Interfacial dynamics and pinch-off singularities for axially symmetric Darcy flow
| Autor: | Morrow, Liam C., Dallaston, Michael C., McCue, Scott W. |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 100, 053109 (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.100.053109 |
| Popis: | We study a model for the evolution of an axially symmetric bubble of inviscid fluid in a homogeneous porous medium otherwise saturated with a viscous fluid. The model is a moving boundary problem that is a higher-dimensional analogue of Hele-Shaw flow. Here we are concerned with the development of pinch-off singularities characterised by a blow-up of the interface curvature and the bubble subsequently breaking up into two; these singularities do not occur in the corresponding two-dimensional Hele-Shaw problem. By applying a novel numerical scheme based on the level set method, we show that solutions to our problem can undergo pinch-off in various geometries. A similarity analysis suggests that the minimum radius behaves as a power law in time with exponent $\alpha = 1/3$ just before and after pinch-off has occurred, regardless of the initial conditions; our numerical results support this prediction. Further, we apply our numerical scheme to simulate the time-dependent development and translation of axially symmetric Saffman-Taylor fingers and Taylor-Saffman bubbles in a cylindrical tube, highlighting key similarities and differences with the well-studied two-dimensional cases. Comment: 16 pages, 16 figures |
| Databáze: | arXiv |
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