Viscoelastic flow past a wedge with a soluble coating

Abstract

The steady, two dimensional, incompressible flow of a viscoelastic fluid past a wedge of 90 degrees coated with the viscoelastic material is studied theoretically using constitutive equations proposed by Oldroyd in 1958. The effect of diffusion of the coating as well as its material properties (viscosity, relaxation time, retardation time, etc.) on the frictional force is investigated. A boundary-layer analysis is performed on the constitutive equations as well as on the momentum equations. A similarity transformation is found for the set of boundary-layer equations. Series expansion and Laplace's method are employed to obtain the solution in the asymptotic series of gamma functions. The results obtained show that: The thinner displacement thickness does not necessarily imply a large frictional force for the viscoelastic flow. For a homogeneous viscoelastic flow, the frictional force increases as the degree of dilatancy of the material increases, and decreases with increasing degree of pseudo-plasticity of the material. For a non-homogeneous viscoelastic flow with given material constants, depending on whether the material is pseudoplastic or dilatant and on the ratio of the material concentration of outer flow and the concentration at the body, the frictional coefficient will decrease or increase from that of the homogeneous flow with the concentration at the body as the Schmidt number increases, and will approach a limit when the Schmidt number becomes very large. This limit is the frictional coefficient of the homogeneous flow with the concentration of the outer flow.