New Variational Principle for Incompressible Non-Newtonian Flow

Abstract

A variational principle is given which describes the steady laminar motion of simple non-Newtonian fluids, for which the viscosity is a function of the second invariant of the rate of deformation tensor. This principle simplifies to von Helmholtz's principle for the Newtonian fluid, and to Tomita's principle for the Ostwald-de Waele fluid. For the latter two types of fluids, the equations of continuity and motion are equivalent to the statement that the rate of entropy production in the system is a minimum; for more general fluids, the variational principle does not admit this simple interpretation.