Calculation of viscoelastic bead–rod flow mediated by a homogenised kinetic scale with holonomic constraints

Abstract

We present a new multiscale model for complex fluids based on three scales: microscopic, kinetic and continuum. We choose the microscopic level as Kramers' bead–rod model for polymers, which we describe as a system of stochastic differential equations with an implicit constraint formulation. The associated Fokker–Planck equation is then derived, and adiabatic elimination removes the fast momentum coordinates. Approached in this way, the kinetic level reduces to a dispersive drift equation. The continuum level is modelled with a finite volume Godunov-projection algorithm. We demonstrate the computation of viscoelastic stress divergence using this multiscale approach.

Keywords:

• viscoelasticity
• complex fluids
• multiscale
• microfluidics

Acknowledgements

G.H. Miller, S. Mitran and D. Trebotich were supported by the U.S. Department of Energy Office of Advanced Scientific Computing Research under grants DE-SC0001981 and A10-0486-001, and contract DE-AC02-05-CH11231, respectively.