Gravity-driven instability in a spherical Hele-Shaw cell

Details Gravity-driven instability in a spherical Hele-Shaw cell Gravity-driven instability in a spherical Hele-Shaw cell

2000-10-16

arxiv.org/abs/cond-mat/0010224v2

Physics

Condensed Matter

Soft Condensed Matter

13 pages, 4 ps figures, RevTex, to appear in Physical Review E

Scientific paper

10.1103/PhysRevE.63.016311

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 immiscible fluids flow. We derive the equation of motion for the interface perturbation amplitudes, including both pressure and gravity drivings, using a mode coupling approach. Linear stability analysis shows that mode growth rates depend upon interface perimeter and gravitational force. Mode coupling analysis reveals the formation of fingering structures presenting a tendency toward finger tip-sharpening.

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