Stability of Hele–Shaw flows: The wetting-layer effect

Abstract

The classical viscous instability calculation of Chouke et al. [Trans. AIME 216, 188 (1959)], further clarified by Saffman and Taylor [Proc. R. Soc. London, Ser. A 245, 312 (1958)] in the context of flow in a Hele–Shaw cell, is reconsidered and the importance of the wetting condition and the associated interfacial pressure jump is established. Important qualitative changes appear in the resulting dispersion relation when this effect is included. The wavelength of maximum growth is increased and the growth rate is reduced, however, the critical wavelength for instability remains unchanged. Comparison of the theoretical results with some recent experiments appears to provide support for the new effect.