Clarification of very dilute suspensions of fine particles using microfiltration membranes is being increasingly applied in such water-purification processes as ultrapure water production, sterile water production, effluent polishing, and radioactive contaminants processing. 1 One of the critical issues in the development of effective processes is a rapid flux decline attributed to pore-blocking phenomena arising from particles reaching the membrane as well as the formation of the filter cake. 2 It is thus important to be able to accurately evaluate the dynamic behaviors of both pore plugging and cake formation to facilitate the design of process and operation conditions.Most previous studies of medium clogging during cake filtration have pertained to either the blocking filtration theory or the deep-bed filtration theory. [3][4][5][6][7][8] Tiller et al. 9 empirically derived the correlation on the clogged medium resistance R m , changing with time, to examine clogging phenomena in cake filtration of liquefied coal, as followswhere R m0 and R mϱ are the medium resistance at the initial time and infinite time limit, respectively; w is the net mass of particles within the filter cake per unit effective medium area; and is the empirical constant. Matsumoto et al. 5 proposed the filtration model in which the particles permeate through the formed filter cake on the basis of the mechanism of deep-bed filtration and some of pores of the medium still remain open eventually. Similarly, Tien et al. 7 analyzed the fine particle retention effect in filter cakes as a deep-bed filtration problem, taking the internal structure of filter cakes into account. Recently, Lee 8 clarified the theoretical background of Eq. 1, and evidenced the physical implication for the parameter . Moreover, he proposed the newly developed, more rigorous equation to interpret the experimental data of medium clogging on the basis of the intermediate blocking law for clarification filtration with relatively thin medium. The proposed equation has two fitting parameters, and , as followsIn the present article, a simple and reasonable filtration model is developed of the dynamic behaviors of microfiltration in which the pore blocking occurs during cake filtration. The validity of the model is supported by the measured data for microfiltration of very dilute suspensions of fine particles through track-etched membranes performed under various conditions.
Development of Filtration ModelTo quantify the filtration behaviors in which the blocking of membrane pores and the filter cake formation brought about by the convective transport of particles toward the membrane surface occur simultaneously and continuously, it is necessary that the filtration resistances induced by these fouling phenomena are evaluated individually. The clogged membrane and filter cake may be considered as two resistances in series by the resistance-in-series model based on the cake filtration theory, and the filtration rate q is then related to the total filtration resistance R t , th...
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