Phenomenological behavior of multipolar viscous fluids

Abstract

A constitutive theory is formulated to describe the flow of viscous fluids: the theory of multipolar fluids exhibits nonlinear relations among the stress tensors and spatial derivatives of the velocity of order greater than one and is compatible with the basic principles of continuum mechanics and thermodynamics. For an isothermal, incompressible, dipolar fluid the velocity profiles for various steady flows, such as proper Poiseuille flow in a circular pipe, are computed; the results are compared with the velocity profiles obtained from the steady Navier-Stokes equations through an application of the Prandtl boundary-layer theory.