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.