A strong contradiction in the multi-layer Hele-Shaw model

Gelu Paşa

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arXiv · 1903.01455

A strong contradiction in the multi-layer Hele-Shaw model

Gelu Paşa

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Abstract

The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one in a rectangular Hele-Shaw cell. A surface tension on the interface between the two fluids is improving the stability. The multi-layer Hele - Shaw model, consisting of $N$ intermediate fluids with constant viscosities, was studied in some previous papers and very low growth constants were obtained for large $N$. We prove that this model leads us to a significant instability, even if $N$ is very large. The maximum value of growth constants can not decrease under a certain value, not depending on the surface tensions on the interfaces. This contradiction with the Saffman-Taylor result makes us have some doubts concerning the correctness of multi-layer model.

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Gelu Paşa. 2019-03-04. A strong contradiction in the multi-layer Hele-Shaw model. https://arxiv.org/abs/1903.01455

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