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Homogenization and Porous Media (Paperback, Softcover reprint of the original 1st ed. 1997)
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Homogenization and Porous Media (Paperback, Softcover reprint of the original 1st ed. 1997)
Series: Interdisciplinary Applied Mathematics, 6
Expected to ship within 10 - 15 working days
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For several decades developments in porous media have taken place
in almost independent areas. In civilengineering, many papers were
publisheddealing with the foundations offlow and transport through
porous media. The method used in most cases is called averaging,
and the notion ofa representative elementary vol-
ume(REV)playsanimportantrole.
Inchemicalengineering,papersonconceptual models were written on the
theory ofmixtures. Intheoretical physics and stochas- tic analysis,
percolation theory has emerged, providing probabilistic models for
systems where theconnectedness
propertiesofsomecomponentdominatethebe- havior. In mathematics,
atheoryhasbeendevelopedcalled homogenizationwhich deals with
partial differential equations having rapidly oscillating
coefficients. Early work in these and related areas was - among
others - done by the fol- lowing scientists: Maxwell [Max81] and
Rayleigh [Ray92] studied the effective conductivity of media with
small concentrations of randomly and periodically, respectively,
arranged inclusions. Einstein [Ein06] investigated the effective
vis- cosityofsuspensions with hard spherical particles in
compressible viscous fluids. Marchenko and Khrouslov [MK64] looked
at the asymptotic nature of homog- enization; they introduced a
general approach of averaging based on asymptotic tools which can
handle a variety ofdifferent physical problems. Unfortunately, up
to now, little efforthas been made to bridge the gap between these
different fields of research. Consequently, many results were and
are dis- covered independently, and scientists are almost unable to
understand each other because the respective languages have been
developing in different directions.
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