Miscible viscous fingering in a packed cylindrical column: Theory and numerics

We investigate viscous fingering (VF) during the miscible displacement in a cylindrical packed column using linear stability analysis and numerical solutions. Linear stability theory is carried out in a self-similar domain, and the linearized equations are solved with and without the quasi-steady-state approximation. We obtain the onset of instability and the associated critical parameters as functions of the log-viscosity ratio and Peclet number for the onset of instability using linear stability analysis. Further, we perform nonlinear simulations based on the finite-element method, both in two-and three-dimensional do-mains. It is shown that the critical Peclet numbers obtained from the linear and nonlinear analyses are in good agreement. One of the main objectives of this study is to explore the effects of lateral boundary conditions on VF. Through two-dimensional (2D) and three-dimensional (3D) simulations, we have clearly shown that the onset and the growth of VF are strongly dependent on the lateral boundary conditions. Finally, through our present 3D numerical simulations, we successfully produce the experimental results available in the literature by suitably choosing the parameters that replicate the experimental conditions under consideration.