the experimental results. In the current numerical simulations an optimal coverage of the different membranes was studied, corresponding to the sketches presented in Figure 53b, d and f. The results of the qualitative analysis were the base to define the simplified model geometries for the simulations (Figure 51). The pressure drop across the system for the three scenarios is calculated to assess the contributions of the membrane and the membrane blocking to the total resistance.
The simulation results allow the calculation of the hydraulic resistance of the first layer of particles (blocking layer), which are responsible for the partial blocking of the membrane. In order to compare the hydraulic resistance caused by the first layer with the experimental results, the mean height of the layer of blocking particles is calculated for the total surface based in the geometry of the membrane (specifically Pe). The number of particles depends on the spacing between the slots per unit of membrane surface, for this reason, the height is not the same for the three geometries. The lowest value of Pe (C4Pe7) yields a larger height of the blocking layer; for a higher distance between slots (C4Pe20) there are fewer slots and hence less particles blocking them, this makes the blocking layer height smaller. It must be pointed out that the height the blocking layer for each membrane configuration is always lower than d, the particle diameter, for the previous reason, but also due to particles embedding in the slots. As these simulations were run for the blocking layer, the resistance is represented by a single point for each membrane configuration, which corresponds to the three hollow symbols in Figure 62.
132 Figure 62. Experimental values of the hydraulic resistance caused by membrane blocking for the
different geometries when the first layers are forming (dashed lines with symbols). Symbols represent the simulation results for the membrane blocking resistance (< 1 layer of particles).
Figure 62 shows the comparison of the simulated (<1 layer) and the experimental (~3 layer) hydraulic resistance caused by the cake and the membrane blocking as a function of the cake mean height during the beginning of the filtration. Hollow symbols represent the simulation results for the cake hydraulic resistance when the slots are optimally blocked for each membrane geometry. The values are plotted as a function of the mean height for the corresponding geometry. Note the proximity of the simulations with the respective experimental curve at the early membrane blocking (< 1 layer ~3-7 µm depending on the membrane geometry and particles embedded in the slots). This indicates that the experimental data is in a consistent range. However, there is a difference in the resistance obtained from the simulations for the different geometries. This could be explained by the assumption of an optimal blocking of the slots by the particles; this is not always the case in the real experiments and is likely a reason why the simulations are not in full agreement with the experimental curves. Here the experimental variations of Rc vs. h are assumed to be linear from 0 to the first measured
point.
The results also validate the previous analysis regarding the “pore protection” phenomenon. Using again the definition of the pore protection coefficient pp. The filtration experiment using the
C4Pe7 membrane has the lowest pp = 0.68, which leads to a higher “pore protection” effect. This is
in agreement with the calculated hydraulic resistance, being the lowest of the three membrane configurations. Both C4Pe10 and C4Pe20 have pp > 1 with values of 1.36 and 3.64 respectively, in
0.0E+00 5.0E+07 1.0E+08 1.5E+08 2.0E+08 2.5E+08 3.0E+08 3.5E+08 0 5 10 15 20 25 30 RC (m -1) h (µm) C4Pe7 Sim C4Pe10 Sim C4Pe20 Sim C4Pe7 Exp C4Pe10 Exp C4Pe20 Exp
133 this case there is no effect of the geometry on the “pore protection”. The higher hydraulic resistance for the blocking of the C4Pe20 unit is caused by the effect of a less permeable membrane geometry to the flow (Table 9).
V.Conclusion
The system and the methodology developed based on microfabrication techniques are found to be of high interest when characterizing the early filtration process of micrometric spherical particles. The cake growth and its heterogeneity are analyzed by the cake growth monitoring module (CGM), which easily tracks the cake surface. This information is coupled with the concentration and velocity estimates to evaluate the mass balance and perform an extensive quantitative analysis. An additional qualitative analysis is performed to characterize the structure of the first particle layers. The observations are used to characterize and model the cake geometry for the conducted simulations. The velocity is assessed using image processing and it allows measurements of the flowrate. Combining the velocity information with the pressure measurements makes possible the characterization of filtration processes where both the pressure and the flowrate are variables. The analysis showed a good agreement with previous reported information regarding the porosity and Kozeny coefficient.
The filtration performance for the different membrane geometries is similar, but the pressure drop can be affected by the distance between slots. The initial cake structure is visibly conditioned by the membrane construction parameters, and it has an influence on slot blocking and further cake build up, which impacts the pressure drop. The introduction of the pore protection coefficient (pp)
offers a quantitative characterization of the membrane-particle interaction based on the geometry. It proves to be an accurate parameter when used to characterize and compare the results obtained by Ben Hassan et al. [39].
The numerical simulations provide a means of rationally evaluating the role of the initial conditions of the cake formed at the membrane. The simulation results for the initial layer hydraulic resistance are in close agreement with the experimental data for the current suspension.
With the validation and global characterization, the system is then used to study the filtration of more complex suspensions. The characterization of the filtration of yeast suspensions and the associated cake properties is addressed using the microfiltration set-up and the DO technique.
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