On the higher-order boundary conditions for incompressible nonlinear bipolar fluid flow

Abstract

The higher-order boundary conditions associated with the flow of an incompressible, nonlinear, bipolar viscous fluid in a bounded domain are derived; these boundary conditions differ from the various ad hoc sets of higher-order boundary conditions that have been used in work involving fluid dynamics models employing higher-order gradients of the velocity field. The derivation presented is based on a principle of virtual work and some deep results of Heron on higher-order traces of divergence-free vector fields.

Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow

“…1.4.4 and the resulting modification of the computations presented, below, will then yield the final form of the higher-order boundary conditions associated with the multipolar stress tensor ijk . The analysis presented here is based on the recent work in [BB4]. We begin by rewriting the constitutive equations in the form…”