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Gravity-driven instability in a spherical Hele-Shaw cell
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.Comment: 13 pages, 4 ps figures, RevTex, to appear in Physical Review
Suppression of viscous fluid fingering: a piecewise constant-injection process
The injection of a fluid into another of larger viscosity in a Hele-Shaw cell
usually results in the formation of highly branched patterns. Despite the
richness of these structures, in many practical situations such convoluted
shapes are quite undesirable. In this letter we propose an efficient and easily
reproducible way to restrain these instabilities based on a simple piecewise
constant pumping protocol. It results in a reduction in the size of the viscous
fingers by one order of magnitude.Comment: Published in Phys. Rev.
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