By M Sahini, M Sahimi
This special graduate textual content discusses these functions for which there are well-defined percolations, and the place direct comparability among the predeictions of types and experimental info is feasible.
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Extra resources for Applications Of Percolation Theory
64) 32 MOMENTUM BALANCE. 57)). 31). 32). 3. 69) ADVANCED ANALYSIS 33 ◦ where the term r 1→2 Vf2 − Vf1 accounts for the variation in linear momentum related to the mass rate exchanged between the two porous networks. 71) where ρ stands for the total apparent mass density, namely ρ = ρs (1 − n) + α=1,2 ρfα nα . 71), when multiplied by dt, that is −(pα /ρfα )w(α) · n dadt = −pα nα Vf α − Vs · n dadt, represents the work supplied by the pressure pα in the extraction of the ﬂuid volume nα Vf α − Vs · n dadt from the domain occupied by the skeleton.
12) es stands for the speciﬁc internal energy of the matrix (or equivalently the intrinsic speciﬁc energy of the skeleton). Accordingly the left hand term accounts for the time rate of the energy attached to the whole matter currently contained within the volume t , including its kinetic form. 3), while Q accounts for the rate of heat externally supplied. 13) t where JQ is the surface rate of heat supplied by conduction. This heat supply is due to contact effects and therefore, as it concerns space, depends only on the position vector x and on the outward unit normal n to surface da.
1 Strain Work Rates The strain work rate associated with a velocity ﬁeld V is the sum of the work rates developed in this ﬁeld, both by body and surface forces and by inertia forces, the latter being the opposite of the dynamic forces. 6) this sum is zero for a velocity ﬁeld related to any rigid body motion of the material domain, which assigns the same velocities to the skeleton and to the ﬂuid. Accordingly, let V be any velocity ﬁeld, but let it be the same for the skeleton and the ﬂuid. 39) 28 MOMENTUM BALANCE.