A Weakly Nonlinear Stability Analysis of the Reactive Infiltration Interface
John Chadam, P. Ortoleva, A. Sen · SIAM Journal on Applied Mathematics · 1988
This paper investigates the infiltration flow of a reactive fluid in a porous medium. The reaction-induced porosity changes couple in a nonlinear manner with the transport and may lead to fingering instabilities. A mathematical model for this phenomenon is given in the form of a moving free boundary problem. The morphological instability of a planar dissolution front is demonstrated using a weakly nonlinear stability analysis. The technique used here at each order is to solve the equations uniquely and explicitly, obtaining the resulting restrictions by substituting into the evolution equation for the dissolution interface, as opposed to the more traditional method of integrating against the solution of the homogeneous adjoint problem.