Unraveling instabilities and mixing behavior in two-layered flows: A quest for the optimum viscosity ratio

Abstract

A two-layer miscible displacement of density-matched but viscosity-contrasted fluids through a channel is numerically investigated in a nonlinear regime. The flow is governed by Navier–Stokes equations, which are coupled to a convection-diffusion equation via viscosity dependent concentration. Instabilities in the form of roll-ups or ligament waves are observed when a less viscous fluid is sheared over a more viscous fluid. Through interfacial length calculations, we demonstrate that the temporal evolution of the interface can be divided into three regimes: the initial diffusion-dominated regime, the intermediate convection-dominated regime, and the final diffusion-dominated regime. With the unstable roll-up growth only in a convection-dominated regime, the growth of instability delays at later times in diffusion dominated regime. Moreover, onset time ton vs R plots for each Reynolds number (Re), Péclet number (Pe), initial interface location (h), and thickness of initial mixing zone (q) depict that the instability originates early for intermediate viscosity ratios (R) than larger R. In contrast to earlier studies in the linear regime, we showed that if the viscosity ratio between two fluids is very large or small, the instability doesn't trigger in the nonlinear regime. The analysis of the concentration's global variance-based degree of mixing allows us to find optimum parameters for maximum mixing. We show that the optimal mixing is obtained at an intermediate value of R (optimum R). Furthermore, the degree of mixing is found to increase for increasing Re and decreasing Pe.