A combined network model for membrane fouling

Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances, and deposition on the membrane surface. Each of these fouling mechanisms results in a decline in the observed flow rate over time, and the decrease in filtration efficiency can be characterized by a unique signature formed by plotting the volumetric flux, Q^, as a function of the total volume of fluid processed, V^. When membrane fouling takes place via any one of these mechanisms independently the Q^V^ signature is always convex downwards for filtration under a constant transmembrane pressure. However, in many such filtration scenarios, the fouling mechanisms are inherently coupled and the resulting signature is more difficult to interpret. For instance, blocking of a pore entrance will be exacerbated by the internal clogging of a pore, while the deposition of a layer of contaminants is more likely once the pores have been covered by particulates. As a result, the experimentally observed Q^V^ signature can vary dramatically from the canonical convex-downwards graph, revealing features that are not captured by existing continuum models. In a range of industrially relevant cases we observe a concave-downwardsQ^V^ signature, indicative of a fouling rate that becomes more severe with time. We derive a network model for membrane fouling that accounts for the inter-relation between fouling mechanisms and demonstrate the impact on the Q^V^ signature. Our formulation recovers the behaviour of existing models when the mechanisms are treated independently, but also elucidates the concave-downward Q^V^ signature for multiple interactive fouling mechanisms. The resulting model enables post-experiment analysis to identify the dominant fouling modality at each stage, and is able to provide insight into selecting appropriate operating regimes.