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Journal ArticleDOI

The shear-induced migration of particles in concentrated suspensions

01 Sep 1987-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 181, Iss: -1, pp 415-439
TL;DR: In this article, it was shown that shear-induced migration of particles out of the sheared Couette gap and into the fluid reservoir, which reduces the particle concentration in the gap and thereby the observed viscosity, is consistent with a gap-limited shearinduced diffusion process normal to the plane of shear, with the relevant diffusion coefficient being proportional to the applied shear rate.
Abstract: In the course of viscometric measurements of concentrated suspensions of spheres in Newtonian fluids using a Couette device, Gadala-Maria & Acrivos (1980) observed a decrease in the suspension viscosity after long periods of shearing even though the viscosity of the pure suspending fluid remained constant under identical conditions. In the present work we demonstrate that this phenomenon is due to the shear-induced migration of particles out of the sheared Couette gap and into the fluid reservoir, which reduces the particle concentration in the gap and thereby the observed viscosity. We show further that this rate of viscosity decrease is consistent with a gap-limited shear-induced diffusion process normal to the plane of shear, with the relevant diffusion coefficient being proportional to is the applied shear rate.Additional experiments also uncovered a new phenomenon - a short-term increase in the viscosity upon initial shearing of a suspension in a Couette device - which was attributed to the diffusive migration of particles across the width of the Couette gap and thus was used to infer values of the corresponding diffusion coefficient within the plane of shear parallel to gradients in fluid velocity.In the theoretical part we demonstrate that the particle migrations that led to these observed phenomena may be explained in terms of the irreversible interparticle interactions that occur in these suspensions. From simple arguments, these interactions are shown to lead to effective diffusivities both normal to the plane of shear and normal to the direction of fluid motion within the plane of shear whose estimated magnitudes are comparable with those that were inferred from the experimental measurements. Furthermore, these interactions should induce, within a shear flow, particle drifts from regions of high to low shear stress, which are estimated to be of sufficient intensity to account for the observed initial viscosity increase mentioned above.
Citations
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Journal ArticleDOI
TL;DR: In this article, a review of microfiltration is presented, focusing on the formation of cakes, the behavior of suspension flows and particle transport in simple geometry ducts, and the formation and behavior of fouling layers including those resulting from macromolecules, colloids and particles.

1,317 citations

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TL;DR: A selective overview of the fast-developing field of MIPS, focusing on theory and effects, is given, which generally breaks down at higher order in gradients.
Abstract: Self-propelled particles include both self-phoretic synthetic colloids and various microorganisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: The steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density for either biochemical or steric reasons. This creates positive feedback, which can lead to motility-induced phase separation (MIPS) between dense and dilute fluid phases. At leading order in gradients, a mapping relates variable-speed, self-propelled particles to passive particles with attractions. This deep link to equilibrium phase separation is confirmed by simulations but generally breaks down at higher order in gradients: New effects, with no equilibrium counterpart, then emerge. We give a selective overview of the fast-developing field of MIPS, focusing on theory and...

1,228 citations

Journal ArticleDOI
TL;DR: In this article, the use of acoustic fields, principally ultrasonics, for application in microfluidics is reviewed, and the abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques.
Abstract: This article reviews acoustic microfiuidics: the use of acoustic fields, principally ultrasonics, for application in microfiuidics. Although acoustics is a classical field, its promising, and indeed perplexing, capabilities in powerfully manipulating both fluids and particles within those fluids on the microscale to nanoscale has revived interest in it. The bewildering state of the literature and ample jargon from decades of research is reorganized and presented in the context of models derived from first principles. This hopefully will make the area accessible for researchers with experience in materials science, fluid mechanics, or dynamics. The abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques common in microfluidics, along with the many applications in microfluidics and nanofluidics that appear through the literature.

975 citations

Journal ArticleDOI
TL;DR: In this article, a constitutive equation for computing particle concentration and velocity fields in concentrated monomodal suspensions is proposed that consists of two parts: a Newtonian constitutive equations in which the viscosity depends on the local particle volume fraction and a diffusion equation that accounts for shear-induced particle migration.
Abstract: A constitutive equation for computing particle concentration and velocity fields in concentrated monomodal suspensions is proposed that consists of two parts: a Newtonian constitutive equation in which the viscosity depends on the local particle volume fraction and a diffusion equation that accounts for shear‐induced particle migration. Particle flux expressions used to obtain the diffusion equation are derived by simple scaling arguments. Predictions are made for the particle volume fraction and velocity fields for steady Couette and Poiseuille flow, and for transient start‐up of steady shear flow in a Couette apparatus. Particle concentrations for a monomodal suspension of polymethyl methacrylate spheres in a Newtonian solvent are measured by nuclear magnetic resonance (NMR) imaging in the Couette geometry for two particle sizes and volume fractions. The predictions agree remarkably well with the measurements for both transient and steady‐state experiments as well as for different particle sizes.

886 citations

Journal ArticleDOI
TL;DR: Slip occurs in the flow of two-phase systems because of the displacement of the disperse phase away from solid boundaries as mentioned in this paper, which arises from steric, hydrodynamic, viscoelastic and chemical forces and constraints acting on the dispersed phase immediately adjacent to the walls.
Abstract: Slip occurs in the flow of two-phase systems because of the displacement of the disperse phase away from solid boundaries. This arises from steric, hydrodynamic, viscoelastic and chemical forces and constraints acting on the disperse phase immediately adjacent to the walls. The enrichment of the boundary near the wall with the continuous (and usually low-viscosity) phase means that any flow of the fluid over the boundary is easier because of the lubrication effect. Because this effect is usually confined to a very narrow layer — with typical thickness of 0.1–10 μm—it so resembles the slip of solids over surfaces that it has historically been given the same terminology. The restoring force for all the forces that cause an increase in concentration is usually osmotic, and this will always limit the effective slip. In dilute systems, concentration gradients can be present over relatively large distances out from walls, giving what might be interpreted on an overall basis as a thick solvent-only layer. However, as the concentration of the system increases, the layer gets thinner and thinner because it is more difficult to create with the large reverse osmotic force present. However, the enormous increase in the bulk viscosity with increase in concentration means that although thinner, the layer becomes, paradoxically, even more important. Slip manifests itself in such a way that viscosity measured in different size geometries gives different answers if calculated the normal way — in particular the apparent viscosity decreases with decrease in geometry size (e.g. tube radius). Also, in single flow curves unexpected lower Newtonian plateaus are sometimes seen, with an apparent yield stress at even lower stresses. Sudden breaks in the flow curve can also be seen. Large particles as the disperse phase (remember flocs are large particles), with a large dependence of viscosity on the concentration of the dispersed phase are the circumstances which can give slip, especially if coupled with smooth walls and small flow dimensions. The effect is usually greatest at low speeds/flow rates. When the viscometer walls and particles carry like electrostatic charges and the continuous phase is electrically conducted, slip can be assumed. In many cases we need to characterise the slip effects seen in viscometers because they will also be seen in flow in smooth pipes and condults in manufacturing plants. This is usually done by relating the wall shear stress to a slip velocity using a power-law relationship. When the bulk flow has also been characterized, the flow in real situations can be calculated. To characterise slip, it is necessary to change the size of the geometry, and the results extrapolated to very large size to extract unambigouos bulk-flow and slip data respectively. A number of mathematical manipulations are necessary to retrieve these data. We can make attempts to eliminate slip by altering the physical or chemical character of the walls. This is usually done physically by roughening or profiling, but in the extreme, a vane can be used. This latter geometry has the advantage of being easy to make and clean. In either case—by extrapolation or elimination—we end up with the bulk flow properties. This is important in situations where we are trying to understand the microstructure/flow interactions.

818 citations

References
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Journal ArticleDOI
TL;DR: In this article, the Segre-Silberberg effect of inertia-induced lateral migration of a neutrally buoyant rigid sphere in a Newtonian fluid is studied theoretically for simple shear flow and for two-dimensional Poiseuille flow.
Abstract: The familiar Segre-Silberberg effect of inertia-induced lateral migration of a neutrally buoyant rigid sphere in a Newtonian fluid is studied theoretically for simple shear flow and for two-dimensional Poiseuille flow. It is shown that the spheres reach a stable lateral equilibrium position independent of the initial position of release. For simple shear flow, this position is midway between the walls, whereas for Poiseuille flow, it is 0·6 of the channel half-width from the centre-line. Particle trajectories are calculated in both cases and compared with available experimental data. Implications for the measurement of the rheological properties of a dilute suspension of spheres are discussed.

790 citations

Journal ArticleDOI
TL;DR: In this article, a Couette device of a R•17 Weissenberg Rheogoniometer with suspensions of polystyrene spheres, 40-50 μm in diameter, suspended in a mixture of silicone oils at volume fractions 0⩽φ0.55 was used for steady and transient shear measurements.
Abstract: Two novel phenomena were observed in steady and transient shear measurements which were made in a Couette device of a R‐17 Weissenberg Rheogoniometer with suspensions of polystyrene spheres, 40–50 μm in diameter, suspended in a mixture of silicone oils at volume fractions 0⩽φ0.55. When φ⩾0.3, the steady‐shear viscosity at a given shear rate was found to drift for many hours to an asymptotic value which, in contrast to the scatter of the initial measurements, was very reproducible. Again, when φ⩾0.3, the shear stress showed a memory for the direction of previous shearing when the shear was stopped for a while and then restarted with either the same or the opposite sign. Moreover, during oscillatory shear experiments, these suspensions exhibited a nonlinear response which in fact could be predicted from their response to a sudden reversal of the direction of steady shear. It would appear, therefore, that such concentrated two‐phase systems cannot be modeled as isotropic fluids having a scalar effective viscosity unless the solids concentration is low.

503 citations

Journal ArticleDOI
TL;DR: In this paper, a technique for determining the coefficient of shear-induced particle self-diffusion in concentrated suspensions of solid spheres, which relies on the fact that this coefficient can be computed from the measured variations in the time taken by a single marked particle in the suspension to complete successive circuits in a Couette device, was presented.
Abstract: A novel technique is presented for determining the coefficient of shear-induced particle self-diffusion in concentrated suspensions of solid spheres, which relies on the fact that this coefficient can be computed from the measured variations in the time taken by a single marked particle in the suspension to complete successive circuits in a Couette device. Since this method does not involve the direct measurement of the lateral position of the marked particle, it requires a much simpler experiment than that used by Eckstein, Bailey & Shapiro (1977) which is shown to be constrained by wall effects at high particle concentration. The diffusion coefficient thus determined was found to be proportional to the product γa2, where γ is the shear rate and a the particle radius, and to have the asymptotic form 0.5γa2ϕ2 in the dilute limit when the particle concentration ϕ → 0.

446 citations

Journal ArticleDOI
TL;DR: In this paper, a self-diffusion coefficient for lateral dispersion of spherical and disk-like particles in linear shear flow of a slurry at very low Reynolds number was determined experimentally.
Abstract: Self-diffusion coefficients were determined experimentally for lateral dispersion of spherical and disk-like particles in linear shear flow of a slurry at very low Reynolds number. Using a concentric-cylinder Couette apparatus, recurrent observations were made of the lateral position of a particular radioactively labelled particle. The self-diffusion coefficient D was calculated by means of random-walk theory, using the ergodic hypothesis. Owing to great experimental difficulties, the calculated values of D are not of high accuracy, but are correct to within a factor of two. In the range 0 < ϕ < 0·2, D/a2ω increases from zero linearly with ϕ up to D/a2ω ≅ 0·02 (where ϕ = volumetric concentration of particles, a = particle radius, ω = mean shear rate of suspending fluid). In the range 0·2 < 0·5, the trend of D/a2ω is not clear because of experimental scatter, but in this range D/a2ω ≅ 0·025 to within a factor of two. Within the experimental accuracy, spheres and disks have the same value of D/a2ω.

427 citations

Journal ArticleDOI
01 Apr 1967
TL;DR: In this article, the velocity profiles of dilute suspensions of rigid spheres in Newtonian liquids undergoing Couette or Poiseuille flow were found to be identical with those predicted by the theory with no particles present.
Abstract: In the viscous flow regime the velocity profiles of dilute suspensions of rigid spheres in Newtonian liquids undergoing Couette or Poiseuille flow were found to be identical with those predicted by the theory with no particles present. At concentrations low enough so that the formation of triplets and higher order multiplets could be neglected, a given sphere exhibited fluctuations about a fixed mean radial position. The measured distribution of lateral displacements agreed with a theory based on rectilinear approach and recession of colliding pairs, whereas the time average radial displacements were twice the predicted values. On increasing the concentration partial plug flow developed in the tube with a central core in which the particles traveled with identical velocities without rotating and at fixed radial positions. Outside this central core the particles described irregular paths which, however, were reversible with respect to translation and rotation when the direction of flow was reversed. The concentration profiles were found to be uniform over prolonged periods of flow, and the suspensions showed Newtonian behavior. The phenomena, many of which were similar in suspensions of rods and discs, were shown to result from a wall effect predicted by Vand and were not manifestations of non-Newtonian behavior.

336 citations