Effect of nonlinear drag on the onset and the growth of the miscible viscous fingering in a porous medium - Kim, Min Chan (The Korean journal of chemical engineering, 2022)
The onset and growth of miscible viscous fingering in a porous medium was analyzed analytically. Taking the nonlinear drag into account, new stability equations were derived based on Forchheimer’s extension and solved with the quasi-steady state approximation in a similar domain (QSSA ξ ). Also, the validity of QSSA ξ was tested by the numerical initial value calculation (IVC) study. Through the initial growth rate analysis without the steady state approximation, we showed that initially the system is unconditionally stable even in unfavorable viscosity distribution and there exists an initial condition with the largest growth rate. The present initial growth rate analysis without the QSSA is quite different from the previous analyses based on quasi-steady state approximation in the global domain (QSSAx), where the system is assumed to be unstable if the less viscosity fluid displaces the higher one. Employing the linear stability results as an initial condition, fully non-linear numerical simulations were conducted using the Fourier spectral method. The present linear and non-linear analyses predicted that the non-linear drag makes the system stable, i.e., it delays the onset of instability and suppresses the evolution of fingering motions.