Gravity-driven instability in a spherical Hele-Shaw cell - art. no. 016311

A pair of concentric spheres separated by a small gap form a spherical Hele -Shaw cell. In this cell an interfacial instability arises when two immisci ble fluids flow. We derive the equation of motion for the interface perturb ation amplitudes, including both pressure and gravity drivings, using a mod e coupling approach. Linear stability analysis shows that mode growth rates depend upon interface perimeter and gravitational force. Mode coupling ana lysis reveals the formation of fingering structures presenting a tendency t oward finger tip-sharpening.