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Self-diffusion in sheared suspensions by dynamic simulation

Foss, David R. and Brady, John F. (1999) Self-diffusion in sheared suspensions by dynamic simulation. Journal of Fluid Mechanics, 401 . pp. 243-274. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:FOSjfm99

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Abstract

The behaviour of the long-time self-diffusion tensor in concentrated colloidal dispersions is studied using dynamic simulation. 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, and the volume fraction, [phi]. Here, Pe = &[gamma]dot;a^2/D0, where &[gamma]dot; is the shear rate, a the particle size and D0 = kT/6[pi][eta]a is the Stokes–Einstein diffusivity of an isolated particle of size a with thermal energy kT in a solvent of viscosity [eta]. Two simulations algorithms are used: Stokesian Dynamics for inclusion of the many-body hydrodynamic interactions, and Brownian Dynamics for suspensions without hydrodynamic interactions. A new procedure for obtaining high-quality diffusion data based on averaging the results of many short simulations is presented and utilized. At low shear rates, low Pe, Brownian diffusion due to a random walk process dominates and the characteristic scale for diffusion is the Stokes–Einstein diffusivity, D0. At zero Pe the diffusivity is found to be a decreasing function of [phi]. As Pe is slowly increased, O(Pe) and O(Pe^3/2) corrections to the diffusivity due to the flow are clearly seen in the Brownian Dynamics system in agreement with the theoretical results of Morris & Brady (1996). At large shear rates, large Pe, both systems exhibit diffusivities that grow linearly with the shear rate by the non-Brownian mechanism of shear-induced diffusion. In contrast to the behaviour at low Pe, this shear-induced diffusion mode is an increasing function of [phi]. Long-time rotational self-diffusivities are of interest in the Stokesian Dynamics system and show similar behaviour to their translational analogues. An off-diagonal long-time self-diffusivity, Dxy, is reported for both systems. Results for both the translational and rotational Dxy show a sign change from low Pe to high Pe due to different mechanisms in the two regimes. A physical explanation for the off-diagonal diffusivities is proposed.


Item Type:Article
Additional Information:"Reprinted with the permission of Cambridge University Press." (Received February 2 1999) (Revised July 26 1999) This work was supported in part by grant CTS-9420415 from the National Science Foundation and grant NAG8-1237 from NASA.
Subject Keywords:CONCENTRATED COLLOIDAL DISPERSIONS; ROTATIONAL DIFFUSION; HARD-SPHERES; BROWNIAN DYNAMICS; HYDRODYNAMIC INTERACTIONS; TRACER DIFFUSIVITIES; DILUTE SUSPENSION; PARTICLES; RHEOLOGY; FLOW
Record Number:CaltechAUTHORS:FOSjfm99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:FOSjfm99
Alternative URL:http://www.journals.cambridge.org/action/displayAbstract?fromPage=online&aid=15551
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1583
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:01 Feb 2006
Last Modified:26 Dec 2012 08:45

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