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.