Motion of inviscid fluid tongues and bubbles in a Hele-Shaw cell occupied by a viscoelastic fluid

Problems of steady-state motion of an inviscid fluid tongue or bubble in a Hele-Shaw cell occupied by a viscoelastic fluid are considered. The problems generalize the well-known Saffman-Taylor problems 1, 2] in the approximation in which the pressure jump on the interface between the two fluids depends on the normal velocity of the interface 4]. In the zero approximation the results obtained by means of an iteration technique are in good agreement with the analytic solutions obtained by Saffman and Taylor 1, 2].__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 117–123. Original Russian Text Copyright © 2005 by Entov, Kolganov, and Kolganova.