A paradox in Hele-Shaw displacements
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2018
- DOI:
- 10.48550/arXiv.1807.06591
- arXiv:
- arXiv:1807.06591
- Bibcode:
- 2018arXiv180706591P
- Keywords:
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- Physics - Fluid Dynamics;
- 34B09;
- 34D20;
- 35C09;
- 35J20;
- 76S05