Stokesian Dynamics

Particles suspended or dispersed in a fluid medium occur in a wide variety of natural and man-made settings, e.g. slurries, composite materials, ceramics, colloids, polymers, proteins, etc. The central theoretical and practical problem is to understand and predict the macroscopic equilibrium and transport properties of these multiphase materials from their microstructural mechanics. The macroscopic properties might be the sedimentation or aggregation rate, self-diffusion coefficient, thermal conductivity, or rheology of a suspension of particles. The microstructural mechanics entails the Brownian, interparticle, external, and hydrodynamic forces acting on the particles, as well as their spatial and temporal distribution, which is commonly referred to as the microstructure. If the distribution of particles were given, as well as the location and motion of any boundaries and the physical properties of the particles and suspending fluid, one would simply have to solve (in principle, not necessarily in practice) a well-posed boundary-value problem to determine the behavior of the material. Averaging this solution over a large volume or over many different configurations, the macroscopic or averaged properties could be determined. The two key steps in this approach, the solution of the many-body problem and the determination of the microstructure, are formidable but essential tasks for understanding suspension behavior. This article discusses a new, molecular-dynamics-like approach, which we have named Stokesian dynamics, for dynamically simulating the behavior of many particles suspended or dispersed in a fluid medium. Particles in suspension may interact through both hydrodynamic and nonhydrodynamic forces, where the latter may be any type of Brownian, colloidal, interparticle, or external force. The simulation method is capable of predicting both static (i.e. configuration-specific) and dynamic microstructural properties, as well as macroscopic properties in either dilute or concentrated systems. Applications of Stokesian dynamics are widespread; problems of sedimentation, flocculation, diffusion, polymer rheology, and transport in porous media all fall within its domain. Stokesian dynamics is designed to provide the same theoretical and computational basis for multiphase, dispersed systems as does molecular dynamics for statistical theories of matter. This review focuses on the simulation method, not on the areas in which Stokesian dynamics can be used. For a discussion of some of these many different areas, the reader is referred to the excellent reviews and proceedings of topical conferences that have appeared (e.g. Batchelor 1976a, Dickinson 1983, Faraday Discussions 1983, 1987, Family & Landau 1984). Before embarking on a description of Stokesian dynamics, we pause here to discuss some of the relevant theoretical literature on suspensions, and dynamic simulation in general, in order to put Stokesian dynamics in perspective

Translational and rotational temperatures of a 2D vibrated granular gas in microgravity

We present an experimental study performed on a vibrated granular gas enclosed into a 2D rectangular cell. Experiments are realized in microgravity. High speed video recording and optical tracking allow to obtain the full kinematics (translation and rotation) of the particles. The inelastic parameters are retrieved from the experimental trajectories as well as the translational and rotational velocity distributions. We report that the experimental ratio of translational versus rotational temperature decreases to the density of the medium but increases with the driving velocity of the cell. These experimental results are compared with existing theories and we point out the differences observed. We also present a model which fairly predicts the equilibrium experimental temperatures along the direction of vibration.Comment: 14 pages, 11 figures, submitte

Stokesian Dynamics simulation of Brownian suspensions

The non-equilibrium behaviour of concentrated colloidal dispersions is studied by Stokesian Dynamics, a general molecular-dynamics-like technique for simulating particles suspended in a viscous fluid. The simulations are of a suspension of monodisperse Brownian hard spheres in simple shear flow as a function of the Péclet number, Pe, which measures the relative importance of shear and Brownian forces. Three clearly defined regions of behaviour are revealed. There is first a Brownian-motion-dominated regime (Pe ≤ 1) where departures from equilibrium in structure and diffusion are small, but the suspension viscosity shear thins dramatically. When the Brownian and hydrodynamic forces balance (Pe ≈ 10), the dispersion forms a new ‘phase’ with the particles aligned in ‘strings’ along the flow direction and the strings are arranged hexagonally. This flow-induced ordering persists over a range of Pe and, while the structure and diffusivity now vary considerably, the rheology remains unchanged. Finally, there is a hydrodynamically dominated regime (Pe > 200) with a dramatic change in the long-time self-diffusivity and the rheology. Here, as the Péclet number increases the suspension shear thickens owing to the formation of large clusters. The simulation results are shown to agree well with experiment

Résistivité des élastomères magnétorhéologiques

International audienceDes composites souples sont formés en mélangeant des particules micrométriques de nickel dans une résine réticulable à base de silicone. Le seuil de percolation dépend du traitement thermique et de la structuration de l'échantillon au cours de la réticulation. Nous présenterons les résultats relatifs à la variation de la résistance électrique de ces composites en fonction de la pression appliquée et de la température. Ces résultats seront confrontés au modèle amélioré de résistance de contact

Dynamic simulation of sheared suspensions. I. General method

A general method is presented for simulating the dynamical behavior of a suspension of particles which interact through both hydrodynamic and nonhydrodynamic forces. In the molecular-dynamics-like simulation there are two different procedures for computing the interactions among particles: a pairwise additivity of forces and a pairwise additivity of velocities. The pairwise additivity of forces is the preferred method as it preserves the hydrodynamic lubrication forces which prevent particles from overlapping. The two methods are compared in a simulation of a monolayer of identical rigid non-Brownian spherical particles in a simple shear flow. Periodic boundary conditions are used to model an infinite suspension. Both methods predict the presence of a shear induced anisotropic local structure whose form and strength depend on the concentration of particles, the nonhydrodynamic forces, and the shear rate. Increasing the particle concentration up to near the maximum fraction that can still flow results in a transition to a layered structure in which planes of particles slide relative to one another. The anisotropic local structure and transition to a layered structure predict a non-Newtonian suspension rheology

Dynamic simulation of hydrodynamically interacting suspensions

A general method for computing the hydrodynamic interactions among an infinite suspension of particles, under the condition of vanishingly small particle Reynolds number, is presented. The method follows the procedure developed by O'Brien (1979) for constructing absolutely convergent expressions for particle interactions. For use in dynamic simulation, the convergence of these expressions is accelerated by application of the Ewald summation technique. The resulting hydrodynamic mobility and/or resistance matrices correctly include all far-field non-convergent interactions. Near-field lubrication interactions are incorporated into the resistance matrix using the technique developed by Durlofsky, Brady & Bossis (1987). The method is rigorous, accurate and computationally efficient, and forms the basis of the Stokesian-dynamics simulation method. The method is completely general and allows such diverse suspension problems as self-diffusion, sedimentation, rheology and flow in porous media to be treated within the same formulation for any microstructural arrangement of particles. The accuracy of the Stokesian-dynamics method is illustrated by comparing with the known exact results for spatially periodic suspensions

Discontinuous Shear Thickening (DST) transition with spherical iron particles coated by adsorbed brush polymer

In this work we explore the rheology of very concentrated (0.55<$\Phi$<0.67) suspensions of carbonyl iron (CI) particles coated by a small polymer. A strong DST is observed in a large range of volume fraction presenting some specificities relatively to other systems. In particular, in a given range of volume fraction, the DST transition appears suddenly without being preceded by shear thickening. The presence of a frictional network of particles is confirmed by a simultaneous measurement of the electric resistance of the suspension and of the rheological curve. Using the Wyart-Cates model we show that, increasing the volume fraction, the fraction of frictional contacts grows more and more quickly with the stress that disagrees with the prediction of computer simulations. The same kind of behavior is observed in the presence of a magnetic field with, in addition, a very strong increase of the viscosity with the magnetic field before the transition. We interpret this behavior by the interpenetration of the polymer layer under the effect of the shear stress-and of the magnetic stress-followed by the expulsion of the polymer out of the surfaces. Besides we point that, above the DST transition, we do not observe a jamming in the range of volume fraction whereas it is predicted by the W-C model. Based on the fact that in the absence of shear flow, the polymer should come back to the surface and destroy the frictional contacts we can predict an asymptotic non-zero shear rate and reproduce the experimental behavior

Outstanding magnetorheological effect based on discontinuous shear thickening in the presence of a superplastifier molecule

International audienceWe present experimental results showing an increase of stress of about 150kPa for a weak applied magnetic field (H<10kA/m) in an aqueous suspension of carbony iron particles coated with a superplasticizer molecule used in cement industry. These values, which are several orders of magnitude larger than those classically obtained with magnetorheological suspensions at such low field, can open the way to new applications. These high values result from the triggering of a discontinuous shear thickening induced by the magnetic field. A phase diagram is presented for a volume fraction of carbonyl iron particles of 62%, showing two domains in the plane, magnetic field versus shear rate. The lower one is liquid of quite low viscosity and the upper one corresponds to a jammed phase where the particles are in frictionnal contacts and can only move under very high stresses. The transition between the two states is monitored by the ability of the superplasticizer molecule to resist to the compression forces both hydrodynamic and magnetic

KINETICS AGGREGATION OF MAGNETIC SUSPENSIONS

International audienceWe present results of theoretical and computer study of the kinetics of chain-like aggregate formation in suspensions of non-Brownian magnetizable particles. An analytical model for calculation of the time-dependent function of distribution over chain size is suggested. This model describes the evolution of the chain structure due to the chain-chain aggregation. In order to verify this model we have compared it with the results of computer simulations of two-dimensional model of this suspension. Results of computer simulations and of the analytical model are in reasonable agreement up to 5% of the surface concentration of the particles

Abrupt contraction flow of magnetorheological fluids

International audienceContraction and expansion flows of magnetorheological fluids occur in a variety of smart devices. It is important therefore to learn how these flows can be controlled by means of applied magnetic fields. This paper presents a first investigation into the axisymmetric flow of a magnetorheological fluid through an orifice so-called abrupt contraction flow. The effect of an external magnetic field, longitudinal or transverse to the flow, is examined. In experiments, the pressure-flow rate curves were measured, and the excess pressure drop associated with entrance and exit losses was derived from experimental data through the Bagley correction procedure. The effect of the longitudinal magnetic field is manifested through a significant increase in the slope of the pressure-flow rate curves, while no discernible yield stress occurs. This behavior, observed at shear Mason numbers 10Mnshear100, is interpreted in terms of an enhanced extensional response of magnetorheological fluids accompanied by shrinkage of the entrance flow into a conical funnel. At the same range of Mason numbers, the transverse magnetic field appears not to influence the pressure drop. This can be explained by a total destruction of magnetic particle aggregates by large hydrodynamic forces acting on them when they are perpendicular to the flow. To support these findings, we have developed a theoretical model connecting the microstructure of the magnetorheological fluid to its extensional rheological properties and predicting the pressure-flow rate relations through the solution of the flow equations. In the case of the longitudinal magnetic field, our model describes the experimental results reasonably well