Suspensions: microstructure, diffusion, and inhomogeneous flow

Citation

Morris, Jeffrey Franklin (1996) Suspensions: microstructure, diffusion, and inhomogeneous flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/069F-Z696. https://resolver.caltech.edu/CaltechETD:etd-01102008-085702

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. A theory of self-diffusivity in sheared suspensions valid for any particle volume fraction [phi], Peclet number Pe, and lengthscale of disturbance in [phi] is developed. The theory is applied to the determination of the full tensor self-diffusivity in a weakly- sheared (Pe << 1) suspension of hydrodynamically-interacting hard spheres and a strongly-sheared (Pe >> 1) suspension of hard spheres without hydrodynamic interactions, both at [phi] << 1. The influence of weak Brownian motion alone and in conjunction with a repulsive interparticle force of hard-sphere type upon the pair-distribution function, g(r) where r is the separation vector of a pair of particles, is analyzed for a suspension of spheres at Pe >> 1 and [phi] << 1. At large Pe, the radial fluxes of pair probability due to advection and Brownian diffusion balance in a thin [...] boundary layer at contact, with a the sphere radius. The boundary-layer analyses demonstrate that Brownian diffusion renders g finite at contact in the absence of interparticle forces, and that within the boundary layer there is generally a large excess of pair probability along the compressional axes. By calculation of the bulk normal stress differences in the case with repulsive forces, it is shown how this asymmetry of the microstructure yields non-Newtonian constitutive behavior in the limit Pe[superscript -1] = 0. Hydrodynamic resistance functions relating the particle and bulk motions to the bulk isotropic stress are developed. Application of these functions is demonstrated by calculations of the shear-induced correction to the osmotic pressure and the particle contribution to the pressure in a sheared lattice. Pressure-driven flow in a channel at vanishing Reynolds number of a suspension of particles denser than the suspending fluid has been dynamically simulated by Stokesian Dynamics over ranges of the particle fraction, channel width, and a buoyancy parameter characterizing the relative strength of the buoyancy to shearing forces. The predictions of the flow by the suspension-balance model are in good agreement with simulation results.

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