Interfacial dynamics and pinch-off singularities for axially symmetric Darcy flow.

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ID: 76746
2019
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Abstract
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 analog of Hele-Shaw flow. Here we are concerned with the development of pinch-off singularities characterized by a blowup 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 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 α=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.
Reference Key
morrow2019interfacialphysical Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Morrow, Liam C;Dallaston, Michael C;McCue, Scott W;
Journal physical review e
Year 2019
DOI
10.1103/PhysRevE.100.053109
URL
Keywords Keywords not found

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