Int. J. Numer. Anal. Mod., 4 (2007), pp. 478-488.


Nano-rod suspension flows: A 2D Smoluchowski-Navier-Stokes solver

M. Gregory Forest 1, Ruhai Zhou 2, Qi Wang 3

1 Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA
2 Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
3 Department of Mathematical Sciences, Florida State University, Tallahassee, FL 32306, USA

Received by the editors March 3, 2006
Abstract

We present a numerical algorithm for nano-rod suspension flows, and provide benchmark simulations of a plane Couette cell experiment. The system consists of a Smolouchowski equation for the orientational distribution function of the nano-rods together with the Navier-Stokes equation for the solvent with an orientation-dependent stress. The rigid rods interact through nonlocal excluded-volume and distortional elasticity potentials and hydrodynamic interactions. The algorithm resolves full orientational configuration space (a spherical of lines discretization), and time (spectral deferred corrections), and employs a velocity-pressure formulation of the Navier-Stokes equation. This method extends our previous solver [25] from 1D to 2D in physical space.

AMS subject classifications: 65N06, 65N40, 76M20
Key words: Navier-Stokes; Smoluchowski equation; numerical methods; nano-rods; suspension flow
Email: forest@amath.unc.edu (M. G. Forest), rzhou@odu.edu (R. Zhou), wang@math.fsu.edu (Q. Wang)
 

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