Georges Bossis

Dynamic simulation of hydrodynamically interacting particles

A general method for computing the hydrodynamic interactions among N suspended particles, under the condition of vanishingly small particle Reynolds number, is presented. The method accounts for both near-field lubrication effects and the dominant many-body interactions. The many-body hydrodynamic interactions reproduce the screening characteristic of porous media and the ‘effective viscosity’ of free suspensions. The method is accurate and computationally efficient, permitting the dynamic simulation of arbitrarily configured many-particle systems. The hydrodynamic interactions calculated are shown to agree well with available exact calculations for small numbers of particles and to reproduce slender-body theory for linear chains of particles. The method can be used to determine static (i.e. configuration specific) and dynamic properties of suspended particles that interact through both hydrodynamic and non-hydrodynamic forces, where the latter may be any type of Brownian. colloidal, interparticle or external force. The method is also readily extended to dynamically simulate both unbounded and bounded suspensions.

The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation

The newly developed simulation method known as Stokesian dynamics is used to investigate the rheological behaviour of concentrated suspensions. Both the detailed microstructure (e.g. pair-distribution function) and the macroscopic properties are determined for a suspension of identical rigid spherical particles in a simple shear flow. The suspended particles interact through both hydrodynamic and non-hydrodynamic forces. For suspensions with purely hydrodynamic forces, the increase in the suspension viscosity with volume fraction ϕ is shown to be caused by particle clustering. The cluster formation results from the lubrication forces, and the simulations of a monolayer of spheres show a scaling law for the cluster size: l c ∼ [1 − (ϕ/ϕ m ) ½ ] −1 , where ϕ m is the maximum volume fraction that can shear homogeneously. The simulation results suggest that the suspension viscosity becomes infinite at the percolation-like threshold ϕ m owing to the formation of an infinite cluster. The predicted simulation viscosities are in very good agreement with experiment. A suspension with short-range repulsive interparticle forces is also studied, and is seen to have a non-Newtonian rheology. Normal-stress differences arise owing to the anisotropic local structure created by the interparticle forces. The repulsive forces also reduce particle clustering, and as a result the suspension is shear-thickening.

The rheology of Brownian suspensions

The viscosity of a suspension of spherical Brownian particles is determined by Stokesian dynamics as a function of the Peclet number. Several new aspects concerning the theoretical derivation of the direct contribution of the Brownian motion to the bulk stress are given, along with the results obtained from a simulation of a monolayer. The simulations reproduce the experimental behavior generally observed in dense suspensions, and an explanation of this behavior is given by observing the evolution of the different contributions to the viscosity with shear rate. The shear thinning at low Peclet numbers is due to the disappearance of the direct Brownian contribution to the viscosity; the deformation of the equilibrium microstructure is, however, small. By contrast, at very high Peclet numbers the suspension shear thickens due to the formation of large clusters.

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.

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 Peclet 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 Peclet number increases the suspension shear thickens owing to the formation of large clusters. The simulation results are shown to agree well with experiment.

Hydrodynamic transport properties of hard-sphere dispersions. I: Suspensions of freely mobile particles

The hydrodynamic transport properties of hard-sphere dispersions are calculated for volume fractions (φ) spanning the dilute limit up to the fluid–solid transition at φ=0.49. Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics simulation. The effects of changing the number of particles in the simulation cell are investigated, and the scaling laws for the finite-size effects are derived. The effects of using various levels of approximation in computing both the far- and near-field hydrodynamic interactions are also examined. The transport properties associated with freely mobile suspensions—sedimentation velocities, self-diffusion coefficients, and effective viscosities—are determined here, while the corresponding properties of porous media are determined in a companion paper [Phys. Fluids 31, 3473 (1988)]. Comparison of the simulation results is made with both experiment and theory. In particular, the short-time self-diffusion coefficients and the suspension viscosities are in excellent agreement with experiment.

Self-diffusion of Brownian particles in concentrated suspensions under shear

The self-diffusivity of Brownian hard spheres in a simple shear flow is studied by numerical simulation. Particle trajectories are calculated by Stokesian dynamics, with an accurate representation of the suspension hydrodynamics that includes both many-body interactions and lubrication. The simulations are of a monolayer of identical spheres as a function of the Peclet number: Pe =gamma-dot a^2/D0, which measures the relative importance of shear and Brownian forces. Here gamma-dot is the shear rate, a the particle radius, and D0 the diffusion coefficient of a single sphere at infinite dilution. In the absence of shear, using only hydrodynamic interactions, the simulations reproduce the pair-distribution function of the equivalent hard-disk system. Both short- and long-time self-diffusivities are determined as a function of the Peclet number. The results show a clear transition from a Brownian motion dominated regime (Pe 10) with a dramatic change in the behavior of the long-time self-diffusivity.

Magnetorheology: Fluids, Structures and Rheology

Magnetorheological suspensions are complex fluids which show a transition from a liquid behavior to a solid one upon application of a magnetic field. This transition is due to the the attractive dipolar forces between the particles which have been magnetized by the applied field. The formation of a network of particles or aggregates throughout the suspension is the basic phenomena which is responsible for the strength of the solid phase. In this paper we shall give an overview on the fluids and their properties and we shall especially emphasize the interplay between magnetic forces which are responsible for the gelling of the suspension and on the other hand of hydrodynamic and thermal forces which contribute to break this gel and allow the suspension to flow. The combination of these three forces gives rise to a very rich rheology whose many aspects are still not understood.

Magnetorheology of magnetic holes compared to magnetic particles

We compare the rheological behavior in a shear flow of two types of suspension of magnetic particles in the presence of a magnetic field. The first suspension is made of silica particles in a ferrofluid and the second one is made of carbonyl iron particles in silicone oil. The permeability curves of these two suspensions have been measured for different volume fractions as a function of the magnetic field in order to characterize the magnetic interactions. We show for both cases the existence of two different yield stresses: one associated with the solid friction of the particles on the plates of the rheometer and the second one with the rupture of the aggregates. This second yield stress presents a maximum with the volume fraction for the suspension of magnetic holes but grows faster than linearly with the volume fraction for the suspension of carbonyl iron. These features are explained by theoretical models based, respectively, on the deformation of aggregates of macroscopic size and on ruptures between...

Yield stress in magnetorheological and electrorheological fluids: A comparison between microscopic and macroscopic structural models

The yield stress of a magnetorheological suspension is calculated from two different approaches. The first one is based on a mesoscopic description of the structure taking only into account the shape anisotropy of the strained aggregates. The second one is based on a microscopic approach where the interparticle forces, due to the application of the field, are calculated numerically by taking into account the magnetostatics between the particles inside the aggregates. We show that the macroscopic description well applies to suspensions of nonmagnetic particles in a ferrofluid and that a layered structure, consisting of parallel slabs of magnetizable materials should have a yield stress much higher than a structure made of cylindrical aggregates. On the other hand the microscopic approach is appropriated for the description of suspensions of particles of high permeability. In this case, the yield stress is mainly determined by the rupture between pairs of particles and, consequently, it strongly increases with the angle between the line of centers of the pair undergoing the rupture and the field.