INFLUENCE OF HYDRODYNAMIC PROPERTIES ON THE FOULING MECHANISMS OF MEMBRANES AND THEIR EFFICIENCY AND SELECTIVITY DECREASE

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1 Jr. of Industrial Pollution ontrol 33(1)(017) pp Researh INFLUENE OF HYDRODYNAMI PROPERTIES ON THE FOULING MEHANISMS OF MEMBRANES AND THEIR EFFIIENY AND SELETIVITY DEREASE DMITRIY SPITSOV * AND ALEXEY ANDRIANOV Mosow State University of ivil Engineering (National Researh University), Yaroslavskoye Sh. 6, Mosow, Russia, 19337, Russia (Reeived 06 May, 017; aepted 08 May, 017) Key words: Memranes, Organi moleules, Fouling Mehanisms ABSTRAT This artile disusses and analyses the latest onepts of depositions of olloidal, suspended, and organi sustanes on memranes. The existing models of onentration polarization in apparatuses of various design are desried, the influene of generated deposits on derease in effiieny and seletivity of memranes is estimated. It is demonstrated that the transient flow rate prevents onentrating of partiles and organi moleules near memrane surfae providing their detahment. However, despite favorale influene of hydrodynami onditions on memrane operation, they are not suffiiently studied in order to ontrol fouling whih is also influened y hannel geometry and resistane, as well as adhesive and adsorptive properties of memrane material. EXISTING ONEPTS OF DEPOSITIONS OF SUSPENDED AND OLLOIDAL SUBSTANES ON REVERSE OSMOSIS AND ULTRAFILTRATION MEMBRANES Foreasting of derease in memrane effiieny with time as a onsequene of fouling is an urgent issue of operation of reverse osmosis plants. The relevant proedures are ased on the onepts of fouling mehanisms y various researhers. These onepts also speify the experimental researhes. Review of pulished materials devoted to investigations into fouling of reverse osmosis memranes reveals that quite different mehanisms of this proess are aepted y different researhers. 1. The theory of filtration with fouling forms the asis of models proposed in numerous works y Belfort, et al. (Altena, et al., 1983; Belfort, et al., 1979; Belfort and Marx, 1976; Belfort and Marx, 1978; Belfort, 1980; Belfort, et al., 1985; Green and Belfort, 1980; Reed and Belfort, 198). This theory is used in several proedures foreasting derease in memrane effiieny with time. This mehanism is ased on the assumption that memrane fouling is governed y filtration features. Belfort elieves that the filtration hypothesis is onfirmed y experiments on mirofiltration ells oth upon dead-end filtration and under various veloities of tangential flow aove memrane (Reed and Belfort, 198), simulating the onditions in reverse osmosis apparatuses.. (Belfort, et al., 1985) developed filtration theory with onsideration for alulated paths of partiles moving in the flow as a funtion of their weights and veloities. As mentioned in the artiles y Belfort, et al., 1985, the filtration theory frequently foreasts higher derease in memrane effiieny than atual values. Hene, the filtration mehanism assuming deposition of all partiles ontained in initial treated water on memrane was improved y alulation of fores ating on a partile in the flow. The alulations were performed for laminar flow with paraoli veloity distriution over the hannel height. In addition to pressing fores y onvetive flow and reverse diffusion the partiles near memrane surfae are affeted y uplift fore resulting from the differene in veloities of various fluid layers aove memrane. *orresponding authors SpiovDV@mgsu.ru

2 960 SPITSOV ET AL. Taking into aount the lift fores of partiles, the paths of partile motion in flow were alulated in Belfort, et al., 1985 and it was shown that under ertain onditions (partile weight and veloity) not all partiles are deposited on memrane. These adjustments are onsidered in alulations of deposit amount whih influenes on derease in memrane effiieny aording to the law of filtration with fouling. 3. The theory of staility of olloidal solutions near memrane surfae desried y Brunnele (Brunnele, 1980) and developed in other works (Kaakinen and Moody, 1984) relates the onentration polarization near the surfae of reverse osmosis memrane with partile oagulation. Partile oagulation near memrane surfae ours due to inrease in slat onentration in near-memrane layer and staility loss of olloidal solution. 4. The theory of gel formation or gel polarization (Nakao, et al., 1979) also desries oagulation or gel formation of high moleular solution neat memrane surfae as a onsequene of onentration polarization. Aording to this theory gel is formed upon ahievement of maximum allowale onentration of gel formation near memrane surfae. The theory of gel formation was developed similarly to the theories of formation poorly water solule deposits. 5. The theory of formation of olloidal deposits using adsorption mehanisms was desrie y (Jakson and Landolt, 1973) with regard to olloidal solutions of iron hydroxide. Aording to the proposed mehanism the deposit is formed in two stages: nuleation on memrane surfae and deposit growth. At the stage of deposit growth the authors apply the theory of staility of olloidal solutions. While foreasting derease in effiieny of reverse osmosis memranes due to fouling the most widely applied is the theory of filtration with fouling desried elow. MODELS OF ONENTRATION POLARIZATION In the most ases while analyzing onentration polarization the initial solution in the apparatus hannels is assumed to e well agitated in turulent flow. Aording to the Nernst film model, on memrane surfae there exists thin near-memrane layer where onentration of dissolved sustane is higher than in the main flow of initial solution (Fig. 1). This proess is desried y the well-known mass alane equations: Fig. 1 Distriution of sustane entrapped y memrane near its surfae. d V p + V + D = 0 (1) dx where V is the volumetri water flow rate passing via memrane, m 3 /(m s); is the onentration of dissolved sustane, g/m 3 ; p is the onentration of dissolve sustane in permeate, g/m 3 ; D is the diffusion oeffiient, m /s. The oundary onditions of Eq. (1) are as follows: at x = 0 (near memrane surfae) = w ; at x = δ (at the distane δ from memrane surfae) = (onentration in the flow). Solution of Eq. (1) for these oundary onditions is as follows: w = R i + exp( Vδ ) D ( 1 ) exp( Vδ ) R i D where R i is the memrane seletivity, R i = (1 p / w ). For high seletivity values Eq. () is as follows: w (3) = exp V k o where k o is the oeffiient of mass transfer, k o = D/δ. Sherwood in 1965 presented Eq. (3) as follows: w = () S 3 exp ν (4) J U D where S = V D is the Shmidt numer; v is the kinemati visosity of fluid, m /s; U is the veloity flow rate (in tangential diretion) aove memrane, m/s; J D is the hilton-olerook fator, J D = k o V â S 3 ñ

3 INFLUENE OF HYDRODYNAMI PROPERTIES ON THE FOULING MEHANISMS OF MEMBRANES AND THEIR EFFIIENY AND SELETIVITY DEREASE 961 For the ase of turulent flow in tuular memranes, J D f/, where f is the frition fator, Eq. (4) is as follows: w = exp ν S 3 f U In 1966 Brian proposed the following equation for average onentration polarization in tuular memranes: 3 ν S w (6) = 1, 333 exp 0, 75 f U It follows from Eqs. (5) and (6) that the main fators influening on onentration polarization are memrane effiieny in terms of filtrate and veloity of tangential flow in hannel aove memrane. The frition fator f an e inreased y various approahes thus dereasing w /. For instane, in the hannels formed y flat memranes (in rollers) separating sreens are used in order to inrease frition fator. In hannels of tuular memranes the flow turulene is ahieved y spherial partiles (0.7 mm in diameter), suspended in the flow, whih at existing level of onentration polarization makes it possile to provide lower veloities of transient flow (1 m/s) and signifiantly redue power onsumption (up to 15%) for irulation mode (Potts, et al. 1981). It follows also from Eqs. (5) and (6) that large organi moleules are the most dangerous for onentrating in near-memrane layer, sine they are haraterized y inferior diffusion. In addition, their presene in water an inrease visosity. Both these fators inrease the Shmidt numer S. Analysis of onentration polarization as a funtion of various fators fir laminar flow was performed y Fisher (Potts, et al., 1981). Various hannel types were onsidered (flow etween two flat memranes and flow in tuular memrane hannel). The results of analysis of onentration polarization for tuular memranes are summarized elow. The oordinates used for solution of the prolem are illustrated in Fig.. The veloity field is determined y the Navier Stokes equation and the following equation in ylindrial oordinates: in radial diretion (along the r axis): v v u + v x 1 p v v 1 v v = + V + + ρ x r r (5) (7) in axial diretion (along the x axis): u u 1 p u u 1 u u + v = + V + + x ρ x x r x ( r u) + ( r v) = 0 Stationary state in the flow is desried as follows: 1 u Ds + r v Ds = 0 x x r (8) (9) (10) where v is the veloity in radial diretion, m/s; u is the axial veloity (along the axis of tuular memrane), m/s; ρ is the solution density, g/m 3 ; p is the pressure, Pa; ν is the oeffiient of kinemati visosity, m /s; is the onentration of dissolved sustane (salt), g-mole/m 3. Boundary onditions for the equations desriing the veloity field are as follows: a) u(x, h) = 0 (there is no motion in axial diretion near memrane surfae); ) memrane effiieny is onstant, v(h) = v w ; ) v(0) = 0 Fig. onentration polarization in tuular memranes upon turulent flow. u r= 0 = 0 Boundary onditions for onentration of dissolved sustane are as follows: d) material alane under stationary onditions for indefinite fluid volume near memrane surfae (salt does not pass via memranes): ; v w ( x, h) = D s r= h e) symmetry: ; = 0 r= 0 f) profile of initial onentrations-(0, r) = o (onstant). Approximate analytial solution of this set of differential equations is as follows:

4 96 SPITSOV ET AL. 1 δl 3 δl 1,536 0, 0 4α 4α Γ = 1 δl δl δl 5 1 exp 0,0 + 4α 1α 4α w = Γ where ; is the average onentration of dissolved sustane; δ = v w / u (0); L = x/h; α = D s / v w h. Fisher et al. (Potts, et al. 1981) used these results for desription of onentration of dissolved sustane as a funtion of length of tuular hannel and onentration as a funtion of hannel diameter. Similar analysis was performed y Brian for the ase of flow etween parallel flat memranes (for roller and filter-presses). EXISTING ONEPTS OF FOULING INFLUENE ON DEREASE EFFIIENY AND SELETIVITY OF MEMBRANES In There are numerous onepts of fouling influene on memrane performanes. Kimura, et al. (Bian, et al., 000) elieve that aumulation of deposit as a onsequene of its high hydrauli resistane leads to derease in memrane effiieny. With derease in ion transfer rate via memrane the onentration polarization dereases and seletivity of apparatuses inreases (Fig. 3). Belfort, et al., mentioned that deterioration of memrane seletivity is related with hindered ion diffusion from memrane surfae to solution as a onsequene of existene of fine deposit layer. Suh explanation of derease in seletivity of memranes seems to e the most appropriate. The works y Karelin, 1988 are ased on the Merten model. Aording to their onepts deposit inreases the layer height of onentration polarization y the thikness of deposit layer. Derease in memrane effiieny is proaly aused not y inrease in hydrauli resistane of deposit layer ut y inrease in onentration polarization and derease in ative pressure (P-π osm ). In addition, inrease in pressure drop upon passing of onentrated produt via apparatus should e taken into aount, it results in signifiant derease in ative pressure aove memrane, thus dereasing its effiieny. The value of suh drop an e very important, ausing telesoping of roller elements. The inrease in pressure drop on apparatus is mainly determined y its design. When roller elements were opened and fouled memranes were visually Fig. 3 Inrease in memrane seletivity with inrease in deposit amount aording to Kimura model (a); onentration profile with gel layer (). examined, it was revealed that flow hannels (gaps) etween the fiers of feed spaer are fouled to a higher extent than the remaining memrane surfae. This proaly an e attriuted to the fat that the ontating areas etween feed spaer and memrane are fouled ausing high longitudinal resistane against the flow (Riddle, 199). Therefore, the derease in memrane effiieny is aused y inrease in onentration polarization and derease in ating pressure. Hydrauli resistane of deposit proaly does not influene on memrane effiieny. While dismantling apparatuses it an e seen that the deposit struture is very loose, its hydrauli resistane is negligile in omparison with resistane of memrane. Thus, alulations of hydrauli resistane of deposit and its

5 INFLUENE OF HYDRODYNAMI PROPERTIES ON THE FOULING MEHANISMS OF MEMBRANES AND THEIR EFFIIENY AND SELETIVITY DEREASE 963 ompressiility are pratie. Moreover, impairment of performanes upon operation is refleted mainly on derease in seletivity rather than effiieny. Otherwise, that is, upon derease in effiieny due to resistane of deposit, suh signifiant derease in seletivity would not e oserved. Therefore, the main reason of derease in onentration polarization and main parameter of the model is the thikness of deposit layer. For the ases when onentration polarization is redued to minimum the thikness of polarization layer is assumed to e equal to the thikness of deposit layer and onentration polarization an e alulated as follows: expvβ / D w / = (13) R + (1 R) exp( Vβ / D) While developing the model of influene of deposit on memrane seletivity the Nernst film model was used. Aording to this model a thin oundary layer exists near memrane surfae: stationary film with the thikness β. Salt transfer in this layer is limited y moleular mehanisms: diffusion determined y the moleular oeffiient D. When deposit is formed on memrane surfae the thikness of oundary layer inreases y the height of deposit layer, hene, salt transfer over total thikness of deposit layer ours only due to moleular mehanisms whih signifiantly hinders salt transfer from memrane surfae to the flow ore in omparison with the mode without deposit (Fig. 4). Herewith, proaly, the density of deposit struture an also play its role in derease in memrane seletivity. Turulent pulsations are gradually attenuated, and the thikness of oundary layer near loose deposit an e lower than that of dense deposit of the same height. In laminar flow onentrated oundary layer and veloity field are formed (Namguk, et al., 000). onentration profile in laminar flow is formed y omined ation of longitudinal onvetion and diffusion. The veloity profile is developed already at the hannel input. When deposit layer exists on memrane surfae the onentration gradient is estalished over the height of this stationary layer. The veloity profile already does not influene on transfer in deposit layer. Thus, at hannel input the onentration polarization is determined y the thikness of deposit layer. Proaly, in the hannel end the onentration gradient will e determined y the veloity profile in hannel and in the oundaries of deposit layer y the thikness of deposit layer (Fig. 5). ANALYSIS OF FORMATION MEHANISMS OF OLLOIDAL DEPOSITS ON REVERSE OSMOSIS MEMBRANES Visual examination of deposits on memranes extrated from roller element reveals that the deposits have very loose unompressile struture despite high pressure in the hannels. This invokes new approahes to the mehanism of deposit formation and influene of deposit on deterioration of memrane properties whih annot e a onsequene of high hydrauli pressure of deposit layer. First of all, it should e mentioned that the reverse osmosis transfer has nothing in ommon with mirofiltration, whih is frequently applied for simulation of deposit formation on reverse osmosis memranes. The resistane of mirofilter is negligile, therefore, as a onsequene of high pressure differene the partiles, aptured y the filter, are pressed to its surfae. Reverse osmosis transfer is the transfer of water moleules via memrane wall Fig. 4 onentration profile near the surfae of reverse osmosis memrane without and with deposit formation upon turulent flow. Fig. 5 Development of onentration polarization as a onsequene of memrane fouling upon laminar flow: a) at the hannel input; ) at the middle of the hannel.

6 964 SPITSOV ET AL. at ertain pressure. The partiles in water are not pressed against memrane, sine at relatively low memrane effiieny high pressure on partiles direted to memrane surfae annot exist. All pressure is onsumed for overoming of resistane of memrane and drain hannel. Inrease in the existing pressure leads to inrease in memrane effiieny and, hene, inrease in resistane of water passing via memrane and drain system. Thus, pressing of partiles to memrane as a onsequene if pressure drop is exluded. Mehanism of partile adsorption on memrane surfae is the most proale. At the same time partiipation of reverse osmosis transfer in formation of deposit layer should not negleted. Transfer via memrane auses motion of partiles in flow to memrane. Hene, adsorption of partiles (adhesion) to memrane surfae inreases due to onstant transfer of partiles to memrane surfae. At the same time oagulation of partiles approahing memrane surfae with those already attahed to the surfae is possile. The mehanism proposed y Brunnele, 1980 does not ompletely math atual proesses. oagulation ours upon ertain onditions, ertain onentrations of oagulating partiles are required. Meanwhile, as evidened in pratie, memrane fouling ours even at extremely low onentrations of olloidal partiles in water (for instane, iron: up to zero onentrations). INFLUENE OF HYDRODYNAMI FORES OF PARTILE DETAHMENT ON INTENSITY OF DEPOSIT FORMATION OF SUSPENDED AND ORGANI SUBSTANES The phenomenon of onentration polarization inreases resistane of deposit layer due to aumulation of suspended partiles on memrane surfae. As already shown, numerous models desrie derease in memrane effiieny (oth for ultrafiltration and reverse osmosis, as well as nanofiltration). The model of filtration with fouling is the most widely known and the most suessfully desries fouling upon slurry filtration in the mode of deadend filtration via mirofilters and ultrafilters. However, as mentioned elsewhere (Potts, et al., 1981), this model annot desrie fouling upon tangential mode of memrane apparatuses or upon onstant reirulation of initial water. In suh mode after initial deposit formation on memrane surfae the deposit growth is terminated as a onsequene of influene of tangential disharge: detahment of partiles. When surfae waters are treated y means of memranes, the memranes are fouled with suspended and olloidal partiles as well as organi sustanes (humi aids). Sine the sizes of various olloidal partiles and organi sustanes ontained in water are different, their diffusion properties vary signifiantly. Thus, at the start of the proess memranes are fouled with susequent derease in their effiieny. Upon treatment of surfae water the deposit growth an e stopped after layer formation and growth at the start of the proess, derease in effiieny and, as a onsequene, in onentration polarization. Thus, even in tangential mode the model of filtration with fouling an e applied for desription of deposit formation. As mentioned elsewhere (Potts, et al., 1981), upon ultrafiltration treatment the memrane fouling runs in aordane with the model of filtration with fouling and aumulation of high moleular impurities and olloidal/suspended partiles on memrane surfae. Deposit formation ontinues until memrane effiieny dereases so that onentration polarization drops and partiles are detahed from deposit surfae, thus preventing further deposit growth. When leaning is performed in tangential mode at onstant pressure the deposit formation an e onventionally sudivided into two stages: aumulation of undetahale deposit layer; and ahievement of equilirium etween rates of deposit aumulation and partile detahment. However, as mentioned y some researhers on the asis of experiene, equilirium is ahieved upon signifiant derease in memrane effiieny when faility should e deativated and deposit should e dissolved y hemial washings. In order to ontrol (prevent) fouling various measures are applied: 1. Preliminary oagulation aiming at partile oarsening, derease in resistane of deposit, improvement of reverse diffusion of partiles (improvement of detahment). it should e mentioned that oagulation and inding of small sized partiles redues the hane of logging, whih is proaly the most important fator of retention of memrane effiieny.. Inrease in partile detahment rate y inrease in veloity of transient flow. 3. Inrease in effiieny of hydrauli (ak) washings.

7 INFLUENE OF HYDRODYNAMI PROPERTIES ON THE FOULING MEHANISMS OF MEMBRANES AND THEIR EFFIIENY AND SELETIVITY DEREASE 965 The models of reverse transport are eing developed, that is, mehanism of derease in memrane fouling y inrease in veloity of transient flow. Three developed models are known: diffusion due to Brownian motion for low moleular organi sustanes, detahment diffusion for maromoleules, and migration model for olloids. These models of reverse transport demonstrate that staility of performanes of memrane ultrafiltration failities (effiieny in terms of filtrate) inreases with inrease in detahment rate and size of partiles ontained in water. For olloidal partiles and humi sustanes ontained in surfae water the Brownian diffusion model and the detahment model give different estimations of reverse transport of impurities from memrane surfae into solution. With derease in partile size and moleular weight of organi sustanes the oeffiient of Brownian diffusion inreases and the oeffiient of detahment diffusion dereases. Effiient value of the diffusion oeffiient is the sum of oth diffusion oeffiients. Upon nanofiltration the onentration of high moleular sustanes in near-memrane layer inreases. Large organi moleules with low diffusion oeffiient foul memranes quiker and to a higher extent due to low soluility and higher onentration ahieved in near-memrane layer (ho, et al., 000). Derease in memrane effiieny upon filtration of water ontaining organi ompounds is stipulated y formation of gel layer on memrane surfae and sorption ourring as a onsequene of interation of organi sustanes with memrane material (ho, et al., 000): P J = (14) µ R + R + R ( ) m ads1 ads where R ads1 is the resistane of gel layer plus resistane stipulated y sorption of organi sustanes on memrane surfae; R ads is the resistane stipulated y interation of organi sustanes on memrane surfae and in solution. R ads1 inreases with time to the equilirium value R equil. The main fators whih influene on the dynamis of this proess are onentration of organi sustanes in treated water and speifi flow rate via memrane. Upon extended filtration under onstant pressure without ak washing the formation of deposit layer is desried y the following equation otained from Eq. (14): P = R µ J o + R = K V P + A µ J o (15) where P is the pressure, Pa; J o is the initial memrane filtration rate, m/s; R o is the memrane resistane (m 1 ); V is the permeate volume, m 3 ; A is the memrane surfae area, m ; K is the oeffiient of speifi resistane (K=α), where α is the speifi resistane of deposit, m/kg; is the onentration of impurities; R is the resistane of deposit (m 1 ). Fig. 6 illustrates PA V µ t as a funtion of volume V, desried y diret line. Variation of slope angle of the plot with inrease in veloity of tangential flow is attriuted to detahment of partiles from memrane surfae, derease in their onentration and speifi resistane of the deposit (Bian, et al., 000). The influene of veloities of transient flow on onentration polarization and oeffiient of mass transfer upon treatment of water ontaining solule organi sustanes is illustrated in Fig. 7 and 8. PA Fig. 6 as a funtion of volume of filtered water for V µ t various transient flow rates and turulene onditions. Fig. 7 oeffiient of mass transfer as a funtion of detahment rate.

8 966 SPITSOV ET AL. Fig. 8 onentration polarization as a funtion of detahment rate. ONLUSIONS Deposition veloities of suspended sustanes depend on veloity of water transient flow via hannel: the higher the veloity, the lower the amount of deposits on memranes. Mehanism of deposition on memrane is omprised mainly partile adhesion to memrane surfae. Depending on the memrane properties (hydrophiliity, surfae harge, and so on), the deposition veloities of suspended partiles and organi ompound an vary. urrent projets are oriented at development of memranes with modified surfae whih repulses some inlusions. It should e mentioned that the hannel geometry influenes ritially on the apparatus operation effiieny. Longitudinal hydrauli resistane of the hannel inreases with fouling. Derease in memrane effiieny is diretly related with inrease in hydrauli resistane whih is attriuted to derease in operating pressure. As will e demonstrated in susequent works devoted to testing of apparatuses of new design with dereased hydrauli resistane, the intensity of inrease in hydrauli resistane, hene, of derease in effiieny is signifiantly lower. This makes akground to onsider that operation of reverse osmosis and nanofiltration failities is possile without pre-treatment due to improvements of hannel design, seletion of memrane material and hydrodynami operation mode. REFERENES Altena, F.M., Belfort, G., Otis, T., Fiessinger, F., Roveland, T.M. and Nioletti, T Partile motion in laminar slit flow: a fundamental fouling study. Desalination. 17 : 1-3. Belfort, G., Alexandrowisz, G. and Marx, B Artifiial partiulate fouling of hyper filtration memranes-ii Analysis and protetion from fouling. Desalination. 8 : Belfort, G. and Marx, B Artifiial partiulate fouling of hyperfiltration memranes. Desalination. 19 : 17. Belfort, G. and Marx, B Artifiial partiulate fouling of hyperfiltration memranes-iii Mehanism of memrane protetion, Pro. of 6th International Symposium. Fresh Water Sea. Las Palmas. 4 : Belfort, G Artifiial partiulate fouling of hyperfiltration memranes-iv Dynami protetion from fouling. Desalination. 34 : Belfort, G. and Weigand, R.J. and Mahar, J.I Partiulate memrane fouling and reent development in fluid-mehanis of dilute suspensions. Reverse osmosis and ultrafiltration symposium, 188th Meeting of Amerian hemial Soiety, Philadelphia, Washington, pp , 6-31 Aug Bian, R., Yamamoto, K. and Watanae, Y The effet of shear rate on ontrolling the onentration polarization and memrane fouling. Pro. of the onf. on Memranes in Drinking and Industrial Water Prodution, Paris, Frane, 1, 41-43, 3-6 Otoer 000. Brunnele, M.T olloidal fouling of reverse osmosis memranes. Desalination. 3 : ho, J., Amy, G., Yoon, Y. and Sohn, J Preditive models and fators affeting natural organi matter (NOM) rejetion and flux deline in ultrafiltration (UF) memranes. Desalination. 14 : Green, G. and Belfort, G Fouling of ultrafiltration memranes lateral migration and the partile trajetory model. Desalination. 35 : Jakson, J.M. and Landolt, D Aout the mehanism of formation of iron hydroxide fouling layers on reverse osmosis memranes. Desalination. 1 : Kaakinen, J.W. and Moody,.D harateristis of reverse memrane fouling at the Yuma desalting test faility. Reverse Osmosis and Ultrafiltration Symp. 188th Meet. Am. hem. So., Philadelphia, Pa, Washington D.., Aug. 6-31, pp Karelin, F.N Water desalinization y reverse osmosis. Mosow: Sttoiizdat. Nakao, S.I., Nomura, T. and Kimura, S harateristis of maromoleular gel layer formed on ultrafiltration tuular memrane. AIHE Journal. 4(5) : 615. Namguk, H., Gary, A. and halor, J Seasonal variations of nanofiltration (NF) foulants:

9 INFLUENE OF HYDRODYNAMI PROPERTIES ON THE FOULING MEHANISMS OF MEMBRANES AND THEIR EFFIIENY AND SELETIVITY DEREASE 967 Identifiation and ontrol. Pro. of the onf. on Memranes in Drinking and Industrial Water Prodution, Paris, Frane, 3-6 Otoer, pp Potts, D.E., Alert, R. and Wang, S A ritial review at fouling of reverse osmosis memranes. Desalination. 36 : Riddle, R Opened hannel ultrafiltration for reverse osmosis pretreatment. Pro. of the IDA onferene, Washington, Aug Reed, R.H. and Belfort, G haraterization of fouling potential for pressure-driven memrane proesses a new simulated flow ell. Water Si. Tehnol. 14 :