EFFECT OF YIELD STRESS ON FLOW RATE IN ONE-DIMENSIONAL SHEAR FLOWS OF NONLINEAR VISCOUS MEDIA

Flows of incompressible media with tensor-linear constitutive relations that include an arbitrary scalar nonlinearity in the form of a monotonically increasing hardening function are under study. Two types of media are distinguished: those with no yield stress (nonlinearly viscous fluids) and those with a yield stress (viscoplastic solids); the latter are interpreted as finite perturbations of the corresponding media of the first type. The problem of a one-dimensional steady shear flow in a circular pipe is used as an example to demonstrate how the method for perturbing the yield stress affects the maximum velocity and flow rate. The values of these quantities depend on the sign of the second derivative of the hardening function, i.e., on whether the material of the unperturbed medium is pseudoplastic or hardening.