COMPARATIVE ANALYSIS OF THE DARCY AND BRINKMAN APPROXIMATIONS FOR THE TRANSITION TO INSTABILITY IN A POROUS MEDIUM-Reference-Cited by-同舟云学术

COMPARATIVE ANALYSIS OF THE DARCY AND BRINKMAN APPROXIMATIONS FOR THE TRANSITION TO INSTABILITY IN A POROUS MEDIUM

Published:2023-01-01 Issue:1 Volume:508 Page:30-34
ISSN:2686-7400
Container-title:Доклады Российской академии наук. Физика, технические науки
language:
Short-container-title:Doklady Rossijskoj akademii nauk. Fizika, tehničeskie nauki

Author:

Il’ichev A. T.¹,Tsypkin G. G.¹

Affiliation:

1. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Abstract

We studied the stability of the evaporation front in a porous media. To describe the flow, the generalized Brinkman equation is used. Comparison of the obtained results with the results found within the framework of the Darcy approximation is presented. It is shown, that the use of the Brinkman approximation eliminates the unboundedness of the perturbation growth rate at small scales arising in the case of Darcy’s law. Interface becomes more stable, and in the case of instability the most unstable mode corresponds to the finite value of the wave number.

Publisher

The Russian Academy of Sciences

Reference13 articles.

1. Saffman P.G., Taylor G.I. The Penetration of a Fluid into a Porous Medium or Hele-Shaw Cell Containing a More Viscous Liquid // Proc. R. Soc. London, 1958. A 245. P. 312–329.

2. Rose D.A., Konukcul F., Gowing J.W. Aust. J. Hele-Shaw Cell Containing a More Viscous Liquid // Soil Res. 2005. V. 43. P. 565–573.

3. Il’ichev A.T., Tsypkin G.G., Pritchard D.T., Richardson C.N. Instability of the salinity profile during the evaporation of saline groundwater // J. Fluid Mech. 2008. V. 614. P. 87–104.

4. Schubert G., Straus J.M. Gravitational stability of water over steam in vapor-dominated geothermal system // J. Geophys. Res. 1980. V. 85. P. 6505–6512.

5. Tsypkin G.G., Il’ichev A.T. Gravitational stability of the water-vapor phase transition interface in geothermal systems // Transport in porous media. 2004. V. 55. P. 183–199.