Figure 8 - Volume fractions vs position in the cake as
calculated by our model with the set of coefficients of Eq. (1.30) for
test #1. The position of the filter cloth on the left is fixed. The
total thickness of the filter cake decreases over time. The lower
surface represents ε 1 (the inter-agglomerate
liquid), the middle oneε 2s 1 (the
intra-agglomerate liquid) and the upper one is total solidositys 2s 1 (=s ). The
times t fill , t rest andt press denote the times passed since the start of
the filling, rest, and pressing modes, respectively.
spatial and temporal evolution of the filter cake composition which lies
at the basis of the outflow velocity. Figure 8 presents a typical
result, for test #1, in terms of the volume fractionsε 1 (the inter-agglomerate liquid) andε 2s 1 (the
intra-agglomerate liquid) and the total solidositys 2s 1 (=s ). Each of
these three volume fractions which add up to unity, has been coloured
with a different shade of ochre. Each panel of Figure 8 shows, for a
specific moment in time, the composition of the cake as a function ofx (translated from ω ). The upper curves in the four panels
exhibit the typical propagating error function shape associated with
transient diffusion, with penetration time of the order of 0.2 min
(viz. ,), while three of the four lower, ε 1, curves are rather flat, indicating the release of fat from the
agglomerates is rate limiting for the fat separation through the filter
cloth. This is due to the second-order diffusion equation fore 1 while e 2 obeys a simple
mass balance. The total thickness of the filter cake decreases over time
as indicated by the position of the piston. This decrease clearly slows
down as permeability decreases over time, see Eq. (1.13), while the
elastic modulus increases, see Eq. (1.15).