be consistent with experimental measurements on DNA translocation through nanopores in silicon membranes. Experiments also show a weak dependence of the translocation speed on polymer length that is not accounted for by the present model. It is hypothesized that this is due to secondary effects that are neglected here.
The screened Coulomb interaction between uniformly charged flat plates is considered at very smal... more The screened Coulomb interaction between uniformly charged flat plates is considered at very small plate separations for which the Debye layers are strongly overlapped, in the limit of small electrical potentials. If the plates are of infinite length, the disjoining pressure between the plates decays as an inverse power of the plate separation. If the plates are of finite length, we show that screening Debye layer charges close to the edge of the plates are no longer constrained to stay between the plates, but instead spill out into the surrounding electrolyte. The resulting reduction in the disjoining pressure is calculated analytically. A similar reduction of disjoining pressure due to loss of lateral confinement of the Debye layer charges should occur whenever the sizes of the interacting charged objects become small enough to approach the Debye scale. We investigate the effect here in the context of a two dimensional model problem that is sufficiently simple to yield analytical ...
In capillary electrophoresis, sample ions migrate along a micro-capillary filled with a backgroun... more In capillary electrophoresis, sample ions migrate along a micro-capillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background.Under such conditions, the local migration velocity of sample ions becomes concentration dependent resulting in a nonlinear wave that exhibits shock like features. If the nonlinearity is weak, the sample concentration profile, under certain simplifying assumptions, can be shown to obey Burgers' equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which has an exact analytical solution for arbitrary initial condition.In this paper, we use a numerical method to study the problem in the more general case where the sample concentration is not small in comparison to the concentration of background ions. In the case of low concentrations, the numerical results agree...
Single molecule experiments on bacteriophages show an exponential scaling for the dependence of m... more Single molecule experiments on bacteriophages show an exponential scaling for the dependence of mobility on the length of DNA within the capsid. It has been suggested that this could be due to the "capstan mechanism" -- the exponential amplification of friction forces that result when a rope is wound around a cylinder as in a ship's capstan. Here we describe a desktop experiment that illustrates the effect. Though our model phage is a million times larger, it exhibits the same scaling observed in single molecule experiments.
In capillary electrophoresis (CE), analytes are separated along the axis of a single microcapilla... more In capillary electrophoresis (CE), analytes are separated along the axis of a single microcapillary by virtue of their differential migration in an applied electric field. CE can also be performed in channels etched on solid substrates such as glass or PDMS and can be integrated into a microfluidic chip with a complex network of electric and fluidic circuits. The measure of quality of a CE instrument is resolution which is limited fundamentally by mixing due to various physical processes. The theoretical limit on the best separation that can be achieved is set by molecular diffusion, which is inevitable. The goal is to eliminate or minimize the other sources of dispersion by design. This chapter provides an overview of the various mechanisms of band broadening and the mathematical results that make it possible to estimate their relative contributions.
The charge selective properties of a long planar nanochannel with an embedded finite uniformly ch... more The charge selective properties of a long planar nanochannel with an embedded finite uniformly charged section in the middle are studied. The probability flux of a single test ion initially confined to the inlet reservoir is determined by integrating the Smoluchowski equation using a previously published series solution for the Debye-Hückel potential in this geometry. The charge selective properties are characterized by a dimensionless quantity that we call the "fractional blockage". We study how the fractional blockage depends on the dimensionless parameters that characterize the charge state and channel geometry. In the limit of strongly overlapped wall Debye layers, analytical expressions for the fractional blockage are presented that are found to be in good agreement with numerically computed values in the appropriate asymptotic regimes. These results may be helpful in the design of nanofluidic devices that have a variety of applications.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2017
The screened Coulomb interaction between a pair of infinite parallel planes with spatially varyin... more The screened Coulomb interaction between a pair of infinite parallel planes with spatially varying surface charge is considered in the limit of small electrical potentials for arbitrary Debye lengths. A simple expression for the disjoining pressure is derived in terms of a two dimensional integral in Fourier space. The integral is evaluated for periodic and random charge distributions and the disjoining pressure is expressed as a sum over Fourier-Bloch reciprocal lattice vectors or in terms of an integral involving the autocorrelation function respectively. The force between planes with a finite area of uniform charge, a model for the DLVO interaction between finite surfaces, is also calculated. It is shown that the overspill of the charge cloud beyond the region immediately between the charged areas results in a reduction of the disjoining pressure, as reported by us recently in the long Debye length limit for planes of finite width.
... Contents 1 Microfluidic Transport and Micro-scale Flow Physics: An Overview 1 Debapriya Chakra... more ... Contents 1 Microfluidic Transport and Micro-scale Flow Physics: An Overview 1 Debapriya Chakraborty and Suman Chakraborty 1.1 Introduction..... ... 181 R. Martinez-Duarte, G. Turon Teixidor, PP Mukherjee, Q. Kang, and MJ Madou 5.1 Introduction..... ...
Center for Turbulence Research, NASA Ames/Stanford University, 2003
ANNUAL RESEARCH BRIEFS 2004. Preface Energy conservation in collocated discretization schemes on ... more ANNUAL RESEARCH BRIEFS 2004. Preface Energy conservation in collocated discretization schemes on unstructured meshes F. Ham and G. Iaccarino. On mass conservation and desingularization of the Level Set/Vortex Sheet method M. Herrmann. Accurate and efficient immersed-boundary interpolations for viscous flows S. Kang, G. Iaccarino and P. Moin. A computational and experimental investigation of flow inside branched coral colony S. Chang, G. Iaccarino, C. Elkins, J. Eaton and S. Monismith. ...
BOOK CHAPTER: Applications of Induced-Charge Electrokinetic in Microfluidics, 2014
CEK Microvalve The main function of a microvalve is switching the direction of the flow at the de... more CEK Microvalve The main function of a microvalve is switching the direction of the flow at the desired time to control and regulate the fluid stream. Microvalves are one of the most important components of integrated lab-on-a-chip (LOC) devices. Using microvalves with high performance, the sequential loading and washing processes could be performed accurately and fast. However, the existing microvalves have lots of serious problems which are unsolved. Thus, a new design is highly required to develop practical and efficient microvalves and overcome the current problems. Such a microvalve could be a great step toward developing integrated LOC devices. In this entry a new ICEK microvalve using a heterogeneous particle is introduced. This ICEK microvalve is easily controlled by applying two perpendicular electric fields, stable and fast, has small dead volume and short response time, has no leakage, and is easy ...
Diffusion of colored dye on water saturated paper substrates has been traditionally exploited wit... more Diffusion of colored dye on water saturated paper substrates has been traditionally exploited with great skill by renowned water color artists. The same physics finds more recent practical applications in paper based diagnostic devices deploying chemicals that react with a bodily fluid yielding colorimetric signals for disease detection. During spontaneous imbibition through the tortuous pathways of a porous electrolyte saturated paper matrix, a dye molecule undergoes diffusion in a complex network of pores. The advancing front forms a strongly correlated interface that propagates diffusively but with an enhanced effective diffusivity. We measure this effective diffusivity and show that it is several orders of magnitude greater than the free solution diffusivity and has a significant dependence on the solution pH and salt concentration in the background electrolyte. We attribute this to electrically mediated interfacial interactions between the ionic species in the liquid dye and spontaneous surface charges developed at porous interfaces, and introduce a simple theory to explain this phenomenon.
Single molecule experiments on bacteriophages show an exponential scaling for the dependence of m... more Single molecule experiments on bacteriophages show an exponential scaling for the dependence of mobility on the length of DNA within the capsid. It has been suggested that this could be due to the "capstan mechanism" -the exponential amplification of friction forces that result when a rope is wound around a cylinder as in a ship's capstan. Here we describe a desktop experiment that illustrates the effect. Though our model phage is a million times larger, it exhibits the same scaling observed in single molecule experiments.
In nanopore sensing, changes in ionic current are used to analyse single molecules in solution. T... more In nanopore sensing, changes in ionic current are used to analyse single molecules in solution. The translocation dynamics of polyelectrolytes is of particular interest given potential applications such as DNA sequencing. In this paper, we determine how the dynamics of voltage driven DNA translocation can be affected by the nanopore geometry and hence the available configurational space for the DNA. Using the inherent geometrical asymmetry of a conically shaped nanopore, we examine how DNA dynamics depends on the directionality of transport. The total translocation time of DNA when exiting the extended conical confinement is significantly larger compared to the configuration where the DNA enters the pore from the open reservoir. By using specially designed DNA molecules with positional markers, we demonstrate that the translocation velocity progressively increases as the DNA exits from confinement. We show that a hydrodynamic model can account for these observations.
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Papers by Sandip Ghosal