* Corresponding author. Tel.: #33-4-67-14-37-23; fax: #33-4-67- 54-48-10. E-mail address: heran@univ-montp2.fr (M. He H ran). Chemical Engineering Science 56 (2001) 3075}3082 Prediction of cross-#ow micro"ltration through an inorganic tubular membrane with high-frequency retro"ltration M. He H ran*, S. Elmaleh UMR 5669, UM II/CNRS/IRD, Hydrosciences, Equipe Ge & nie des Proce & de & s, CC 24, Universite & Montpellier II, 34095 Montpellier Cedex 5, France Received 30 June 2000; received in revised form 27 November 2000; accepted 18 December 2000 Abstract High-frequency retro"ltration is a promising technique of #ux enhancement, which should contribute to the development of cross-#ow micro"ltration. Most published models have assumed cake deposit in the forward "ltration phase, incomplete cleaning by backwash, and delays in cake formation and erosion. However, they were "tted to the overall net #ux since the transient signals could not be monitored. The experimental set-up of this work allowed obtaining the forward #ux response to periodical backpulsing and measuring the average reverse #ux. The tested suspensions were bentonite in tap water and biologically treated wastewater. Average reverse #ux was accurately measured by two di!erent methods leading to the same results. Moreover most parameters, introduced in the published models, were experimentally measured and not "tted to the results as previously, e.g. the cleaning e$ciency, which has been an adjusted parameter, was measured by two methods leading to the same value. The forward #ux responses are not in agreement with the models. Moreover, the models do not accurately predict the average reverse #ux when the suspension interacted with the membrane. The average reverse #ux could even be higher than the forward #ux, which could hamper the economical achievement of the technique. However, the optimal frequency was fairly well predicted by all the models for both the suspensions. A method of determination of the net #ux and the optimal conditions was proposed. This method is based on the forward #ux response to one pulse obtained when the system is well stabilised; it accurately predicted the net #ux.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Filtration; Fouling; Mass transfer; Membranes; Modelling; Transient response 1. Introduction Cross-#ow micro"ltration is a constantly developing technique in the "eld of water and wastewater treatment. However it is often hampered by mass transport limita- tion. Back#ush is one of the most frequently used techniques of #ux enhancement: periodically reversing transmembrane pressure induces cleaning by the reverse #ow. The deposit and even internal foulants are then lifted o! the membrane and swept away by the cross- #ow. However, even with very short back#ush duration (1}5 s), performed 1}10 times per minute, at 1}10 bar di!erential pressure, back#ushing accounts for about 10}20% of the total operation time (Su, Liu, & Wiley, 1993). Moreover, the reverse #ux has to be taken into account and net results are then poor, i.e. the net #ux can only be increased by 10}30%. However, good results were obtained with such short backwash time as 0.05 s with a period less than 5 s (Parnham & Davis, 1996; Wenten, Koenhen, Roesink, Rasmussen, & Jonsson, 1996). It is thought that the deposit is removed from the membrane wall before it has fully formed and compacted. This technique is called high-frequency retro"ltration, high-frequency backpulsing or backshock (Wenten, 1995). Many suspensions and membranes have been tested. Rodgers and Sparks (1992) studied backpulsing in 10gl BSA ultra"ltration. Fluxes, for 0.05 s back#ow at 0.5 s period, increased up to 3 times under laminar cross-#ow (Re"8) but the technique was ine$cient in turbulent regime. When feed concentrate was between 10 and 30gl, backpulsing was always e$cient but at 100 g l, the #ux was no more enhanced (Rodgers & Sparks, 1992). Wilharm and Rodgers (1996) con- cluded that the #ux increase was due to concentration 0009-2509/01/$-see front matter  2001 Elsevier Science Ltd. All rights reserved. PII:S0009-2509(00)00550-9