TY - JOUR

T1 - Viscosity-stratified flow in a Hele–Shaw cell

AU - Chesnokov, Alexander

AU - Liapidevskii, Valery

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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 propagation velocity of the viscous fingers.

AB - 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 propagation velocity of the viscous fingers.

KW - Fingering instability

KW - Hele-Shaw flow

KW - Kinematic-wave model

UR - http://www.scopus.com/inward/record.url?scp=85007552194&partnerID=8YFLogxK

U2 - 10.1016/j.ijnonlinmec.2016.12.016

DO - 10.1016/j.ijnonlinmec.2016.12.016

M3 - Article

AN - SCOPUS:85007552194

VL - 89

SP - 168

EP - 176

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

ER -