4(%3)3 - Ecole nationale supérieure de chimie de Montpellier

The resistance R can be further expressed in terms of measurable parameters using the Kozeny-Carman equation which is based on the fact that the porous medium can be assimilated to a bundle ofcircular capillary tubes: = () ……….. Eq. (2.2)where s , d p and represent the sphericity of the particles, the particle diameter, and the bedporosity, respectively. L is the porous material thickness. The constant 150 includes classical values of thetortuosity and pore circularity in such porous material (spherical particles and porosity below 0.6).Combining equations 1 and 2, the empty-tower velocity can be expressed as: = () ……….. Eq. (2.3)Furthermore, the filtration characteristics of polymer particles under various conditions havebeen reported in the literature 30-33 ; the instantaneous material porosity can be relied to the compressiontime as follow:( )( ) = 1 e/ ……….. Eq. (2.4)Where t is the material porosity at time t, 0 is the porosity before compression and f theporosity at equilibFinally, the empty-tower velocity can be written as: = / / ……….. Eq. (2.5)Following the aforementioned equation, the fluid flow resistance of the membrane wascalculated at various pressure drops by following the water flux through the beds of polymer particlesduring time. All curves exhibited the same trend: a low resistance (high flux) at initial time eventuallyincreasing (flux decreasing) with time as the compression of the bed begin (Figure – 2.11). Theexperiments were ended once an equilibrium state was reached. At constant pressure, the increase inresistance i.e., decrease of the water flux indicated that the permeability decreased during the filtrationprocess due to the bed compression.56