In filtration of high concentrated slurry, formation of cake takes place at the surface of filter medium. The pressure drop across the cake can be found by modifying the Kozeny-Carman equation which is used for finding pressure drop through bed of particles in laminar flow conditions.
As resistance is defined as driving force divided by flux. similarly here driving force is ΔPcA and flux is velocity v. and specific resistance will be resistance per unit mass of cake. Therefore, resistance is
Here, the resistance also includes the resistance due to viscosity . Therefore the specific cake resistance (α)would be
and the expression of specific cake resistance also is
The expression represents the properties like porosity, density, surface to volume ratio or size and shape of particle which are the characteristics of the cake. For an incompressible cake, specific cake resistance would be constant.
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