Advances in Water Treatment and Enviromental Management

FOULING PHENOMENON IN CROSS-FLOW MICROFILTRATION PROCESSES 179Influence of the number of reentrairaient N rThis parameter fixes the sensitivity of a suspended particle concerning entrainment by theflow when it makes contact with a previously aggregated object. The simulations drawn inFig.10 present deposit morphology variations for different values of the number ofreentrainment, from branching out (N r small) to compact structures (N r high).Secondary parameters such as θ v, P and R d do not have a significant influence on themorphology of theoretical deposits.Fig. 10: Simulation for N r =0 (up) and 3 (down) with α=20°, θ i =1°, θ v =1°3.3 DiscussionThe main question is: do such statistical aggregates really represent what happens when afilter surface is clogged by solid particle deposition during a cross-flow microfiltration processθ Of course it is very difficult to give an answer because of the difficulty to experimentallyobserve phenomena appearing at a microscopic scale (the pore diameter is about 1µm andthe particle diameter is supposed to be smaller). Experiments already performed by HOUI(1989) in a 2D micromodel for the filtration of dilute well-muds have shown surface depositswhose structures are qualitatively in good agreement with some of our statistical simulations.We hope that further investigations using the original technique of nuclear magnetic resonancewill provide us with useful information on the time dependant of the thickness all along ahollow fiber.Fig. 11: Horizontal density variations with a=20°, θ i =1°, θ v =1°, N r =4The horizontal density variations, plotted in Fig. 11 for the aggregation depicted in Fig. 6,show that the statistical simulator ensures a uniform distribution of particles all over thestudied filter surface except at the downstream and upstream boundaries. Furthermore itcan be concluded that deposits formed during a cross flow microfiltration process have auniform thickness over a filtration length covering a few pores.It is important to notice that statistical deposits are homogeneous. Bensimon (1983) andMeakins (1985) have demonstrated that this can be proved by the following relation, settingε equal to 1: