For fine suspended solids with particles that are too small to be separated from the liquid by gravitational or centrifugal methods, a "barrier" method such as a filter may be used. The liquid is passed through a filter medium (usually a cloth or screen) that provides a support for the solid particles removed from the slurry. In actuality, the pores in the filter medium are frequently larger than the particles, which penetrate some distance into the medium before being trapped. The layer of solids that builds up on the surface of the medium is called the cake, and it is the cake that provides the actual filtration. The pressure-flow characteristics of the porous cake primarily determine the performance of the filter.

A. Governing Equations

A schematic of the flow through the cake and filter medium is shown in Fig. 13-6. The slurry flow rate is Q, and the total volume of filtrate that passes through the filter is V. The flow through the cake and filter medium is inevitably laminar, so the resistance can be described by Darcy's law and the permeability of the medium (K):

Applying this relationship across both the cake and the filter medium in series gives p - p2=(KUf) <13-3ยป)

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