Effect of non-normal interactions on the interfacial instability of multilayer viscoelastic channel flows

Abstract

The effect of non-normal interactions on the interfacial instability of multilayer pressure driven channel flow of viscoelastic fluids in the limit of vanishingly small Reynolds number has been investigated. Specifically, it is shown that for the upper convected Maxwell (UCM), the Oldroyd-B, and the modified Phan-Thien–Tanner (MPTT) constitutive models the short time dynamics are significantly influenced by non-normal effects both in two- and three-layer flows. Moreover, the departure from the normal exponential behavior is most pronounced in the velocity perturbations. Furthermore, in two- and three-layer symmetric flows, the non-normal effects that arise from the interaction of the interfacial mode with bulk mode dissipate very quickly and therefore do not significantly influence the growth of interfacial disturbances. However, in asymmetric three-layer flows the non-normal behavior that results from the interaction of the two interfacial modes can be very significant and can persist over very long time periods. Hence, non-normal behavior can play a very significant role in determining the growth/decay rate of interfacial disturbances. Our analysis shows that the discrepancy observed in the measured and predicted growth rates of interfacial disturbances in earlier investigations [J. Non-Newtonian Fluid Mech. 79 (1998) 315] can be attributed to the presence of non-normal interactions.