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 -