Linear analysis on the stability of miscible dispersion of shear-thinning fluids in porous media

The effect of shear-thinning on the onset of miscible viscous fingering in porous media is analyzed theoretically. Using the Carreau model, new stability equations are derived in the similar domain and solved analytically and numerically with and without the quasi-steady state approximation (QSSA). Through the initial growth rate analysis without the steady state approximation, it is shown that initially the system is unconditionally stable even in the unfavorable viscosity distribution and there exists the most unstable initial condition, which is quite different from the previous analyses based on the conventional QSSA. A flow where displacing fluid is a shear-thinning (nN–N) is always more unstable than the Newtonian counterpart (N–N). For the case of a Newtonian fluid displacing a Newtonian one (N–nN), the shear-thinning effect in general makes the system stable.

► A new approach has been applied to study the onset of miscible viscous fingering in porous media.
► The effect of shear thinning on the instability has been considered in the analysis.
► Initial growth rate has been conducted without the quasi-steady state approximation (QSSA).
► The analytical eigenanalysis without QSSA and the numerical shooting method under QSSA have been compared.