Secondary flow of an elasto-visco-plastic fluid in an eccentric annulus

In this paper we study the flow an elasto-visco-plastic fluid whose deviatoric stress is made up by a “seemingly” visco-plastic part (regularized Bingham fluid) and a viscoelastic part (Rivlin–Ericksen fluid) in a “slightly” eccentric annulus. The flow is driven by an applied horizontal pressure gradient and by the motion of the inner cylinder. Using the eccentricity as perturbation parameter we show that secondary flows appear at the first order approximation. We investigate the various flow patterns depending on the different non-dimensional groups appearing in the governing equations. In particular we observe the occurrence of rotating and counter-rotating vortices depending on the material and geometrical parameters of the system.