The Kozeny-Carman relationship (Billings and Wilder 1970; Carman 1956) is often used to describe pressure drop across a dust deposit. Rudnick and First (1978) showed that the Happel (1958) cell model corrected for slip flow gives better K2 estimates than the Kozeny-Carman relationship for a dust cake with no interaction between the fabric and cake. All theoretical models for K2 are sensitive to dust deposit porosity and dust particle size distributions. Porosity cannot usually be estimated correctly and varies with filtration velocity, humidity, and other factors. Whenever possible, K2 should be measured rather than calculated from theory. Leith and Allen (1986) suggest that the dust collected on a membrane filter and K2 should be calculated from the increase in pressure drop (AP2 - AP1) with filter weight gain (M2 - M1) as follows:
where A is the surface area of the membrane filter. Cleaning Fabric Filters
Dennis and Wilder (1975) present a comprehensive study on cleaning mechanisms. For a dust cake to be removed from a fabric, the force applied to the cake must be greater than the forces that bond the cake to the fabric. The major factors that combine to create both adhesion and cohesion are van der Waals, coulombic and induced dipole electrostatic forces, and chemical reactions between the gas and the dust. Capillary forces caused by surface tension are important under high relative humidity conditions.
The following equation calculates the drag across a single bag:
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