Accession Number : AD0421948

Title :   A RECURSIVE APPROACH TO THE THEORY OF SLOW, STEADY-STATE VISCOELESTIC FLOW,

Corporate Author : INTERNATIONAL BUSINESS MACHINES CORP SAN JOSE CALIF

Personal Author(s) : Langlois,W. E.

Report Date : 30 OCT 1962

Pagination or Media Count : 79

Abstract : The slow, steady-state motion of an arbitrary Rivlin-Ericksen 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 ex7licitly 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. Several elementary flow problems of technological importance are solved: flow between parallel plates; the Poiseuille problem; helical flow in an annular region; torsional flow between discs. It is shown that, in a rather fundamental sense, there is no fluid-film lubrication theory of viscoelastic flow. The components of stress differ among themselves, and vary across the film, by amounts comparable with the lubrication pressure. Hence, boundary conditions cannot be satisfied and it must be concluded that viscoelastic lubrication presents a fully three-dimensional flow problem. (Author)

Descriptors :   (*VISCOELASTICITY, FLUID FLOW), PERTURBATION THEORY, EQUATIONS, THEORY, VISCOSITY, ELASTIC PROPERTIES, TENSOR ANALYSIS, HELIXES, COUETTE FLOW, LUBRICATION, PRESSURE, ACCELERATION, METAMATHEMATICS

Distribution Statement : APPROVED FOR PUBLIC RELEASE