Shear-induced Diffusion Research Articles

Cooperativity and segregation in confined flows of soft binary glasses.

When a suspension containing particles of different sizes flows through a confined geometry a size gradient can be established, with large particles accumulating in the channel center. Such size separation driven by hydrodynamic interactions is expected to facilitate membrane filtration and may lead to the design of novel and innovative separation techniques. For this, a wide range of particle concentrations has to be investigated, in order to clarify whether shear-induced migration can be utilized at concentrations close to or above the colloidal glass transition, where particle motion is severely hindered and hydrodynamic interactions are screened. We explore this scenario by studying the flow of binary mixtures of soft colloidal microgels, well above their liquid-solid transition, through narrow microchannels. We find that, even though the flow becomes strongly heterogeneous, in both space and time, characterized by a large cooperativity length, size segregation still occurs. This suggests that even above the glass transition shear-induced diffusion could still be used as a fractionation mechanism, which is of great relevance for process intensification purposes.

The effect of shear flow on the rotational diffusion of a single axisymmetric particle

Understanding the orientation dynamics of anisotropic colloidal particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in shear flow, the orientation dynamics of non-spherical Brownian particles are poorly understood. Here we analytically calculate the time-dependent orientation distributions for non-spherical axisymmetric particles confined to rotate in the flow–gradient plane, in the limit of small but non-zero Brownian diffusivity. For continuous shear, despite the complicated dynamics arising from the particle rotations, we find a coordinate change that maps the orientation dynamics to a diffusion equation with a remarkably simple ratio of the enhanced rotary diffusivity to the zero shear diffusion:$D_{eff}^{r}/D_{0}^{r}=(3/8)(p-1/p)^{2}+1$, where$p$is the particle aspect ratio. For oscillatory shear, the enhanced diffusion becomes orientation dependent and drastically alters the long-time orientation distributions. We describe a general method for solving the time-dependent oscillatory shear distributions and finding the effective diffusion constant. As an illustration, we use this method to solve for the diffusion and distributions in the case of triangle-wave oscillatory shear and find that they depend strongly on the strain amplitude and particle aspect ratio. These results provide new insight into the time-dependent rheology of suspensions of anisotropic particles. For continuous shear, we find two distinct diffusive time scales in the rheology that scale separately with aspect ratio$p$, as$1/D_{0}^{r}p^{4}$and as$1/D_{0}^{r}p^{2}$for$p\gg 1$. For oscillatory shear flows, the intrinsic viscosity oscillates with the strain amplitude. Finally, we show the relevance of our results to real suspensions in which particles can rotate freely. Collectively, the interplay between shear-induced rotations and diffusion has rich structure and strong effects: for a particle with aspect ratio 10, the oscillatory shear intrinsic viscosity varies by a factor of${\approx}2$and the rotational diffusion by a factor of${\approx}40$.

Comparison of first principles model of beer microfiltration to experiments via systematic parameter identification

A first principles microfiltration model based on shear-induced diffusion is compared to experiments performed on the clarification of beer. After performing an identifiability and sensitivity analysis, the model parameters are estimated using global minimization of the sum of least squares. The model is compared to different series of experiments, where either crossflow or permeate flux is varied. This study is concluded with a parameter study on the scaling of the filtration time with various model parameters. We have found that the filtration time primarily depends on two dimensionless numbers, namely the normalized critical distance for cake layer formation, and the dimensionless time required to plug all pores in the selective layer. We have found that there is an optimal setting of these parameters, rendering a maximal amount of filtrated beer in one cycle.

Modeling concentration polarization in crossflow microfiltration of oil-in-water emulsion using shear-induced diffusion; CFD and experimental studies

Membrane filtration has become firmly established as a primary technology for ensuring treatment of oily wastewater. A detailed study on concentration polarization (CP) during microfiltration (MF) of oil-in-water emulsions was carried out in order to predict permeate flux decline. A two dimensional computational fluid dynamics (CFD) modeling was conducted using the finite difference method. A combination of molecular and shear-induced diffusion coefficient was employed to describe back-diffusion of oil droplets from the membrane wall toward the bulk. Evaluation of the proposed approach was carried out by comparing the results to the experimental data in which good agreement was observed almost in every operating condition. The effects of oil concentration, trans-membrane pressure (TMP), and cross-flow velocity (CFV) on the model precision were also studied. Finally, the growth rate of CP layer along the membrane length was predicted in different operating conditions, in which the obtained trend was found to be in agreement with the CP theory.

A Continuum Model for Platelet Transport in Flowing Blood Based on Direct Numerical Simulations of Cellular Blood Flow

Computational modeling of arterial thrombus formation based on patient-specific data holds promise as a non-invasive tool for preventive diagnosis of atherosclerotic lesions. Platelet transport to the surface of a growing thrombus may be a rate limiting step in rapid thrombus formation, so accurate modeling of platelet transport may be essential for computational modeling of arterial thrombus formation. The presence of red blood cells (RBCs) in blood greatly affects platelet transport. In flowing blood, RBCs migrate away from the walls and platelets marginate toward the walls. We investigate the mechanics of platelet margination by direct simulation of cellular blood flow. We show that platelet margination can be explained by RBC-enhanced shear-induced diffusion of platelets in the RBC-filled region combined with platelet trapping in the RBC-free region. A simple continuum model is introduced based on the proposed mechanism. Using an experimental correlation for effective diffusivity in blood, the continuum model can recover experimental results from the literature over a wide range of tube diameters.

Interfacial instabilities in sediment suspension flows

AbstractWe report the existence of interfacial instability in the two-dimensional channel flow of a sediment suspension whose particles diffuse in the carrier fluid due to shear-induced collisions. We derive partial differential equations that govern the deformations of the interface between the sediment suspension and the clear fluid, and devise a perturbation method that preserves the positivity of the particle volume fraction. We solve perturbed momentum, particle transport and deforming interface equations to show that a Kelvin–Helmholtz-type unstable wave develops at the interface for wavelengths longer than a critical value. Short-wavelength oscillations of the interface are damped due to shear-induced diffusion of particles. We also show that the lowest critical Reynolds number, above which the interface is unstable, occurs for intermediate values of the total volume fraction of particles.

A two-phase flow model of sediment transport: transition from bedload to suspended load

AbstractThe transport of dense particles by a turbulent flow depends on two dimensionless numbers. Depending on the ratio of the shear velocity of the flow to the settling velocity of the particles (or the Rouse number), sediment transport takes place in a thin layer localized at the surface of the sediment bed (bedload) or over the whole water depth (suspended load). Moreover, depending on the sedimentation Reynolds number, the bedload layer is embedded in the viscous sublayer or is larger. We propose here a two-phase flow model able to describe both viscous and turbulent shear flows. Particle migration is described as resulting from normal stresses, but is limited by turbulent mixing and shear-induced diffusion of particles. Using this framework, we theoretically investigate the transition between bedload and suspended load.

Critical flux of surface-patterned ultrafiltration membranes during cross-flow filtration of colloidal particles

Previous work has suggested that membrane patterning is a promising approach to fouling mitigation. In this systematic study, we describe performance metrics for the cross-flow filtration of colloidal suspensions through ultrafiltration membranes with lithographically patterned surfaces. The effects of particle size, cross-flow velocity, pattern size, and flow configuration on membrane performance are specifically considered. Using an unpatterned membrane as a reference, results show that the presence of surface patterns increases the critical flux associated with filtration of colloidal feed solutions. For the patterned membranes, the critical flux increases with particle size, cross-flow velocity, the angle between the feed flow and the pattern lines, and the pattern height. These experimental findings can be correlated with a back-transport mechanism such as shear-induced diffusion, which ultimately increases the threshold permeation flux associated with the onset of particle deposition.

Steady State Permeate Flux Estimation in Cross-Flow Ultrafiltration of Protein Solution

In the membrane separation process, the cross-flow configuration in which the fluid flows parallel to the membrane is widely utilized. Due to the shear stress exerted by the tangential feed flow, the accumulation of the retained species in the membrane is reduced, and the nearly steady state operation can be attained. The determination of steady state permeate flux is significant in the design and optimization problem. Several mechanisms of transport phenomena have been proposed to estimate the steady state permeate flux such as concentration polarization and Brownian diffusion, shear-induced diffusion, inertial lift, and surface transport. Another approach is using dimensional analysis to give the correlation equation with the operating condition instead of a deep focus on mechanism. In this study, we apply the model proposed in our previous study to predict the steady state permeate flux from the experimental data. After that, a new method using dimensional analysis is also developed to predict the steady state permeate flux from the operating conditions such as the trans-membrane pressure, the feed flow rate, and the feed volume fraction in a wide range. The correlation equation provides a good estimation of the experimental results.

Time-Dependent and Shear-Dependent Transient Viscosity of an Alumina Suspension

The transient viscosity of a well-dispersed Alumina–polyvinyl butyral tape-casting slurry have been investigated at the shear domain of 1–8 s−1 with the help of a conventional Couette device. The slurry under these shear rates shows a combination of shear dependence and time dependence based upon the applied shear. Attempts have been made to explain the diverse rheological behavior of the slurry. Many studies involving powder loading, milling time, extended shear up ramp, extended shear down ramp, time- and shear-dependent viscosities of the supernatant, and continual shearing have been conducted to explore the probable reasons behind such diverse behavior of the slurry. The findings of these studies strongly suggest that at the shear rates, shear-induced hydrodynamic diffusion plays a major role in dictating the time-dependent viscosity profile of the suspension. Further analysis of the results points out that the observed viscosity profiles are the resultant of the two major competitive processes of shear-induced hydrodynamic disffusion and shear rejuvenation. The results obtained in the present investigation also strongly indicate that the time-dependent behavior of the suspensions under shear opens up an alternative route of characterization of well-dispersed ceramics suspensions.

Shear-induced diffusion in dilute curved fiber suspensions in simple shear flow

Shear-induced self-diffusion of fibers suspended in an incompressible Newtonian fluid in simple shear flow at low Reynolds number is studied by simulation. Two models are employed: a linked rigid rod model and a bead chain model. Hydrodynamic interactions are neglected in both models. The shear-induced diffusivity of suspensions of fibers increases with increasing concentration and increasing static friction between contacts. The diffusivities in both the gradient and vorticity directions are larger for suspensions of curved fibers than for suspensions of straight fibers. For suspensions of curved fibers, significant enhancements in the diffusivity in the gradient direction are observed. The enhanced diffusivities are attributed to fiber drift observed in prior work for isolated curved fibers [J. Wang, E. J. Tozzi, M. D. Graham, and D. J. Klingenberg, “Flipping, scooping, and spinning: Drift of rigid curved nonchiral fibers in simple shear flow,” Phys. Fluids 24, 123304 (2012)]. Here, for some initial orientations, curved fibers will drift in the positive or negative gradient direction with nearly constant speed. In dilute suspensions, this drift occurs for a fraction of the fibers, which increases the mean-squared displacement in the gradient direction, and thus increases the diffusivity in the gradient direction.

Generalized criterion for the onset of particle deposition in crossflow microfiltration via DOTM – Modeling and experimental validation

The concept of a critical permeation flux for the onset of particle deposition in crossflow microfiltration (CFMF) is well-established. However, the critical flux is known to be a function of process parameters such as the particle size, bulk concentration and crossflow velocity. In the present study, the critical modified Peclet number (Pecrit) is explored instead as a generalized criterion for the onset of particle deposition that incorporates the effects of these process parameters as well as the axial position along the membrane. A proper determination of Pecrit requires an accurate prediction of the concentration polarization boundary layer thickness δc and shear-induced diffusion coefficient Ds. The classical Lévêque model is adapted to allow for the effect of the permeation flux on the velocity profile. Moreover, the assumptions of a constant concentration at the membrane surface cw and constant Ds that have been made in prior studies are relaxed in an improved numerical solution to the convective diffusion equation that is used to predict δc and Ds. The critical permeation flux is determined from particle deposition data taken for 6 and 10μm latex spheres via Direct Observation Through the Membrane (DOTM) characterization. A constant value of Pecrit=4.00±0.08 is found to characterize the effects of particle diameter, bulk concentration and crossflow velocity as well as axial position on the onset of particle deposition.

Pairwise hydrodynamic interactions and diffusion in a vesicle suspension

The hydrodynamic interaction of two deformable vesicles in shear flow induces a net displacement, in most cases an increase of their distance in the transverse direction. The statistical average of these interactions leads to shear-induced diffusion in the suspension, both at the level of individual particles which experience a random walk made of successive interactions, and at the level of suspension where a nonlinear down-gradient diffusion takes place, an important ingredient in the structuring of suspension flows. We make an experimental and computational study of the interaction of a pair of lipid vesicles in shear flow by varying physical parameters, and investigate the decay of the net lateral displacement with the distance between the streamlines on which the vesicles are initially located. This decay and its dependency upon vesicle properties can be accounted for by a simple model based on the well established law for the lateral drift of a vesicle in the vicinity of a wall. In the semi-dilute regime, a determination of self-diffusion coefficients is presented.

Far-from-equilibrium sheared colloidal liquids: Disentangling relaxation, advection, and shear-induced diffusion

Using high-speed confocal microscopy, we measure the particle positions in a colloidal suspension under large-amplitude oscillatory shear. Using the particle positions, we quantify the in situ anisotropy of the pair-correlation function, a measure of the Brownian stress. From these data we find two distinct types of responses as the system crosses over from equilibrium to far-from-equilibrium states. The first is a nonlinear amplitude saturation that arises from shear-induced advection, while the second is a linear frequency saturation due to competition between suspension relaxation and shear rate. In spite of their different underlying mechanisms, we show that all the data can be scaled onto a master curve that spans the equilibrium and far-from-equilibrium regimes, linking small-amplitude oscillatory to continuous shear. This observation illustrates a colloidal analog of the Cox-Merz rule and its microscopic underpinning. Brownian dynamics simulations show that interparticle interactions are sufficient for generating both experimentally observed saturations.

Short-term and long-term irreversibility in particle suspensions undergoing small and large amplitude oscillatory stress

The short-term and long-term irreversible behaviors of suspensions of rigid particles in oscillatory shear flow are studied by measuring the evolution of complex viscosity in time and applying of nonlinear analysis of the responded strain signal under the controlled-stress mode, and complemented by optical measurements on the particle motion. The short-term transition time for the system to reach a quasisteady state is an approximately bell-shaped function of the amplitude of the strain response, thus showing a critical strain amplitude accounting for the peak transition time. The short-term behavior is caused by the particle self-organization due to collisions between particles. At longer time scales, the complex viscosity of the suspension increases when probed by forces that elicit small strain amplitudes and decreases when stresses that result in large strain amplitudes are applied. It is proposed that the long-term behavior for stresses eliciting small strain amplitude is induced by the shear-induced diffusion of particles which self-organize into a crystal-like microstructure that can be easily annulled in oscillatory flow with large strain amplitude, while for stresses causing large strain amplitude the dominant microstructure is formed immediately via the oscillation.

Local mobility and microstructure in periodically sheared soft particle glasses and their connection to macroscopic rheology

Oscillatory shear is a widely used characterization technique for complex fluids but the microstructural changes that produce the material response are not well understood. We apply a recent micromechanical model to soft particle glasses subjected to oscillatory flow. We use particle scale simulations at small, intermediate and large strain amplitudes to determine their microstructure, particle scale mobility, and macroscopic rheology. The macroscopic properties computed from simulations quantitatively agree with experimental measurements on well-characterized microgel suspensions, which validate the model. At the mesoscopic scale, the evolution of the particle pair distribution during a cycle reveals the physical mechanisms responsible for yielding and flow and also leads to quantitative prediction of shear stress. At the local scale, the particles remain trapped inside their surrounding cage below the yield strain and yielding is associated with the onset of large scale rearrangements and shear-induced diffusion. This multiscale analysis thus highlights the distinct microscopic events that make these glasses exhibit a combination of solid-like and liquid-like behavior.

Heat transfer across sheared suspensions: role of the shear-induced diffusion

AbstractSuspensions of non-Brownian spherical particles undergoing shear provide a unique system where mixing occurs spontaneously at low Reynolds numbers. Through a combination of experiments and simulations, we investigate the effect of shear-induced particle diffusion on the transfer of heat across suspensions. The influence of particle size, particle volume fraction and applied shear are examined. By applying a heat pulse to the inner copper wall of a Couette cell and analysing its transient temperature decay, the effective thermal diffusivity of the suspension, $\alpha $, is obtained. Using index matching and laser-induced fluorescence imaging, we measured individual particle trajectories and calculated their diffusion coefficients. Simulations that combined a lattice Boltzmann technique to solve for the flow and a passive Brownian tracer algorithm to solve for the transfer of heat are in very good agreement with experiments. Fluctuations induced by the presence of particles within the fluid cause a significant enhancement (${\gt }200\hspace{0.167em} \% $) of the suspension transport properties. The effective thermal diffusivity was found to be linear with respect to both the Péclet number ($\mathit{Pe}= \dot {\gamma } {d}^{2} / {\alpha }_{0} \leq 100$) and the solid volume fraction ($\phi \leq 40\hspace{0.167em} \% $), leading to a simple correlation $\alpha / {\alpha }_{0} = 1+ \beta \phi \mathit{Pe}$ where $\beta = 0. 046$ and ${\alpha }_{0} $ is the thermal diffusivity of the suspension at rest. In our Couette cell, the enhancement was found to be optimum for a volume fraction, $\phi \approx 40\hspace{0.167em} \% $, above which, due to steric effects, both the particle diffusion motion and of the effective thermal diffusion dramatically decrease. No such correlation was found between the average particle rotation and the thermal diffusivity of the suspension, suggesting that the driving mechanism for enhanced transport is the translational particle diffusivity. Movies are available with the online version of the paper.

Shear-induced diffusion of red blood cells in a semi-dilute suspension

AbstractThe diffusion of red blood cells (RBCs) in blood is important to the physiology and pathology of the cardiovascular system. In this study, we investigate flow-induced diffusion of RBCs in a semi-dilute system by calculating the pairwise interactions between RBCs in simple shear flow. A capsule with a hyperelastic membrane was used to model an RBC. Its deformation was resolved using the finite element method, whereas fluid motion inside and outside the RBC was solved using the boundary element method. The results show that shear-induced RBC diffusion is significantly anisotropic, i.e. the velocity gradient direction component is larger than the vorticity direction. We also found that the motion of RBCs during the interaction is strongly dependent on the viscosity ratio of the internal to external fluid, and the diffusivity decreases monotonically as the viscosity ratio increases. The scaling argument also suggests that the diffusivity is proportional to the shear rate and haematocrit, if the suspension is in a semi-dilute environment and the capillary number is invariant. These fundamental findings are useful to understand transport phenomena in blood flow.

The dam-break problem for concentrated suspensions of neutrally buoyant particles

AbstractThis paper addresses the dam-break problem for particle suspensions, that is, the flow of a finite volume of suspension released suddenly down an inclined flume. We were concerned with concentrated suspensions made up of neutrally buoyant non-colloidal particles within a Newtonian fluid. Experiments were conducted over wide ranges of slope, concentration and mass. The major contributions of our experimental study are the simultaneous measurement of local flow properties far from the sidewalls (velocity profile and, with lower accuracy, particle concentration) and macroscopic features (front position, flow depth profile). To that end, the refractive index of the fluid was adapted to closely match that of the particles, enabling data acquisition up to particle volume fractions of 60 %. Particle migration resulted in the blunting of the velocity profile, in contrast to the parabolic profile observed in homogeneous Newtonian fluids. The experimental results were compared with predictions from lubrication theory and particle migration theory. For solids fractions as large as 45 %, the flow behaviour did not differ much from that of a homogeneous Newtonian fluid. More specifically, we observed that the velocity profiles were closely approximated by a parabolic form and there was little evidence of particle migration throughout the depth. For particle concentrations in the 52–56 % range, the flow depth and front position were fairly well predicted by lubrication theory, but taking a closer look at the velocity profiles revealed that particle migration had noticeable effects on the shape of the velocity profile (blunting), but had little impact on its strength, which explained why lubrication theory performed well. Particle migration theories (such as the shear-induced diffusion model) successfully captured the slow evolution of the velocity profiles. For particle concentrations in excess of 56 %, the macroscopic flow features were grossly predicted by lubrication theory (to within 20 % for the flow depth, 50 % for the front position). The flows seemed to reach a steady state, i.e. the shape of the velocity profile showed little time dependence.

Complex Oscillatory Yielding of Model Hard-Sphere Glasses

The yielding behavior of hard sphere glasses under large-amplitude oscillatory shear has been studied by probing the interplay of Brownian motion and shear-induced diffusion at varying oscillation frequencies. Stress, structure and dynamics are followed by experimental rheology and Browian dynamics simulations. Brownian-motion-assisted cage escape dominates at low frequencies while escape through shear-induced collisions at high ones, both related with a yielding peak in G''. At intermediate frequencies a novel, for hard sphere glasses, double peak in G'' is revealed reflecting both mechanisms. At high frequencies and strain amplitudes a persistent structural anisotropy causes a stress drop within the cycle after strain reversal, while higher stress harmonics are minimized at certain strain amplitudes indicating an apparent harmonic response.