Miscible displacement in a Hele-Shaw cell
type: Item
instance of: scholarly article
title: Miscible displacement in a Hele-Shaw cell
zbMATH Open document ID: 0756.76078
DOI: 10.1007/BF00946254
author: Howard H. Hu
author: D. D. Joseph
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1993-01-16T00:00:00Z
review text: A theory of viscous isothermal gravity driven flow in a Hele-Shaw cell model for two miscible incompressible each one homogeneous and isotropic liquids (such as glycerin displacing water or vice versa) is presented. The governing time and space depending partial differential equations for the laminar velocity field, pressure and volume concentration distribution of the mixture are given and discussed in detail. They are then solved under further simplifying assumptions, for given density and viscosity dependence on the concentration and appropriate initial and boundary conditions. The crucial assumption of non-solenoidal mass averaged velocity field, as it is correct from physical point of view by this problem, enables concentration gradient stresses (Korteweg's stresses) to be taken into account, too. The stability problem of this flow is also studied and solved for the case of steady miscible displacement. The numerical methods employed for solving the final partial differential equation of the problem are only mentioned. As one of the possible applications of this theory could be the problem of miscible displacement in oil-bearing sand.
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 76E17
Mathematics Subject Classification ID: 76E99
zbMATH DE Number: 92529
zbMATH Keywords: Korteweg's stresses
zbMATH Keywords: viscous isothermal gravity driven flow
zbMATH Keywords: homogeneous and isotropic liquids
zbMATH Keywords: volume concentration distribution
zbMATH Keywords: non-solenoidal mass averaged velocity field
zbMATH Keywords: oil-bearing sand
reviewed by: Tomislav Zlatanovski
MaRDI profile type: Publication
cites work: Short-wave instabilities and ill-posed initial value problems
full work available at URL: https://doi.org/10.1007/bf00946254
OpenAlex ID: W2008700471
description: scientific article; zbMATH DE number 92529