Deposit membrane fouling: inuence of specic cake layer resistance and tangential shear stresses A. Char, J. Harmand, N. Ben Amar, A. Grasmick and M. Heran ABSTRACT Cake fouling is the leading cause of membrane permeability decrease when ltering mixed liquor suspension containing high suspended solid concentrations. A simple model is proposed to simulate the cake resistance evolution with time by considering a macro-scale fouling only linked to the accumulation of particles on the membrane surface. This accumulation appears as the difference between the ux of deposited particles due to the ltration and the ux of particles detached from the membrane surface due to the tangential shear stresses caused by, recirculation ow in sidestream membrane bioreactor (MBR) or gas sparging close to the membrane surface for submerged MBR conguration. Two determining parameters were then highlighted: the specic cake resistance and the shear parameter. Based on these parameters it is possible to predict model outputs as cake resistance and permeate ux evolution for short-time ltration periods. A. Char(corresponding author) A. Grasmick M. Heran Institut Européen des Membranes (IEM), Université Montpellier 2, place Eugene Bataillon, CC05, 34095 Montpellier, France E-mail: amine.char@ymail.com A. Char N. Ben Amar Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de lIngénieur, ENIT, B. P 37 Le Belvédère 1002 Tunis, Tunisia and Institut National des Sciences Appliquées et de Technologie, B. P. 676, 1080 Tunis Cedex, Tunisia J. Harmand Laboratoire de Biotechnologie de lEnvironnement, INRA, UR0050, Avenue des étangs, 11100 Narbonne, France and MODEMIC Research Group, INRIA, Laboratoire de Mathématiques, Informatique et Statistique pour lEnvironnement et lAgronomie-INRA, 2 Place Viala, 34060 Montpellier, France Key words | cake formation, membrane fouling modelling, specic cake resistance, tangential shear stresses NOMENCLATURE m acc Specic mass of accumulated cake (g/m 2 ) m acc,lim Maximum specic mass of accumulated cake (g/m 2 ) m in Specic mass of particles approaching the mem- brane surface (g/m 2 ) m out Specic mass of particles removed from the mem- brane by shear forces (g/m 2 ) X Total suspended solids concentration (gTSS/L) J p Permeate ux (Lm À2 h À1 ) TMP Trans-membrane pressure (Pa) μ Dynamic viscosity (Pa s) R 0 Clean membrane resistance (m À1 ) R c Cake resistance (m À1 ) J 0 Initial permeate ux (Lm À2 h À1 ) β Shear parameter (kg À1 ) α Specic cake resistance (mk g À1 ) R c,max Resistance at steady state (m À1 ) J p,end Permeate ux at steady state (Lm À2 h À1 ) INTRODUCTION Many studies have tried to model fouling in membrane pro- cesses. Many are based on the four basic fouling mechanisms introduced by Hermia () namely cake foul- ing, pore constriction, complete blocking, and intermediate blocking. Despite being established for dead-end ltration at constant pressure, these models have been also used for cross-ow ltration (Ho & Sung ; Charfi et al. ) or have been adapted to cross-ow ltration (Field et al. ) by taking into account the role of shear forces to eliminate particle deposition on the membrane surface (De Bruijn et al. ). More realistic models are also presented when considering simultaneous fouling mechanisms; while Bolton et al.() combined Hermias models, Wu et al. () established a model considering simultaneously three fouling mechanisms namely pore constriction, pore blockage, and cake ltration associated to soluble, colloidal and suspended activated sludge components, respectively. Abdelrasoul et al.() considered the probability of par- ticle deposition on the membrane surface or on another 1 © IWA Publishing 2014 Water Science & Technology | in press | 2014 doi: 10.2166/wst.2014.186 Uncorrected Proof