Soil Physics - Chapter 3 - Fluids In Porous Media - Skript - Kurt Roth - Institut FR Umweltphysik - UniversitT Heidelberg - 2006.pdf

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Fluids in Porous Media
In a large partment – a river, lake, or the atmosphere – the dynamics
is typically dominated by the nonlinear inertia term [v ]v which causes
turbulence. Boundary conditions on the other hand are ·simpl∇ e because the
direct influence of the boundaries extends only through a small fraction of
the flow domain. In contrast, the dynamics of fluids in porous media is
generally dominated by the porous matrix which pervades the entire volume
and causes a very efficient dissipation of the fluid’s momentum and ic
energy. This also leads to a simple internal dynamics, essentially described
by Stokes’ law. In the following, we thus first look at the nature of porous
media and then at mon approach to handle the difficulties introduced
by plicated shape of the flow domain.

Porous Media
As essential properties of a porous medium we postulate:
1. The total volume is divided into solid matrix and pore space, with the
latter filled by one or more fluids.
2. Every volume element down to a characteristic size ! contains solid
matrix as well as pore space.
3. Since we focus on fluid movement, only the connected fraction of the
pore space is of interest.
Closer scrutiny of the last two points reveals that a precise and general
definition of a porous medium is cumbersome. What is the size of !, for
instance? Choosing it too small would exclude stony soils while a value that
is too large would modate strange media like karstic caverns. Whatever
the eventually chosen size, ! has to be very much smaller than the extent
of the total volume of interest. After all, there is no point in considering
three grains of sand and the space between them as a porous medium. For
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40 3 Fluids in Porous Media
Figure .
Artificial porous medium created from sieved sand
poured between two parallel glass plates, a so-called
Hele-Shaw cell. This may serve as a simple two- 1 mm
dimensional model for a porous medium.
such objects, the shape of t