Abstract
A mathematical model is developed of an abrupt pressure impact applied to a compressible fluid flowing through a porous medium domain. Nondimensional forms of the macroscopic fluid mass and momentum balance equations yield two new scalar numbers relating storage change to pressure rise. A sequence of four reduced forms of mass and momentum balance equations are shown to be associated with a sequence of four time periods following the onset of a pressure change. At the very first time period, pressure is proven to be distributed uniformly within the affected domain. During the second time interval, the momentum balance equation conforms to a wave form. The behavior during the third time period is governed by the averaged Navier-Stokes equation. After a long time, the fourth period is dominated by a momentum balance similar to Brinkman's equation which may convert to Darcy's equation when friction at the solid-fluid interface dominates.
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References
Barta, E., Israeli, M., and Kivity, Y., 1982, Wave structure in the aorta with initial axial tension, in R. Huiskes, D. Van Campen, and J. De Wijn (eds.), Biomechanics, Principles and Applications, Martinus Nijhoff, The Hague, pp. 339–343.
Bear, J. and Bachmat, Y., 1986, Macroscopic modeling of transport phenomena in porous media, 2: Applications to mass, momentum and energy transport, Transport in Porous Media 1, 241–270.
Kivity, Y. and Collins, R., 1973, Nonlinar wave propagation in viscoelastic tubes: Application to aortic rupture, J. Biomech. 1, 67–76.
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Sorek, S., Bear, J. Evolution of governing mass and momentum balances following an abrupt pressure impact in a porous medium. Transp Porous Med 5, 169–185 (1990). https://doi.org/10.1007/BF00144602
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DOI: https://doi.org/10.1007/BF00144602