Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-30T15:26:32.418Z Has data issue: false hasContentIssue false
  • English
  • Français

Moving boundary problems in the flow of liquid through porous media

Published online by Cambridge University Press:  17 February 2009

A. A. Lacey
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The movement of the interface between two immiscible fluids flowing through a porous medium is discussed. It is assumed that one of the fluids, which is a liquid, is much more viscous than the other. The problem is transformed by replacing the pressure with an integral of pressure with respect to time. Singularities of pressure and the transformed variable are seen to be related.

Some two-dimensional problems may be solved by comparing the singularities of certain analytic functions, one of which is derived from the new variable. The implications of the approach of a singularity to the moving boundary are examined.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 2 , October 1982 , pp. 171 - 193
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]McGeough, J. A., Principles of electro-chemical machining (Chapman and Hall, London, 1974).Google Scholar
[2]Muskat, M., The flow of homogeneous fluids through porous media (McGraw-Hill, New York, 1937).Google Scholar
[3]Ockendon, J. R., “Numerical and analytic solutions of moving boundary problems”, in Moving boundary problems (eds. Wilson, D. G., Solomon, A. D. and Boggs, P. T.), (Academic, New York, 1978).Google Scholar
[4]Richardson, S., “Hele-Shaw flows with a free boundary produced by the injection of fluid into a narrow channel”, J. Fluid Mech. 56 (1972), 609–618.Google Scholar
[5]Rose, W., “Fluid-fluid interfaces in steady motion”, Nature 191 (1961), 242–243.CrossRefGoogle Scholar
[6]Strakhov, V. N., “Notes concerning the plane gravimetry problem”, Physics of the Solid Earth 6 (1970), 774–779.Google Scholar
[7]Zhdanov, M. S., “Some problems in the theory of interpretation of gravitational anomalies depending on three co-ordinates”, Physics of the Solid Earth 10 (1974), 565–571.Google Scholar