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A first principles microfiltration model based on shear-induced diffusion is compared to experiments performed on the clarification of beer. After performing an identifiability and sensitivity analysis, the model parameters are estimated using global minimization of the sum of least squares. The model is compared to different series of experiments, where either crossflow or permeate flux is varied. This study is concluded with a parameter study on the scaling of the filtration time with various model parameters. We have found that the filtration time primarily depends on two dimensionless numbers, namely the normalized critical distance for cake layer formation, and the dimensionless time required to plug all pores in the selective layer. We have found that there is an optimal setting of these parameters, rendering a maximal amount of filtrated beer in one cycle.

Models of fouling during beer clarification, previously validated for dead-end filtration, are combined with a model describing the build-up of the cake layer of yeast cells via shear-induced diffusion induced by crossflow. For describing shear-induced diffusion, we have taken the most recent model, which is based on the effective temperature concept. Via scale analysis we show that (1) effects of polydispersity are negligible and (2) the cake layer growth model still be reduced to the earlier model of Romero and Davis, albeit with different parameter values. The adapted Romero and Davis model has been coupled to the earlier reviewed models of fouling by aggregates and macromolecules, for which we have performed computer simulations. In this paper we report on striking results on the downstream movement of the critical point, xcr, where the cake layer starts building up. We show that this is due to strong coupling between the cake layer build-up and the other fouling modes. Hence, this means that the concept of critical flux can not be viewed any more as a time-invariant value. This finding has implications beyond the application of beer, and especially for biotechnological broths which have similar composition of beer.

For micro-machined membranes, it is possible to choose pore size, pore geometry and membrane porosity, within certain limits. Different pore geometries (circular, square, slit shaped and triangular pores), particle size to pore size ratios, pore edges and membrane porosities were evaluated with lattice-Boltzmann computer simulations and torque balance considerations for various modes of operation. We focused on hydrodynamic interactions and assumed uncharged neutral surfaces of the particle and the pore. However, the model can easily be extended with additional relations for such interactions in practical systems with defined properties. It was concluded that pore geometry can have a large effect on the flux (up to 60%). Further, the effect of shielding could be quantified. Above a surface coverage of 0.05, the particles effectively shield each other from the flow field, therewith necessitating either a higher cross flow velocity or a lower transmembrane pressure for particle removal. Based on the simulations, an extended criterion for the critical flux was developed, which includes the effects of pore geometry, particle to pore size ratio and membrane porosity. Different optimal membrane choices follow for processes aimed at retention of all particles, and for processes aimed at fractionation of particles into different fractions.

During cross-flow membrane emulsification, droplet formation at a micro-engineered membrane with uniform pores was visualized by microscopy. Although the membrane pores were uniform in size, the obtained emulsions were polydisperse. Observations showed this to be due to steric hindrance of droplets forming simultaneously. At some pores close together, the droplet formation frequencies were almost identical (0.86 and 0.88 s −1 ). This was confirmed by the cross-correlation value (around 0.8). Because the droplets hindered each other during growth, the droplet diameter decreased with an increasing number of active pores. In spite of the uniform pore size and shape, the number of active pores only gradually increased upon increasing transmembrane pressure. We suggest this to be due to the dynamics of the flow of the to-be-dispersed phase towards and through the membrane. Under the process conditions used, interactions can only be prevented by using a membrane with a lower porosity.