Summary
The present paper is based onBiot's theory of flow of fluids through a porous deformable medium. The presence of a distribution of sources of fluids in the medium gives rise to an additional term in the generalizedDarcy's law. The present note is concerned with solutions of the displacement equations ofBiot's theory for the case of fluid sources. The regular solution of these equations is given in terms of special functions. The singular solution — connected with the action of fluid sources — is obtained with the aid of the principle of reciprocity of displacements.
Zusammenfassung
Die vorliegende Arbeit benützt dieBiotsche Theorie der Flüssigkeitsströmung durch ein poröses deformierbares Medium. Das Vorhandensein einer Quellverteilung gibt Anlaß zu einem zusätzlichen Glied im verallgemeinertenDorcyschen Gesetz. Für diesen Fall werden Lösungen derBiotschen Verschiebungs-gleichungen angegeben. Die reguläre Lösung wird in speziellen Funktionen angegeben. Die singuläre Lösung — mit den Flüssigkeitsquellen verknüpft — wird mit Hilfe der Reziproxität der Verschiebungen erhalten.
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Derski, W. Some contributions to the theory of flow of fluids through porous deformable media. Acta Mechanica 4, 13–26 (1967). https://doi.org/10.1007/BF01291084
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DOI: https://doi.org/10.1007/BF01291084