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Viscosity-Stratified Flow in a Hele-Shaw Cell

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.

preprint2016arXivOpen access
Alexander ChesnokovValery Liapidevskii
physics.flu-dyn
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Open access2 authors1 topic
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Alexander ChesnokovValery Liapidevskii

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