Cannan-Kozeny equation

In principle, filter bed permeabilities can be calculated using the Cannan-Kozeny equation 2.53. For slurries containing irregular particles, however, cake filtrabilities together with filter medium resistance are determined using the Leaf Test (Figure 4.13). In this technique, a sample of suspended slurry is drawn through a sample test filter leaf at a fixed pressure drop and the transient volumetric flowrate of clear filtrate collected determined. 

When the pressure is increased further the flux increases linearly with pressure, see figure IV - 13). The Hagen-PoLscuillc relationship assumes that the pores in the membrane are cylindrical but generally this is not the case. Therefore, these limitations should be considered carefully in applying this equation.The Kozeny-Cannan equation can be used instead of the Hagen-Poiseuille equation. It is assumed in this equation that the pores are interstices between close-packed spheres as can be found in sinter structures. Tlie flux is given by cq. IV - 6. 

Ihe permeability method can be used both for microfiltration and ultrafiltiatimi membranes. As with most methods of characterisation, one of the main problems encountered is the pore geometry. As mentioned above, the Hagen-Poisseuille equation assumes that the pores are cylindrical whereas the Kozeny-Cannan equation assumes that the pores are interstices between close-packed spheres. Such pores are not commonly found in sjoithetic membranes. 

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