Effect of non-affine motion on the centrifugal instability of circular Couette flow

Abstract

In the present work, the effect of non-affine motion of the constituents in a complex fluid system (say, a polymeric liquid) is theoretically investigated on the centrifugal instability of circular Couette flow. To achieve this goal, use was made of the linearized Phan-Thien/Tanner (LPTT) model thanks to its allowing non-affine deformation for the polymer strands in a temporary network of junctions through invoking a slip parameter. Knowing the basic-flow velocity and stress fields from the literature, they were subjected to infinitesimally-small, normal-mode perturbations and their time-evolution was monitored using a linear stability analysis for both the axisymmetric and non-axisymmetric modes. An eigenvalue problem was obtained this way which was solved numerically using the pseudo-spectral, Chebyshev-based, collocation method. Based on the results obtained in this work, it is concluded that the non-affine motion can have a stabilizing or destabilizing effect on circular Couette flow depending on the Weissenberg number and the sign/magnitude of the angular velocity ratio.