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arXiv · 1807.06591

A paradox in Hele-Shaw displacements

Gelu Paşa
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Abstract

We study the Hele-Shaw immiscible displacements when all surfaces tensions on the interfaces are zero. The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one, in a rectangular Hele-Shaw cell. We prove that an intermediate liquid with a variable viscosity can almost suppress this instability. On the contrary, a large number of constant viscosity liquid-layers inserted between the initial fluids gives us boundless growth rates with respect to the wave numbers of perturbations. The same amount of intermediate liquid is used in both cases.

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Gelu Paşa. 2018-07-17. A paradox in Hele-Shaw displacements. https://arxiv.org/abs/1807.06591

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