A RECURSIVE APPROACH TO THE THEORY OF SLOW STEADY-STATE VISCOELASTIC FLOW

摘要

The slow, steady-state motion of an arbitrary Rivlin-Erieksen fluid is considered. By perturbing about a state of rest, equations governing the first, second, and third order flow fields are developed in such a way that the second order theory uses explicitly the first order results, etc. The first order equations are those of creeping viscous flow; the second order theory introduces two parameters associated with the viscoelasticity of the fluid; the third order theory brings in three more. Fluid inertia is neglected throughout. To facilitate application, the flow equations, derived in Cartesian tensor notation, are rewritten in general tensor notation; the equations are explicitly given both for cylindrical and spherical coordinate systems.