Figure 3 - The domain of the expression with the cloth filter
(taken infinitely thin) at the LHS and the pressure piston at the RHS,
plus the notation and the two coordinate systems
At Γ 2 , the liquid flux u always equals
zero, implying that , thanks to Darcy’s law, and therefore, as in Eq.
(1.12):
A similar Neumann boundary condition for u is applied atΓ 1 during the rest mode after the filling has
been completed, resulting in similar boundary equation fore 1 at Γ 1 as Eq. (1.20).
With the view of the boundary condition for e 1 atΓ 1 during the filling mode and the pressing mode,
we use Eq. (1.1) to find
We then need values for e 2 and e atΓ 1, and to calculate e , given Eqs. (1.8)
and (1.14), also values for the strain εls and
the pressure at Γ 1 . For the latter, we need the
pressure drop Δpc over the cake which due to
Darcy’s law relates to the piston pressure ppapplied at Γ 2 :
in which R f denotes the flow resistance of the
filter cloth and R c that of the cake which
follows from
The void ratio e 2 is a function of time only and
therefore we need just an initial value for e 2for the whole domain:
withdenoting the solid fat volume fraction at random close packing. The
initial condition for e 1 runs as
Finally, the total void ratio e 0 of the porous
medium at the start of the expression step, needed in Eqs. (1.18) and
(1.19), is related to according to