On a two-phase Hele-Shaw problem with a time-dependent gap and distributions of sinks and sources

A two-phase Hele-Show problem with a time-dependent gap describes the evolution of the interface, which separates two fluids sandwiched between two plates. The fluids have different viscosities. In addition to the change in the gap width of the Hele-Shaw cell, the interface is driven by the presence...

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Bibliographic Details
Published in:arXiv.org 2017-11
Main Authors: Savina, T V, Akinyemi, L, Savin, A
Format: Article
Language:English
Subjects:
Cusps
Domains
Free boundaries
Surface tension
Time dependence
Online Access:Get full text
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Summary:A two-phase Hele-Show problem with a time-dependent gap describes the evolution of the interface, which separates two fluids sandwiched between two plates. The fluids have different viscosities. In addition to the change in the gap width of the Hele-Shaw cell, the interface is driven by the presence of some special distributions of sinks and sources located in both the interior and exterior domains. The effect of surface tension is neglected. Using the Schwarz function approach, we give examples of exact solutions when the interface belongs to a certain family of algebraic curves and the curves do not form cusps. The family of curves are defined by the initial shape of the free boundary.
ISSN:2331-8422
DOI:10.48550/arxiv.1711.02533