Abstract
In this chapter we develop the coupled diffusion and seepage problem using the theory of mixtures. It is clearly understood that the diffusion problem is strongly linked to the seepage problem through the mass conservation law. Adsorption on the solid surface is treated using the concept of an ‘adsorption isotherm’.
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Notes
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In most textbooks, the shearing kinematic viscosity is denoted as ν, whereas we employ the notation μ ‡ and ν ‡ for shearing and volumetric kinematic viscosities, respectively, since we consider the fluid to be compressible.
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Note that under the base vectors \(\{{\mathbf{e}}_{i}^{{_\ast}}\}\) differential operators in the normalized space are defined by \({\text{ grad}}^{{_\ast}} = {\nabla }^{{_\ast}} ={ \mathbf{e}}_{i}^{{_\ast}} \frac{\partial \ } {\partial {x}_{i}^{{_\ast}}},\qquad {\text{ div}}^{{_\ast}} = {\nabla }^{{_\ast}}\cdot,\qquad {\Delta }^{{_\ast}} = {\nabla }^{{_\ast}}\cdot {\nabla }^{{_\ast}}.\)
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© 2012 Springer-Verlag Berlin Heidelberg
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Ichikawa, Y., Selvadurai, A.P.S. (2012). Classical Theory of Diffusion and Seepage Problems in Porous Media. In: Transport Phenomena in Porous Media. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25333-1_5
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DOI: https://doi.org/10.1007/978-3-642-25333-1_5
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25332-4
Online ISBN: 978-3-642-25333-1
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