Linear stability analysis of miscible displacement by nanofluid with concentration-dependent diffusivity

Abstract The present study performs linear stability analysis to examine viscous fingering in miscible displacement when displacing fluid is laden with nanoparticles. The diffusion of nanoparticles controls viscosity and hence fingering instability. In contrast to earlier studies treating diffusivity of nanoparticles as constant, the present study considers concentration-dependent diffusivity of nanoparticles. Two different regimes, dilute and concentrated suspensions, are examined. For dilute suspension, diffusivity is function of solute concentration. For concentrated suspensions, particle-particle interaction is significant, hence diffusivity is additionally function of local particle concentration. The stability analysis suggests that growth rate for fingering is significantly reduced or even suppressed for concentrated suspensions. In general, the instability is weakened (strengthened) for slower (faster) diffusing particles. The variation in growth rate with time shows that concentrated suspensions can delay the onset of instability at early times. The mechanism responsible for stabilization is described in terms of viscosity profiles near the diffused interface.