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arXiv · 1501.00366

Viscosity-Stratified Flow in a Hele-Shaw Cell

Alexander Chesnokov·Valery Liapidevskii
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Abstract

A hierarchy of mathematical models describing viscosity-stratified flow in a Hele-Shaw cell is constructed. Numerical modelling of jet flow and development of viscous fingers with the influence of inertia and friction is carried out. One-dimensional multi-layer flows are studied. In the framework of three-layer flow the interpretation of the Saffman--Taylor instability is given. A kinematic-wave model of viscous fingering taking into account friction between the fluid layers is proposed. Comparison with calculations on the basis of two-dimensional equations shows that this model allows to determine the velocity of propagation and the thickness of the viscous fingers.

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Alexander Chesnokov, Valery Liapidevskii. 2015-01-02. Viscosity-Stratified Flow in a Hele-Shaw Cell. https://arxiv.org/abs/1501.00366

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