Slow Viscoelastic Flow

Abstract

Constitutive equations based on the linear response functions are not adequate for most problems of viscoelastic flow. In the present chapter we first discuss the general problem of choosing a constitutive equation that can describe the stress response adequately in whatever specific problem is at hand. We then turn to a specific class of flows for which the Navier-Stokes equation is a good first approximation. These flows are slow in the sense that nothing changes much in one relaxation time, but may be arbitrarily fast if by “fast” one means something to do with the Reynolds number. We discuss the nature of approximations based on this notion of slowness and show how to solve flow problems within this approximation scheme.