ABSTRACTThe “pom-pom” model of McLeish and Larson (J. Rheol. 42, 81, 1998) provides a simple mole... more ABSTRACTThe “pom-pom” model of McLeish and Larson (J. Rheol. 42, 81, 1998) provides a simple molecular theory for the nonlinear rheology of long chain branched polymer melts. The Edwards-de Gennes tube concept is used to derive a constitutive equation for a simple branched molecule composed of two star polymers linked by a single backbone chain. A feature of this model is that the backbone section of tube can stretch up to maximum length given by the maximum entropic drag-force from the arms, after which the star arms are withdrawn into the backbone tube. This produces a sharp transition in the extensional viscosity at this maximum stretch. This unphysical feature results from an over-simplification of the behaviour near the branch points.In this paper we introduce a simple treatment of the coupling between relaxed and unrelaxed polymer segments at branch-points. This allows for localised displacements of branch-point within a quadratic potential before maximum extension is reached. Displacing the branch-point reduces the length of arm outside the tube and so reduces in the drag on the star arms. This smoothes out the sharp transitions in extensional viscosity in the original “pom-pom” model at the cost of introducing an extra unknown parameter.This modification improves the prediction of the nonlinear rheology of H-polymers whose molecular structure is known. Alternatively, for polymers of unknown structure such as commercial Low Density Polyethylene, the model parameters may be fitted from linear viscoelastic and uniaxial extension data, to provide predictions for the behaviour in transient nonlinear shear and planar extension. By including local branch-point displacement we find improved agreement with the data for Low-Density Polyethylene.
Jet formation and break-up in inkjet printing has been studied and understood mainly for pure liq... more Jet formation and break-up in inkjet printing has been studied and understood mainly for pure liquids. Questions remain as to the role of surfactants on the inkjet printing process at the microsecond timescale. Here, numerical and experimental results demonstrating the effects of surfactants on jet break-up and drop formation at the scales relevant to drop-on-demand inkjet printing are presented. The rapid expansion of the free surface during the fast jetting process results in a depletion of surfactants along the air–liquid interface, resulting in surface tension gradients. During ejection, surfactants are concentrated toward the head of the droplet, while the trailing ligament is found to be almost devoid of surfactants. As a consequence, the initial evolution and pinch-off of the jet from the nozzle are found to be very similar to that of pure water, even though the equilibrium surface tension of the surfactant solution is lower by a factor of two. However, particularly for stron...
As inkjet technology develops to produce smaller droplets, substrate features such as accidental ... more As inkjet technology develops to produce smaller droplets, substrate features such as accidental scratches or manufacturing defects can potentially affect the outcome of printing, particularly for printed electronics where continuous tracks are required. Here, the deposition of micro-droplets onto a scratch of commensurate size is studied. The scratch is considered as a groove of rectangular cross-section, with rectangular side ridges representing material displaced from the substrate, and seven equilibrium morphologies are identified as a result of inertial spreading, contact-line pinning, imbibition into the scratch and capillary flow. A regime map is constructed in terms of scratch depth and width, and theoretical estimates of the regime boundaries are developed by adapting droplet spreading laws for flat surfaces to account for liquid entering the scratches. Good agreement is seen with numerical results obtained using a graphical processing unit-accelerated three-dimensional mul...
The formation and evolution of micron-sized droplets of a Newtonian liquid generated on demand in... more The formation and evolution of micron-sized droplets of a Newtonian liquid generated on demand in an industrial inkjet printhead are studied experimentally and simulated numerically. The shapes and positions of droplets during droplet formation are observed using a high-speed camera and compared with their numerically obtained analogs. Both the experiments and the simulations use practical length scales for inkjet printing. The results show how fluid properties, specifically viscosity and surface tension, affect the drop formation, ligament length, and breakoff time. We identify the parameter space of fluid properties for producing single drops at a prescribed speed and show this is not simply a restriction on the Ohnesorge number, but that there is an additional restriction on the Reynolds number that is distinct from the Reynolds number limit associated with the prevention of splashing. This phase diagram provides more precise guidance on the space of fluid parameters for jetting single droplets in drop-on-demand inkjet printers.
This is a repository copy of Modelling contraction flows of bi-disperse polymer blends using the ... more This is a repository copy of Modelling contraction flows of bi-disperse polymer blends using the RoliePoly and Rolie-Double-Poly equations.
This is a repository copy of Design and operation of a Rayleigh Ohnesorge Jetting Extensional Rhe... more This is a repository copy of Design and operation of a Rayleigh Ohnesorge Jetting Extensional Rheometer (ROJER) to study extensional properties of low viscosity polymer solutions.
Rapid advances in experimental biophysical techniques are generating a wealth of information abou... more Rapid advances in experimental biophysical techniques are generating a wealth of information about the mechanical operation of the cellular cytoskeleton and its motors. However, each of these tools typically provides only a limited piece of a highly complex puzzle. There is a need to develop new computational tools that can integrate these data together into a central model. Here we discuss the experimental advances alongside the computational tools, and propose how these could be developed to successfully combine the emerging structural and dynamic experimental data on cytoskeletal motors. We consider examples of both single motors and arrays of motors within a biological cell
The capillary driven thinning and break-up of non-Brownian suspensions are considered. Experiment... more The capillary driven thinning and break-up of non-Brownian suspensions are considered. Experiments show that in the final stages of break-up (when the filament diameter is approximately five times that of the suspended particles) the thinning no longer follows the behaviour predicted by the bulk viscosity; instead thinning is accelerated due to the effects of finite particle size. A simple onedimensional model is described in which the viscosity is determined from the local particle density, found by tracking individual particles within the suspension. Despite its simplicity this model is able to reproduce quantitively the thinning behaviour observed in experiments.
KOBRA is a coarse-grained algorithm for parameterising and simulating slender proteins using Kirc... more KOBRA is a coarse-grained algorithm for parameterising and simulating slender proteins using Kirchoff rods.
The jetting of dilute polymer solutions in drop-on-demand printing is investigated. A quantitativ... more The jetting of dilute polymer solutions in drop-on-demand printing is investigated. A quantitative model is presented which predicts three different regimes of behaviour depending upon the jet Weissenberg number Wi and extensibility of the polymer molecules. In regime I (Wi L) the chains remain fully extended in the thinning ligament. The maximum polymer concentration at which a jet of a certain speed can be formed scales with molecular weight to the power of (1-3ν), (1-6ν) and -2ν in the three regimes respectively, where ν is the solvent quality coefficient. Experimental data obtained with solutions of mono-disperse polystyrene in diethyl phthalate with molecular weights between 24 - 488 kDa, previous numerical simulations of this system, and previously published data for this and another linear polymer in a variety of “good” solvents, all show good agreement with the scaling predictions of the model
... heat flux-r. Jt**", For the case of a spherical droplet, a solu... more ... heat flux-r. Jt**", For the case of a spherical droplet, a solution for the fields ip, i/i, y?'and!/>'may be found as a Rayleigh series expansion ... T or r We rewrite the boundary conditions (10) to (13) as -&+<,),16) or eiKacose+ e'* V+ e"'V= p (y+ 0),(17) eiKaco'e+ eiKa $)+ rvtai/;= I ...
ABSTRACT PEDOT:PSS is commonly inkjet printed in aqueous solutions with surfactant additives for ... more ABSTRACT PEDOT:PSS is commonly inkjet printed in aqueous solutions with surfactant additives for improved electrical properties in organic electronics applications. These shear thinning complex fluids have been found to DoD jet surprisingly well over a wide range of drive voltages and drop speeds, behaving rather like Newtonian fluids with far (ten times) lower viscosities than measured at low shear-rate. As ∼ 1 wt% PEDOT:PSS solutions showed little evidence for satellite production even at high jet speeds this would suggest that the fluid has regained high viscosity levels, in order to slow the necking rate, on timescales ≪ 100 μs and much faster than accessible to conventional mechanical testing means.Experimental work on the break-up of Newtonian ligaments was recently extended to DoD-scale ligaments, and supports the interpretation that the PEDOT:PSS ligaments attain higher viscosity during flight than during the jet emergence from the print head nozzle, although such rapid recovery timescales for PEDOT:PSS were not predicted from its measured rheology.Our recent work has focused on oscillating drop (OD) techniques for determination of properties of DoD (50 μm) scale aqueous PEDOT:PSS solutions (with and without surfactants) and on a larger (3mm) dispensing scale for more general shear thinning fluids. Imaging studies by one of us (SW) evaluated diffraction effects on OD analyses.The small effects of weak elasticity on the drop oscillations, as assessed theoretically by Khismatullin and Nadim (2001), have been exploited to provide new limits to the recovery time for aqueous PEDOT:PSS based on the fluid viscosity deduced from measured rheology and OD decay rate. These limits are consistent with recent numerical simulations of shear thinning fluid jetting.
This work looks at the sensitivity of large amplitude oscillatory shear (LAOS) to micro-scale str... more This work looks at the sensitivity of large amplitude oscillatory shear (LAOS) to micro-scale structure of long chain branched polymer melts. Fourier Transform Rheology is used in combination with LAOS to extract the odd harmonic contributions within the stress response of a material under oscillation for shear strains of up to unity. This work focusses on the third harmonics and experimental measurements of three long chain branched (LCB) polyethylene samples which are compared to the Pompom constitutive model. The polyethylenes consist of two LCB-HDPEs which have well quantified low levels of branching, and one highly branched commercial LDPE. The Pompom model is a constitutive model which is parametrised by various aspects of molecular detail. The Pompom model can capture the rheology of industrial branched resins using a multi-mode approach, with each Pompom mode consisting of two linear parameters and two non-linear parameters. Typically, the non-linear parameters are fitted us...
The problem of scattering of ultrasound by particles in the long wavelength limit has a well-esta... more The problem of scattering of ultrasound by particles in the long wavelength limit has a well-established solution in terms of Rayleigh expansions of the scattered fields. However, this solution is ill-conditioned numerically, and recent work has attempted to identify an alternative method. The scattered fields have been expressed as a perturbation expansion in the parameter Ka (the wavenumber multiplied by the particle radius), which is small in the long wavelength region. In the work reported here the problem has been formulated so as to be valid for all values of the thermal wavelength, which varies in order of magnitude, from much smaller to much larger than the particle size in the long wavelength region. Thus the present solution overlaps the limiting solutions for very small thermal wavelength (geometric theory) and very large thermal wavelength (low frequency) previously reported. Close agreement is demonstrated with the established Rayleigh expansion solution.
ABSTRACTThe “pom-pom” model of McLeish and Larson (J. Rheol. 42, 81, 1998) provides a simple mole... more ABSTRACTThe “pom-pom” model of McLeish and Larson (J. Rheol. 42, 81, 1998) provides a simple molecular theory for the nonlinear rheology of long chain branched polymer melts. The Edwards-de Gennes tube concept is used to derive a constitutive equation for a simple branched molecule composed of two star polymers linked by a single backbone chain. A feature of this model is that the backbone section of tube can stretch up to maximum length given by the maximum entropic drag-force from the arms, after which the star arms are withdrawn into the backbone tube. This produces a sharp transition in the extensional viscosity at this maximum stretch. This unphysical feature results from an over-simplification of the behaviour near the branch points.In this paper we introduce a simple treatment of the coupling between relaxed and unrelaxed polymer segments at branch-points. This allows for localised displacements of branch-point within a quadratic potential before maximum extension is reached. Displacing the branch-point reduces the length of arm outside the tube and so reduces in the drag on the star arms. This smoothes out the sharp transitions in extensional viscosity in the original “pom-pom” model at the cost of introducing an extra unknown parameter.This modification improves the prediction of the nonlinear rheology of H-polymers whose molecular structure is known. Alternatively, for polymers of unknown structure such as commercial Low Density Polyethylene, the model parameters may be fitted from linear viscoelastic and uniaxial extension data, to provide predictions for the behaviour in transient nonlinear shear and planar extension. By including local branch-point displacement we find improved agreement with the data for Low-Density Polyethylene.
Jet formation and break-up in inkjet printing has been studied and understood mainly for pure liq... more Jet formation and break-up in inkjet printing has been studied and understood mainly for pure liquids. Questions remain as to the role of surfactants on the inkjet printing process at the microsecond timescale. Here, numerical and experimental results demonstrating the effects of surfactants on jet break-up and drop formation at the scales relevant to drop-on-demand inkjet printing are presented. The rapid expansion of the free surface during the fast jetting process results in a depletion of surfactants along the air–liquid interface, resulting in surface tension gradients. During ejection, surfactants are concentrated toward the head of the droplet, while the trailing ligament is found to be almost devoid of surfactants. As a consequence, the initial evolution and pinch-off of the jet from the nozzle are found to be very similar to that of pure water, even though the equilibrium surface tension of the surfactant solution is lower by a factor of two. However, particularly for stron...
As inkjet technology develops to produce smaller droplets, substrate features such as accidental ... more As inkjet technology develops to produce smaller droplets, substrate features such as accidental scratches or manufacturing defects can potentially affect the outcome of printing, particularly for printed electronics where continuous tracks are required. Here, the deposition of micro-droplets onto a scratch of commensurate size is studied. The scratch is considered as a groove of rectangular cross-section, with rectangular side ridges representing material displaced from the substrate, and seven equilibrium morphologies are identified as a result of inertial spreading, contact-line pinning, imbibition into the scratch and capillary flow. A regime map is constructed in terms of scratch depth and width, and theoretical estimates of the regime boundaries are developed by adapting droplet spreading laws for flat surfaces to account for liquid entering the scratches. Good agreement is seen with numerical results obtained using a graphical processing unit-accelerated three-dimensional mul...
The formation and evolution of micron-sized droplets of a Newtonian liquid generated on demand in... more The formation and evolution of micron-sized droplets of a Newtonian liquid generated on demand in an industrial inkjet printhead are studied experimentally and simulated numerically. The shapes and positions of droplets during droplet formation are observed using a high-speed camera and compared with their numerically obtained analogs. Both the experiments and the simulations use practical length scales for inkjet printing. The results show how fluid properties, specifically viscosity and surface tension, affect the drop formation, ligament length, and breakoff time. We identify the parameter space of fluid properties for producing single drops at a prescribed speed and show this is not simply a restriction on the Ohnesorge number, but that there is an additional restriction on the Reynolds number that is distinct from the Reynolds number limit associated with the prevention of splashing. This phase diagram provides more precise guidance on the space of fluid parameters for jetting single droplets in drop-on-demand inkjet printers.
This is a repository copy of Modelling contraction flows of bi-disperse polymer blends using the ... more This is a repository copy of Modelling contraction flows of bi-disperse polymer blends using the RoliePoly and Rolie-Double-Poly equations.
This is a repository copy of Design and operation of a Rayleigh Ohnesorge Jetting Extensional Rhe... more This is a repository copy of Design and operation of a Rayleigh Ohnesorge Jetting Extensional Rheometer (ROJER) to study extensional properties of low viscosity polymer solutions.
Rapid advances in experimental biophysical techniques are generating a wealth of information abou... more Rapid advances in experimental biophysical techniques are generating a wealth of information about the mechanical operation of the cellular cytoskeleton and its motors. However, each of these tools typically provides only a limited piece of a highly complex puzzle. There is a need to develop new computational tools that can integrate these data together into a central model. Here we discuss the experimental advances alongside the computational tools, and propose how these could be developed to successfully combine the emerging structural and dynamic experimental data on cytoskeletal motors. We consider examples of both single motors and arrays of motors within a biological cell
The capillary driven thinning and break-up of non-Brownian suspensions are considered. Experiment... more The capillary driven thinning and break-up of non-Brownian suspensions are considered. Experiments show that in the final stages of break-up (when the filament diameter is approximately five times that of the suspended particles) the thinning no longer follows the behaviour predicted by the bulk viscosity; instead thinning is accelerated due to the effects of finite particle size. A simple onedimensional model is described in which the viscosity is determined from the local particle density, found by tracking individual particles within the suspension. Despite its simplicity this model is able to reproduce quantitively the thinning behaviour observed in experiments.
KOBRA is a coarse-grained algorithm for parameterising and simulating slender proteins using Kirc... more KOBRA is a coarse-grained algorithm for parameterising and simulating slender proteins using Kirchoff rods.
The jetting of dilute polymer solutions in drop-on-demand printing is investigated. A quantitativ... more The jetting of dilute polymer solutions in drop-on-demand printing is investigated. A quantitative model is presented which predicts three different regimes of behaviour depending upon the jet Weissenberg number Wi and extensibility of the polymer molecules. In regime I (Wi L) the chains remain fully extended in the thinning ligament. The maximum polymer concentration at which a jet of a certain speed can be formed scales with molecular weight to the power of (1-3ν), (1-6ν) and -2ν in the three regimes respectively, where ν is the solvent quality coefficient. Experimental data obtained with solutions of mono-disperse polystyrene in diethyl phthalate with molecular weights between 24 - 488 kDa, previous numerical simulations of this system, and previously published data for this and another linear polymer in a variety of “good” solvents, all show good agreement with the scaling predictions of the model
... heat flux-r. Jt**", For the case of a spherical droplet, a solu... more ... heat flux-r. Jt**", For the case of a spherical droplet, a solution for the fields ip, i/i, y?'and!/>'may be found as a Rayleigh series expansion ... T or r We rewrite the boundary conditions (10) to (13) as -&+<,),16) or eiKacose+ e'* V+ e"'V= p (y+ 0),(17) eiKaco'e+ eiKa $)+ rvtai/;= I ...
ABSTRACT PEDOT:PSS is commonly inkjet printed in aqueous solutions with surfactant additives for ... more ABSTRACT PEDOT:PSS is commonly inkjet printed in aqueous solutions with surfactant additives for improved electrical properties in organic electronics applications. These shear thinning complex fluids have been found to DoD jet surprisingly well over a wide range of drive voltages and drop speeds, behaving rather like Newtonian fluids with far (ten times) lower viscosities than measured at low shear-rate. As ∼ 1 wt% PEDOT:PSS solutions showed little evidence for satellite production even at high jet speeds this would suggest that the fluid has regained high viscosity levels, in order to slow the necking rate, on timescales ≪ 100 μs and much faster than accessible to conventional mechanical testing means.Experimental work on the break-up of Newtonian ligaments was recently extended to DoD-scale ligaments, and supports the interpretation that the PEDOT:PSS ligaments attain higher viscosity during flight than during the jet emergence from the print head nozzle, although such rapid recovery timescales for PEDOT:PSS were not predicted from its measured rheology.Our recent work has focused on oscillating drop (OD) techniques for determination of properties of DoD (50 μm) scale aqueous PEDOT:PSS solutions (with and without surfactants) and on a larger (3mm) dispensing scale for more general shear thinning fluids. Imaging studies by one of us (SW) evaluated diffraction effects on OD analyses.The small effects of weak elasticity on the drop oscillations, as assessed theoretically by Khismatullin and Nadim (2001), have been exploited to provide new limits to the recovery time for aqueous PEDOT:PSS based on the fluid viscosity deduced from measured rheology and OD decay rate. These limits are consistent with recent numerical simulations of shear thinning fluid jetting.
This work looks at the sensitivity of large amplitude oscillatory shear (LAOS) to micro-scale str... more This work looks at the sensitivity of large amplitude oscillatory shear (LAOS) to micro-scale structure of long chain branched polymer melts. Fourier Transform Rheology is used in combination with LAOS to extract the odd harmonic contributions within the stress response of a material under oscillation for shear strains of up to unity. This work focusses on the third harmonics and experimental measurements of three long chain branched (LCB) polyethylene samples which are compared to the Pompom constitutive model. The polyethylenes consist of two LCB-HDPEs which have well quantified low levels of branching, and one highly branched commercial LDPE. The Pompom model is a constitutive model which is parametrised by various aspects of molecular detail. The Pompom model can capture the rheology of industrial branched resins using a multi-mode approach, with each Pompom mode consisting of two linear parameters and two non-linear parameters. Typically, the non-linear parameters are fitted us...
The problem of scattering of ultrasound by particles in the long wavelength limit has a well-esta... more The problem of scattering of ultrasound by particles in the long wavelength limit has a well-established solution in terms of Rayleigh expansions of the scattered fields. However, this solution is ill-conditioned numerically, and recent work has attempted to identify an alternative method. The scattered fields have been expressed as a perturbation expansion in the parameter Ka (the wavenumber multiplied by the particle radius), which is small in the long wavelength region. In the work reported here the problem has been formulated so as to be valid for all values of the thermal wavelength, which varies in order of magnitude, from much smaller to much larger than the particle size in the long wavelength region. Thus the present solution overlaps the limiting solutions for very small thermal wavelength (geometric theory) and very large thermal wavelength (low frequency) previously reported. Close agreement is demonstrated with the established Rayleigh expansion solution.
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Papers by Oliver Harlen