Multiscale Rheology: New Results for the Kinetic Scale

We present several new results on the kinetic, i.e., mesoscale, level of a continuum–kinetic–microscopic approach to multiscale modeling of complex fluids. 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, a comparatively simple result is obtained consisting of drift but no diffusion terms. We demonstrate computation of viscoelastic stress divergence using this multiscale approach.