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We investigated the fractionation of casein micelles and the whey protein β-lactoglobulin (β-LG) of skim milk by crossflow microfiltration (0.1 μm) for the first time by a novel approach as a function of membrane length and membrane resistance. A special module was constructed with 4 sections and used to assess the effects of membrane length by measuring flux and β-LG permeation (or transmission) as a function of transmembrane pressure and membrane length. Depending on the position, the membranes were partly controlled by a deposit layer. A maximum for β-LG mass flow through the various membrane sections was found, depending on the position along the membrane. To study the effect of convective flow toward the membrane, membranes with 4 different intrinsic permeation resistances were assessed in terms of the permeation and fouling effects along the flow channel. From these findings, we derived a ratio between transmembrane pressure and membrane resistance, which was useful in reducing the effect of deposit formation and, thus, to optimize the protein permeation. In addition, the fouling effect was investigated in terms of reversible and irreversible fouling and, in addition, by differentiation between pressure-induced fouling and adsorption-induced (pressure-independent) fouling, again as a function of membrane length.

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The volume of a liquid bridge between two spherical particles can be used to calculate the critical separation distance and the rupture energy. There exist a number of explicit but very complex equations for the calculation of the bridge volume as a function of the half-®lling angle. In this paper, an empirical equation is presented that strongly simpli®es these calculations. In addition, the presented approach leads to a calculation of the half-®lling angle from the bulk liquid saturation which may be used for the estimation of the tensile strength of a wet powder.