A new insight into the stability of variable viscosity diffusive boundary layers in porous media under gravity field

Abstract

We study the stability of gravitationally unstable transient diffusive boundary layers with variable viscosity in porous media. The previous studies characterize the effect of viscosity variation only in terms of viscosity contrast and generalize their findings. However, conclusions of different studies seem contradictory. Our results demonstrate that stability of diffusive fronts is governed by the boundary layer viscosity and not solely by the viscosity contrast. In other words, the use of viscosity contrast to ascertain the stability of the system cannot be generalized. Nonlinear simulations are conducted based on a finite difference scheme to validate the results of linear stability analysis for which the amplification theory is adopted. We also revisit other available scaling approaches used to characterize the effect of viscosity variation on the onset of convective dissolution and explain why previously made conclusions are not inclusive and sometimes appeared to be contradictory. A critical Rayleigh number is found to predict stability of Rayleigh‐Darcy convection in a porous layer with variable viscosity. The results reveal that this critical value can differ highly from the conventional value of 4π2. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1083–1094, 2018