Compression of a Fouling Layer

During a membrane filtration process, the fouling layer is compressed due to frictional drag and the mass of the particulate layer accumulated. For any given control mass, the value of (1—e)Ax as indicated in the right hand side of Equation (15.2) 

Taking a mass balance for a flowing fluid within the controlled mass, the difference between inward and outward permeate flow is equal to the decreased void volume per unit area in a time increment, that is  

Equation (15.6) is known as the continuity equation of cake compression [43]. This equation can be employed to describe the relationship between the change of the flow rate of the filtrate and the porosity variation of fouling layer. Moreover, since some flowing fluid is squeezed out toward the permeate side due to compression of the fouling layer, the fluid flow rate of permeate is larger than that at the layer surface. Taking a mass balance for the whole fouling layer, the ratio of the fluid flow rate at the layer surface, to the flow rate of the permeate, q, can be estimated by [44]  

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Fouling layers, in general, are compressible, that is they become more compact as the extent of their compression increases. Solid compressive pressure is responsible for the compression of a fouling layer according to basic filtration theory [46]. In traditional filtration theory, the derivation of the drag equations of filtration for rigid particle slurries assume that particles are in point contact mode and that compression attends instantaneously. Under this assumption, a force balance can be obtained between liquid pressure over the entire cross-section and the solid compressive pressure on the total mass within the porous layer as ... 

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