Stability of thinly diffuse layers in shear flow

Unstable interfaces are central to pattern formation, atomization, and mixing processes. Understanding the behavior of instabilities can lead to a better understanding of these processes, which are present in a wide range of industrial and natural flows. This work seeks to elucidate the physics of the multiple instability types in shear flows. The immiscible fluid instability arising due to viscosity jump (sharp interface) is well-established. But only a couple of attempts have been made to study the stability of a steep gradient in viscosity (diffuse layer) as in between two slightly miscible fluids. The present work provides the first accurate results on the stability of flows with diffuse layers. The results were achieved by using a linear stability analysis, which included the effects of variable viscosity and viscosity fluctuations. To overcome the challenges in solving the diffuse layer stability equations, a numerical solution method was developed to obtain convergent solutions by resolving gradients in flow properties and minimizing numerical round-off errors.;The linear stability analysis led to new discoveries on instabilities that arise due to the presence of viscosity gradients and provided a more clear understanding of the well-known shear and inviscid modes. The diffuse layer instability has all the features of the sharp interface instability, and in fact it approaches it asymptotically as the diffuse layer becomes thinner and thinner. Collectively, they are named Viscosity-Gradient-Induced (VGI) instabilities. Also, VGI modes were shown to interact with Tollmien-Schlichting instabilities, and the conditions for interaction were determined. The inviscid, Kelvin-Helmholtz instabilities were found to be the limit of VGI modes as Reynolds number becomes larger and larger.;The findings are particularly relevant for the commonly used Diffuse Interface Method (DIM) for numerical simulations of interfacial instabilities with shear. In a DIM, the sharp interface is replaced with a diffuse layer with varying properties. As such, the requirements of resolving properties in the diffuse layer and the steepening requirement of the diffuse layer instability to approach the sharp interface instability must be considered.