Double diffusive effects on pressure-driven miscible channel flow: Influence of variable diffusivity

The pressure-driven displacement of one fluid (initially filled inside a channel) by another (injected at the inlet) in a horizontal channel is studied. Both the fluids are the same, but consist of two scalars in different proportion. These scalars are diffusing at different rates and influencing the viscosity. The focus is on the situation when the invading fluid is more viscous than the resident fluid. The Navier-Stokes and continuity equations coupled to two convective-diffusion equations for the concentration of both the scalars through concentration-dependent viscosity are solved using a finite-volume approach. The Stokes-Einstein relationship is used to model the variable diffusivity of the scalars. The viscosity is modeled as an exponential function of the concentration of both scalars, while density contrast is neglected. The objective of the study is to investigate the effects of variable diffusivity on the flow dynamics in this system. The present results demonstrate that the double-diffusive effects destabilize the flow, resulting many interesting patterns with some features qualitatively different from those in the constant diffusivity case. The variable diffusivity delays the formation of Kelvin-Helmholtz-type instability, but increases the size of the "cap-type" instability, which appears at the finger tip of the invading fluid when the faster-diffusing scalar is stabilizing while the slower diffusing scalar is destabilizing. The saw-tooth shaped low intensity instabilities are observed when the faster-diffusing scalar is destabilizing while the slower diffusing scalar is stabilizing. The effects of the log-mobility ratios of the faster and slower diffusing scalar are also investigate