Linear instability in two-layer channel flow due to double-diffusive phenomenon

Abstract

The linear stability characteristics of a pressure-driven channel flow of two miscible fluids flowing in a layered manner are investigated in the presence of two scalar components diffusing at different rates [double-diffusive (DD) phenomenon]. The fluids are assumed to have the same density but different viscosities. The parameters varied are the Reynolds number, Schmidt number, and thickness of the bottom layer. It is observed that the linear stability behavior in the presence of the DD effect is strikingly different from that observed in the single-component (SC) system. While the SC two-layer configuration is stable, the DD two-layer flow becomes unstable at low and moderate Reynolds numbers. It is found that increasing the diffusivity ratio of the faster to the slower diffusing scalar destabilizes the system. A region of instability distinct from that of the Tollmien–Schlichting (TS) mode appears for some combinations of the log-mobility ratios of the slower and faster diffusing scalars. This unstable region grows as the diffusivity ratio increases and the thickness of the bottom layer decreases. For a constant diffusivity ratio, decreasing the Schmidt number of the slower diffusing scalar also increases the region of instability. An energy budget analysis is conducted to understand the underlying mechanism of this instability. Two mechanisms, namely, (i) the rate of energy transfer from the basic flow to the disturbance and (ii) the disturbance energy due to mean viscosity gradient, are found to be the significant contributors to the increase in the rate of change of the disturbance kinetic energy.