Viscosity-Stratified Flow in a Hele-Shaw Cell

Alexander Chesnokov, Valery Liapidevskii

Published 2015-01-02Version 1

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 the forces of inertia and friction is carried out. One-dimensional multi-layer flows are studied. In the framework of three-layer flow scheme the interpretation of the Saffman--Taylor instability is given. A kinematic model of viscous fingering taking into account the formation of the intermediate mixing layer is proposed. Comparison with calculations on the basis of two-dimensional equations shows that this model allows one to determine the velocity of propagation and the thickness of the viscous fingers.