Effect of slip boundary conditions on interfacial stability of two-layer viscous fluids under shear

TL;DR

This paper theoretically investigates how slip boundary conditions at interfaces and external boundaries affect the stability of two-layer viscous fluids under shear, revealing that slip can induce instability even in symmetric configurations.

Contribution

It provides a theoretical analysis of the impact of slip boundary conditions on interfacial stability in shear flows of two-layer viscous fluids, highlighting conditions that lead to instability.

Findings

Slip at interfaces increases perturbation growth rate.

Interfacial slip can destabilize flows with equal viscosities and densities.

Boundary conditions significantly influence long-wave propagation.

Abstract

The traditional approach in the study of hydrodynamic stability of stratified fluids includes the stick boundary conditions between layers. However, this rule may be violated in polymer systems and as a consequence various instabilities may arise. The main objective of this paper is to analyze theoretically the influence of slip boundary conditions on the hydrodynamic stability of the interface between two immiscible viscous layers subjected to simple shear flow. It is found that the growth rate of long-wave disturbances is fairly sensitive to the slip at the interface between layers as well as at the external boundary. These phenomena are shown to give different contributions to the stability of shear flow depending on viscosity, thickness, and density ratios of the layers. Particularly, the interfacial slip can increase the perturbation growth rate and lead to unstable flow. An important consequence of this effect is the violation of stability for sheared layers with equal viscosities and densities in a broad range of thickness ratios. The conditions of long-wave propagation are analyzed as well, showing a strong dependence on the type of boundary conditions.