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).