Flow of a limited stress fluid between plates rotating about different axes

Abstract

In this paper we study the flow of a particular type of non-Newtonian fluids generated by the rotation of parallel infinite plates about distinct axes. The constitutive law of these fluids mimics the response of a class of seemingly viscoplastic or “yield stress” materials in which the norm of the stress is bounded by a critical threshold (limited stress fluids). We assume that the plates rotate with the same angular velocity and we show that, in this case, the mathematical problem can be reduced to solving a BVP where the unknowns are the coordinates of the center of rotation. We solve the problem numerically (by means of a spectral collocation method), and we investigate the dependence of the locus of the center of rotation on the material parameters. We prove that, even for small Reynolds numbers, the flow may exhibit boundary layers depending on the particular choice of the parameters.