Nanoparticles impact on miscible viscous fingering with absorbing boundary condition at inlet

Abstract

The addition of nanoparticles in fluids significantly influences the fluid's viscosity and can be helpful to control viscosity-driven instability. In this work, we analyze how such nanoparticles modulate viscosity and impact miscible viscous fingering (VF) dynamics. We consider the flow configuration such that the Hele-Shaw cell is initially filled with a viscous fluid and then displaces it with other viscous fluid-carrying nanoparticles through the inlet boundary, which corresponds to the absorbing boundary condition. A closed-form solution of base-state flow using the Laplace-transform method is obtained, which overcomes the discrepancy of the base-state solution known in the form of an infinite series as available in the literature. Due to the time-dependency and nonmonotonic nature of the base state, nonmodal linear stability analysis in the self-similar domain is used to determine the onset time of instability. In this work, the effects of various governing flow parameters such as nanoparticles diffusive coefficient (αnp), effective log-mobility ratio (R), and deposition rate of nanoparticles (Dadep) on the instability are studied. Our finding suggests that the onset occurs early with increasing Dadep for αnp>1, whereas such onset time is a nonmonotonic function of Dadep for smaller values of αnp. In addition, our results indicate that the onset time is a nonmonotonic function of αnp for the smaller value of Dadep, whereas such onset time is an increasing function of αnp for the larger value of Dadep. Further, nonlinear simulations are performed using comsol multiphysics, and the nonmonotonic nature on the onset of instability for different αnp is observed which is in good agreement with the linear stability analysis results. The present investigation removes various inconsistencies in the literature about the impact of the nanoparticles on VF with the quasi-steady-state approximation.