Viscosity-Stratified Flow in a Hele-Shaw Cell
Fluid Dynamics
2016-03-22 v3
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.
Cite
@article{arxiv.1501.00366,
title = {Viscosity-Stratified Flow in a Hele-Shaw Cell},
author = {Alexander Chesnokov and Valery Liapidevskii},
journal= {arXiv preprint arXiv:1501.00366},
year = {2016}
}