Analysis of polarized layer resistance during ultrafiltration of PEG-6000: an approach based on filtration theory

Abstract

A mathematical model based on filtration theory, coupled with resistance in series model and gel polarization/film model has been developed in the present study. Unlike the cake filtration equipment where cake deposition continues until the wash cycle comes, in case of continuous stirred ultrafiltration the deposited solutes are allowed to build up over the membrane indefinitely, along with continuous back transport of deposited solutes into bulk by the turbulence created by stirring action. To account for this back transport, a coefficient called back transport coefficient has been defined which is found to be independent of any operating variables. Variation of polarized layer resistance was also studied with different operating variables like bulk concentration, stirrer speed and pressure differential. A correlation was also developed relating polarized layer resistance with those operating variables. A comparative study has been made between experimentally found polarized layer resistance value, using ultrafiltration data of Bhattacharjee and Bhattacharya, with those found from correlation and this developed model based on filtration theory. The model has been found to predict the polarized layer resistance reasonably well once the three parameters describing the model viz. permeability coefficient, back transport coefficient and membrane hydraulic resistance are known along with the operating condition. Using the above-mentioned parameters, it is also possible to predict flux and/or total permeate volume at any time under a given operating condition.