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Perturbing Hele-Shaw flow with a small gap gradient
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A controlled perturbation is introduced into the Saffman-Taylor flow problem by adding a gradient to the gap of a Hele-Shaw cell. The stability of the single-finger steady state was found to be strongly affected by such a perturbation. Compared with patterns in a standard Hele-Shaw cell, the single Saffman-Taylor finger was stabilized or destabilized according to the sign of the gap gradient. While a linear stability analysis shows that this perturbation should have a negligible effect on the early-stage pattern formation, the experimental data indicate that the characteristic length for the initial breakup of a flat interface has been changed by the perturbation.
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ZHAO, H., et al. Perturbing Hele-Shaw flow with a small gap gradient. Physical Review A. 1992. Vol. 45, num. 4, pags. 2455-2460. ISSN 1050-2947. [consulted: 29 of June of 2026]. Available at: https://hdl.handle.net/2445/9551