Nano-Rod Suspension Flows: A 2D Smoluchowski-Navier-Stokes Solver

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 Smoluchowski 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 harmonic Galerkin expansion), two dimensional physical space (method 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.