Viscosity-stratified flow in a Hele–Shaw cell

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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.

Original languageEnglish
Pages (from-to)168-176
Number of pages9
JournalInternational Journal of Non-Linear Mechanics
Publication statusPublished - 1 Mar 2017


  • Fingering instability
  • Hele-Shaw flow
  • Kinematic-wave model


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