Poiseuilles’ cake filtration equation

In the case of multiparticle blockage, as the suspension flows through the medium, the capillary walls of the pores are gradually covered by a uniform layer of particles. This particle layer continues to build up due to mechanical impaction, particle interception and physical adsorption of particles. As the process continues, the available flow area of the pores decreases. Denoting as the ratio of accumulated cake on the inside pore walls to the volume of filtrate recovered, and applying the Hagen-Poiseuille equation, the rate of filtration (per unit area of filter medium) at the start of the process is ... 

In developing the filtration rate equation, it is assumed that the velocity of fluid through cake pores obeys the Hagen-Poiseuille Law ... 

The flow of the filtrate through the packed bed of cake can be described by an equation similar to Poiseuille s law, assuming laminar flow occurs in the filter channels. Equation (2.10-2) gives Poiseuille s equation for laminar flow in a straight tube, which can be written... 

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