Calibration of the model
A straightforward validation of model predictions by means of
experimental data collected in these tests is hampered by several
experimental technicalities. First of all, as the model is 1-D, it
presumes a uniform composition of the medium in the other two directions
and it ignores fluid motion and mixing, which certainly is not the case
during the filling stage. A combined filtration and consolidation
process already starts spontaneously during the filling of the filter
chambers without any pressure being imposed. The simulation of the
expression starts as soon as in the filling stage the inter-aggregate
porosity ε 1 falls below at the random close
packing when the agglomerates start feeling they get compressed. In the
tests, the filling is followed by a waiting period of some 20 s before
the pressure is applied. In the simulations, this waiting period, or
rest mode, is realized by imposing a zero outflow atΓ 1. Then, pressure is applied and expression
resumes resulting in a continued outflow. Another awkward technicality
is that in the tests the separated liquid is staying behind in the
tubing and piping between filter and collecting bin, while also the
residence time in the collecting system leading to a retarded response
of the balance is not in the model. A perfect match between model
simulation and experiment is therefore not to be expected. We therefore
carried out a calibration step first.
Table 2 presents model constants, physical properties, dimensions and
simulation parameters used in both the calibration study and the
validation study. The number of intervals J was selected after a
sensitivity analysis with the view of balancing computational burden and
accuracy. The flow resistance Rf of the filter
cloth had been measured separately by filtering oil without solid fat.
The solidosity srcp at random close packing was
obtained by measuring the solid fat content of a cake in centrifugation
experiments. The initial value e 0 follows fromsrcp thanks to Eq. (1.26). In its turn,e 0 is used in estimatingCe 0 with Eq. (1.18). The initial
thickness L 0 of the filter cake was set to 2.05
cm in an attempt to correct for the loss of liquid in the first phase of
the filling stage when there was outflow without pressure being applied.
Then, Eq. (1.2) was used to calculate Ω withsrcp = 0.228 as found in our experiments.
However, the model contains three more parameters we actually do not
know from the onset, viz. the aggregate diameterda occurring in Eqs. (1.18) and (1.19), the
inter-aggregate solidosity at random close packing needed to calculate
the initial values e 1,0 ande 2,0 with Eqs. (1.24) and (1.25), and the solid
fat content, or total solidosity s , at the start of the
expression process.