Abstract
In cross-flow membrane filtration, fouling results from material deposit which clogs the membrane inner surface. This hinders filtration, which experiences the so-called limiting flux. Among the models proposed by the literature, we retain a simple one: a steady-state reversible fouling is modelled with the use of a single additional parameter, i.e., , the ratio of the critical concentration for deposition to the feed concentration at inlet. To focus on fouling, viscous pressure drop and osmotic (counter-)pressure have been chosen low. It results in a minimal model of fouling. Solved thoroughly with the numerical means appropriate to enforce the nonlinear coupling between permeation and concentration polarization, the model delivers novel information. It first shows that permeation is utterly governed by solute transfer, the relevant non-dimensional quantities being hence limited to and , the transverse Péclet number. Furthermore, when the role played by and moderate (say ) is investigated, all results can be interpreted with the use of a single non-dimensional parameter, , the so-called fouling number, which simply reads . Now rendered possible, the overall fit of the numerical data allows us to put forward analytical final expressions, which involve all the physical parameters and allow us to retrieve the experimental trends.
Highlights
Membrane filtration systems are conceived to perform species separation
A situation of permeation controlled by Darcy’s law in cross-flow filtration has been studied together with the implications of a standard model of reversible fouling, which consists of imposing a material deposit, as long as a critical concentration is reached
Deposit stops—and the related wall resistance reaches a steady state—when the permeation diminishes and causes a polarization of concentration that corresponds to the critical concentration
Summary
Membrane filtration systems are conceived to perform species separation. They consist of selecting semi-permeable membranes that retain the targeted species, while some others cross the membranes. The retained species accumulate in a mass boundary layer that develops along the membrane inner surface, giving rise to the so-called polarization of concentration Such an increase in concentration at the membrane, which results from the competition between advection towards the membrane and diffusion back to the bulk, may induce two types of hindrance to permeation: osmotic (counter-)effects and membrane fouling. Prandtl equations offer a simplified model which allows us to reduce the computational cost and to enforce the nonlinear coupling between filtration and concentration polarization at the membrane surface [41] In this way, the present paper numerically investigates the reversible fouling within the framework of a 2D channel flow. The role played by the main physical parameters is investigated
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