Analysis of shear banding phenomena in non-isothermal flow of fluids governed by the diffusive Johnson–Segalman model

Abstract

This article investigates phenomena associated with shear banded flows of viscoelastic fluids in both pipe flow and coaxial annular flow. We in particular computationally analyze the effects of stress diffusion, non-isothermal flow conditions and annular gap size on the shear stress path selection (and the selected shear stress value) in shear banded flow of viscoelastic fluids described by the non-local Diffusive Johnson–Segalman (DJS) constitutive model. The DJS model is one of such constitutive models which allows us for a non-zero inter-facial layer between regions of high and low shear rates within the flow field. Temperature effects due to polymer orientation changes, entropic effects (resulting from stress work), conduction heat transfer, Arrhenius chemical kinetics as well as the influence of slip and related frictional heating on the wall are all accounted for. The time dependent model formulated to capture gap effect in the axial annular flow problem (under certain values of the relevant parameters), reduces to the system of equations governing a pipe flow setup. Semi-implicit finite difference methods are employed for the solution process of the coupled nonlinear time dependent partial differential equations governing the flow problem. We discuss with graphical representations the effect of temperature, stress diffusion, wall slip, suction/injection and annular gap size on the related shear rate path selection phenomena for certain material parameter values.