A continuous filtration process that starts with a new, particle-free filter medium usually goes through the following phases in the typical theoretical description: The initial depth filtration in the given filter medium, the clogging phase in the given filter medium and the cake-forming filtration. These successive phases have been described using different modeling concepts, which make a holistic view of the entire filtration process difficult.

In the new multi-layer construction model presented by Zhang, the particle separation takes place during the entire filtration process in two coexisting filtering systems: In the case of a fiber layer as a filter medium, a fiber packing represents the one filtering system. All particles deposited in and on the fiber packing are regarded as the other coexisting filtering system, in which all these particles can be described together in form of a granular bed. Model calculation of the continuous filtration process can be carried out on this basis.

This multi-layer construction model does not consider interactions between the filtering elements or the filtering systems, such as momentum transfer and therefore no movement or release of already deposited particles, the reduction of the filtering surface of the existing filtering elements or other effects. The modeling of the reduction of the effective filtering surface due to particle contacts and its integration into the multi-layer construction model of Zhang is subject of this contribution. The decrease in the effective filtering surface of the fiber packing can be taken into account using information about the number of contact points between fiber and deposited particles, whereas the describing of the reduction of the effective filtering surface of the granular bed is more difficult. One approach is to apply the traditional dendrite model with a corresponding adjustment. The results of the improved model calculation, taking interactions into account, are compared with the results obtained without these interactions...