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].