Some analytical aspects of the radial fingering in porous medium

Abstract

In this study, the onset of the azimuthal instability and its growth is analyzed by using linear theory. In the self-similar domain, the stability equations are derived and the principle of the exchange of the stabilities is considered. The resulting stability equations are solved analytically by expanding the disturbances as a series of orthogonal functions. It is found that the long-wave mode of disturbances has a negative growth constant, and the related system is always stable. For the limiting case of the infinite Peclet number, Pe → ∞, and the small viscosity variation with the concentration, i.e., R ≪ 1, the stability equations are rescaled and the disturbances are decomposed using the spectral approach. It is shown that the short-wave mode is the preferred mode for the high \({R^\ast\left( {= R \sqrt{Pe}}\right)}\). Analytically, the present study recovers and complements the previous work.