Onset of radial viscous fingering in a Hele-Shaw cell

Abstract

The onset of viscous fingering in a radial Hele-Shaw cell was analyzed by using linear theory. In the selfsimilar domain, the stability equations were derived under the normal mode analysis. The resulting stability equations were solved analytically by expanding the disturbances as a series of orthogonal functions and also numerically by employing the shooting method. It was found that the long wave mode of disturbances has a negative growth rate and the related system is always stable. For the limiting case of the infinite Péclet number, Pe→∞, the analytically obtained critical conditions are R _c =11.10/$\sqrt {Pe}$ and n _c =0.87$\sqrt {Pe}$. For Pe≥100, these stability conditions explain the system quite well.