Time-dependent Poiseuille flows of visco-elasto-plastic fluids

A general constitutive equation of the stress tensor for non-Newtonian fluids is presented, which contains many well-known constitutive models, e.g., Oldroyd-B, Maxwell-A, Maxwell-B, Johnson-Segalman and Bingham models. We examine this constitutive equation with reference to a simple plane fluctuating flow of an incompressible fluid through a horizontal channel bounded by two infinite parallel plates under the exertion of a periodic longitudinal pressure gradient. Numerical solutions are obtained and discussed, especially in connection with viscous, elastic and plastic behaviors of such non-Newtonian fluids