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.

Methods are described for calculating the effects of hydrodynamic interactions on the hindered transport of solid spherical macromolecules in ordered or disordered fibrous media. These methods are applied to a medium made up of a square lattice of straight, bead-andstring-type fibers. Hydraulic permeabilities and coefficients governing hindered diffusion and convection are obtained from a detailed hydrodynamic model, and the hindered transport coefficients are shown to be in very good agreement with an effective medium approach based on Brinkman's equation. The use of Brinkman's equation for the calculation of hindered transport rates in fibrous membranes and gels is validated further by comparing with experimental data from the literature.

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 Ewaid 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.

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