The role of porosity in filtration: Part V. Porosity variation in filter cakes

Abstract

Expressions are derived in which local porosity in a filter cake is determined as a function of the distance through the cake. Under conditions where the superficial flow rate through the cake is constant and the medium pressure can be neglected, local porosity and the hydraulic pressure are functions of the fractional cake distance.Equations are derived that give the average porosity of a cake as a function of applied filtration pressure.

Properties of Filter Cake in Cake Filtration and Membrane Filtration

“…In the compressible filter cake formed by ultrafiltration of BSA solutions, it is demonstrated that a pronounced variation of characteristic values of the filter cake can be seen. This is in agreement with the results obtained for filtration of particulate suspensions [9,18]. The local mass fraction c of the solute in the filter cake may be calculated from the local void ratio e in the form c҃ (19) Thus, the concentration distributions in the protein filter cake may be predicted from Eqs.…”

“…The figure distinctly demonstrates that there exists a concentration distribution within the filter cake formed on the membrane. The concentration c has a maximum at the membrane surface (x҃0) and decreases markedly with the increase of x, which shows the same trend as that observed for the cake filtration of particulate suspensions [9,18]. It was verified that the solutes forming the cake are compact and dry at the membrane whereas the surface layer is in a wet and soupy condition.…”

“…(15) and (16) where e av,ω is the average void ratio from the membrane surface to the distance w from the membrane. The thickness L of the protein filter cake is expressed based on the material balance as L҃ v (18) As shown in the figure, high specific filtration resistance can be obtained although the porosity in the cake is not so small [2,17]. The figure obviously demonstrates that both p s and a decrease with the distance x.…”

Consolidation and expansion of a granular bed of superabsorbent hydrogels

“…Below pressure p i , the porosity is assumed constant. 17 Term b is an indication of the compressibility of the compressed cake and is determined from the slope of the line in Figure 7. The larger the value of b, the higher the compressibility.…”

“…The value of b for the packed hydrogels examined in this study was determined to be about 0.95. Given that it is reported that the value of b for kaolin with moderate compressibility is 0.054, 17,18 it is considered that the packed hydrogels are highly compactible materials, with hydraulic permeability decreasing dramatically with increasing applied pressure. In general, the side friction 19,20 between the compressed cake and the wall of the C-P cell often affects the uniformity of the cake packing.…”