Pressure Oscillation Effects on the Saffman-Taylor Instability

We studied experimentally the stability of the front between two immiscible fluids in a Hele-Shaw cell, which consists of two parallel glass plates separated by a narrow spacing. The fluid flow in a Hele-Shaw cell is governed by the Laplace’s equation (pressure field) and Darcy’s law (fluid transport), which makes of this experimental setup a two-dimensional analog of a porous medium (FABER, 1997). SAFFMAN and TAYLOR (1958) demonstrated that when the injected fluid is less viscous than the displaced one, the front between the fluids can be unstable and fingers may develop along the interface. We investigated the possibility of influencing the development of the Saffman-Taylor instability by modulating the injection pressure with weak periodic oscillations of low frequency (5 to 15 Hz). A series of experiments were performed, in which the evolution of the interface between the injected air and the displaced silicon oil was recorded with the help of a numerical photo camera. We observed that the oscillations of the injection pressure inhibit the development of fingers. We quantified the observed stabilization effect by performing a harmonic analysis of the shape of the front, and suggested an interpretation in terms of ‘‘stiffening’’ of the interface.