A General Approach for Predicting the Filtration of Soft and Permeable Colloids: The Milk Example

Abstract

Membrane filtration operations (ultra-, microfiltration) are now extensively used for concentrating or separating an ever-growing variety of colloidal dispersions. However, the phenomena that determine the efficiency of these operations are not yet fully understood. This is especially the case when dealing with colloids that are soft, deformable, and permeable. In this paper, we propose a methodology for building a model that is able to predict the performance (flux, concentration profiles) of the filtration of such objects in relation with the operating conditions. This is done by focusing on the case of milk filtration, all experiments being performed with dispersions of milk casein micelles, which are sort of ″natural″ colloidal microgels. Using this example, we develop the general idea that a filtration model can always be built for a given colloidal dispersion as long as this dispersion has been characterized in terms of osmotic pressure Π and hydraulic permeability k. For soft and permeable colloids, the major issue is that the permeability k cannot be assessed in a trivial way like in the case for hard-sphere colloids. To get around this difficulty, we follow two distinct approaches to actually measure k: a direct approach, involving osmotic stress experiments, and a reverse-calculation approach, that consists of estimating k through well-controlled filtration experiments. The resulting filtration model is then validated against experimental measurements obtained from combined milk filtration/SAXS experiments. We also give precise examples of how the model can be used, as well as a brief discussion on the possible universality of the approach presented here.

Ultrafiltration of charge-stabilized dispersions at low salinity

“…There exists a larger number of theoretical works on the UF of charge-stabilized dispersions, both for nonsteady dead-end (frontal) [2,[19][20][21] and steady crossflow [3,22,23] setups. In most of these works, the concentration and salt content (salinity) dependence of Π and D c has been described using approximate expressions and numerical results.…”

Effect of pH, transmembrane pressure and whey proteins on the properties of casein micelle deposit layers

“…Two different approaches can be found in recent literature, explaining particle-particle interaction in CM suspensions or deposit layers. Some studies relate repulsive forces to a macroscopic concentration based on the so called osmotic pressure concept [6][7][8]. Another model is based on microscopic particle-particle interactions based on DLVO-theory [9] or xDLVO-theory [10,11].…”

Negatively charged tangential flow ultrafiltration membranes for whey protein concentration

“…Therefore, if the flux is not controlled, the polarization index β¼ J v /k is too high, leading to a thick deposit layer, and flux decline. Others have also described this phenomenon [18][19][20][21][22]29,30]. Several studies have also shown constant flux operation increases the lifetime of the membrane and reduces the time for cleaning-in-place compared to constant trans-membrane pressure operation [31,32].…”