In forward osmosis, defects on the selective active layer and changes in the porous structure of the support layer can be detrimental factors a ecting the membrane performance. This study focuses on the impacts of (i) the possible presence of defects and (ii) the changes in pore structures on the water ux and membrane selectivity via computational uid dynamics analyses. Results suggest that di usion of the draw solute through the support layer, i.e. internal concentration polarization, can be strongly enhanced or reduced by widening or narrowing the shape of the pore, respectively, while no signi cant e ect on water permeation can be associated with the change in draw solution cross- ow velocity or in the loss of draw solute during ltration. Interestingly, defects within the active layer may a ect the water ux exponentially as function of the defect size, suggesting the presence of a threshold below which the convective passage of contaminated water ux through the defect is not a ecting the membrane productivity. Moreover, the presence of defects may not be a detrimental factor for membrane operating with high nominal rejection ( >90%) and low percentage of defected area ( <1%). Keywords: Forward osmosis, defected area, pore support structure, ICP, pore shape geometry, cross- ow velocity, computational uid dynamics, tortuosity Nomenclature AL active layer CFD computational uid dynamics DM defect model DS draw solution 5 ECP external concentration polarization FO forward osmosis ICP internal concentration polarization PM porous model PSS porous support structure 10 TFC thin lm composite Corresponding author Email address: fynnja@math.auu.dk (Fynn Jerome Aschmoneit) Preprint submitted to International Journal of Membrane Science November 4, 2022 1. Introduction Membrane separation is an environment friendly, simple, and easily operated application process in water and wastewater treatment operations [1]. Considering the fact that the demand for clean and irrigation water are gradually increasing while 1.2 million people currently have limited access to clean and fresh water 15 sources [2], the membrane separation process gains extra importance thanks to its advantages in operation and a ordability. To deal with the current problems and near-future challenges, forward osmosis (FO) is one of the promising membrane separation processes as it uses the osmosis, which is a natural phenomenon, as its main driving force; therefore, it has the advantages of energy-ecient and sustainable operation [3]. The recent developments in membrane manufacturing process extended the FO applications since FO membranes are 20 expected to be stable in the feed solution [3] with an asymmetric structure that has a selective thin layer and a thick support layer [4]. However, changes in both selective thin layer and the support layer can negatively a ect the FO performance. Defects are the most known and possible changes on the selective thin layer, which result in performance decrement during the FO membrane operation. As Louie et al. [5] and Albo et al. [6] stated, the mesoporous and/or microporous defects remarkably decrease the gas separation capabilities 25 of membranes, which can be used in FO process, in the dry state. Up to now, there are no noteworthy e orts on the understanding of defects in the selective thin layer and the impact of support structure on the FO performance. Ali et al. [7] worked on FT-30-type RO membrane and proposed an \in-situ" plugging approach for minimizing defects in the membrane. In the proposed approach, the mesoporous defects, which occurred during the short reaction time at the interface (between the organic and aqueous phases), were plugged 30 by newly polymers. The increase in i) reaction temperature, ii) reaction time, and iii) degree of membrane crosslinking were main ways to achieve in-situ plugging approach. Hereby, a crucial performance improvement was observed in the gas separation properties, which can also re ect the performance improvement potential of separation process in a liquid environment. In the following study of Ali et al. [8], the developed defect- free membrane achieved the maximum rejection of 99.6% for the separation process of sodium chloride while 35 the maximum rejection was obtained with 99.0% for separating boron. Besides the \in-situ' plugging or similar approaches, the Loeb-Sourirajan process can create defect-free membranes for RO process in cellulose acetate or triacetate (CTA) membranes [9], but it is not very clear for polyamide (PA) membrane types [10]. Refs. [5, 6, 11] showed that the PA membranes have defects on the selective layer that decreases the separation performance. Duan et al. [10] investigated the impacts of membrane properties and hydraulic 40 pressure on the FO performance and found that the PA-TFC membranes had defects on the selective layer and hence there were remarkable performance decrement compared to CTA and PEBAX-coated PA-TFC membranes. Peters et al. [12] also pointed out the fact that the active layer properties crucially a ect the permeability and compaction; therefore, higher operating pressure conditions (e.g. FO membranes) have dominant impacts on the intrinsic properties of the membrane and may result in defects in porous medium. 45 Binger et al. [13] focused on the relation between the power density and speci c energy consumption and recovery. It is emphasized that the power density can be enhanced by improvements in membrane conditions that include the minimization of defects under high pressure environments; otherwise, the defects limit the energy recovery potential. Besides the defects in the active layer of the membrane, the porous structure of the support layer has also an impact of the separation performance. Tiraferri et al. [14] stated that the best 50 performance of the FO membrane process was based on the optimum structural characteristics of the support layer, which depended on the solvent quality, dope polymer concentration, fabric layer wetting, and casting. Hereby, the maximum porosity and minimum concentration polarization were achieved. Ren et al. [15] used commercially available ultra ltration membranes and investigated the impact of the support layer pore size on the ltration performance. Four di erent molecular weight cut-o values were analyzed; 10 kDa, 50 kDa, 55 100 kDa, and 500 kDa. It was found that the roughness of the active layer was a ected by the support layer pore size; thus, high uxes could be operated with rougher membranes. Tang and Ng [16, 17] highlighted that the FO membranes made by looser ber resulted in less resistance and high water di usion, which increased the separating performance in the FO process. Bendoy et al. [18] added silicene nanosheets into polysulfone (Psf) support layer and observed the impact of silicene nanosheet loading, varied between 0% wt and 1.0%, 60 on the FO performance. It was inferred that the loading of 0.25 wt% silicene nanosheet (SN0.25) had a nger- 2 like pore structure and the highest porosity and permeability while the low loadings of silicene nanosheet had negligible impact on the FO process. With a similar motivation, Ndiaye et al. [19] prepared two di erent poly (vinylidene uoride)/polyacrylonitrile (PVDF/PAN) membranes with the mean ber diameters of 7545 nm and 894 nm, respectively; thus they had di erent support layer thickness and porosity values. Even 65 though both membrane types achieved higher selectivity than the reference commercial membrane (CTA) in FO process, the membrane with smaller ber diameter had a better selectivity performance as it provided higher degree of crosslinking of the active layer. Another FO performance improvement study was presented by Dai et al. [20]; a graphene oxide (GO)-doped membranes were prepared for FO processes and nano-scale water channels were formed in perpendicular to the GO-doped membrane surface. The results showed that 70 GO doping enhanced the surface morphology with the optimum GO doping of 0.15% wt, while the formed nan-scale water channels decreased the resistance and increase the water di usion; thereby, a remarkable ux improvement was observed. The above-mentioned studies implied the impacts of the defects in the active layer and the porous structure in the support layer on the FO performance. Although the provided outputs improved the FO performance, there are still research gaps to be lled in for enhancing the FO performance 75 with better understanding of the defects and the porous structure in the active layer and the support layer, respectively. This study points out those points and presents a generic framework for analysis of defects and porous structures in the active and support layers with di erent shapes and areas by using computational uid dynamics (CFD). Thereby, the CFD method is proposed as an engineering approach for designing and analysis of pore structures in future FO membrane processes. Following the generic framework, two main 80 contributions are i) various defect areas in the active layer, and ii) six di erent pore structure in the support layer. Then, the water ux trends are generated based on the various defect areas and pore structures. 2. Methods Two separate models, namely (i) Porous Model - PM and (ii) Defect Model - DM were developed and their schematic representations are illustrated in Figure 1 while a detailed overview including the CFD boundary 85 conditions are reported in the Supporting Information. Figure 1: Schematic representation of the draw and feed channel with a porous support (grey) and an active layer (black) in a counter cross- ow setup. The draw solute gets diluted along the draw channel and inside the support pores (ICP). The two rectangles indicate the two models of this study: The Porous Model is used to investigate the in uence of the porous support geometry, as well as the e ect of (i) the reverse salt ux and (ii) the draw cross ow velocity on the ICP and the relative water ux through the AL. The Defect Model quanti es the potential contamination of the draw side ascribed to the convective passage of ow from the feed to the draw channel due to the presence of a defected Active Layer. The PM was deployed to investigate the in uence of the PSS geometry as well as the e ect of (i) the reverse salt ux and (ii) the draw cross ow velocity on the internal concentration polarization (ICP) and the relative water ux through the AL. The model includes the TFC-FO membrane, designed as the combination of the membrane active layer (AL) and the porous support structure (PSS). The uid dynamics of the draw 90 solution (DS) was included in the PM by incorporating a section of the DS cross- ow channel while de ning a parabolic pro le to describe the relative cross- ow velocity. As described in next section and reported in 3 Fig3a, di erent porous geometries were investigated while xing the operating boundary conditions of the PM. The DS was modeled as seawater, with an intrinsic NaCl concentration of 35 g/L and a representative bulk osmotic pressure of 28 bar. The di usion coecient of NaCl was included in the model as well as the 95 its relative reverse salt ux B through the AL of the membrane (equal to 0.94 L m2h1). To model the water ux through the membrane an intrinsic permeability value A of 2.74 L m2h1was taken into account. The choice of A and B was lab-based and obtained by testing an hand-made thin- lm composite polyamide membrane during FO characterization experiments. Same values were used in previous studies to perform modelling analysis of forward osmosis systems [21, 22]. 100 The DM includes a section of the cross- ow channel of the feed solution and only the relative AL of the TFC-FO membrane. With the goal of isolating and investigating the e ects associated with the presence of defects within the AL, the draw side was intentionally not included in the model while the simulations were performed without considering the osmotic permeation through the AL, as this has no e ect on the ow through the defects. The AL was modelled as a solid, impermeable wall, into which holes (defects) allow for 105 local convective transport of feed ow. The CFD model thus models the ow in the feed channel in the direct vicinity of the AL, quantifying how much of the feed cross ow is convected into the defect, in dependence of cross- ow velocity and the defect size. Furthermore, with the goal of identifying a model describing the pure convective ow through the defected AL, simulations were performed considering pure water owing within the feed channel, without accounting for potential contaminants dissolved in solution. 110 Based on the results obtained, a similarity relation for the convective passage of water from the feed to the draw site due to the presence of defects in the AL was derived. At a second stage, further simulations were developed adjusting the PM to include the similarity relation obtained through the DM with the goal of investigating e ects of a defected AL on FO membrane behaviour, i.e., in uence on ICP, the relative water ux and the potential changes in membrane selectivity due to contamination of the draw solution. 115 All CFD simulations were performed with OpenFoam v2012. As already reported in literature [23, 24, 25], this CFD tool is able to resolve the mass and momentum transfer across the geometries de ned. The PM models the ow bu solving the incompressible Navier-Stokes equations, while the solute transport is modelled by the convection-di usion equation. The solute density is not a function of the concentration but constant. Therefore, the bulk ow is a ected by the local solute concentration. However, the boundary condition at 120 the AL acts a ow inlet, in dependence of the solute concentration directly at the AL. The DM only considers ow; a solute concentration is not modelled. The ow eld is not a ected by the solute distribution 3. Results 3.1. Understanding the in uence of di erent PSS and DS parameters on the resulting FO water ux In uence of di erent pore shapes . The CFD simulations were performed on fundamental pore 125 geometries, which are tailored to investigate the aspects of tortuosity and varying cross sectional areas. A schematic representation of the curved pore geometry is reported in Fig. 2a. An overview of all fundamental pore geometries is found in Fig. 3a. The straight pore channel ( ) is used as reference to investigate the e ect of pore shape variations on the ICP development. The overall results of these CFD simulations are reported in Fig.3. As expected, the results suggest that a geometrical variation of the porous support may 130 strongly a ect the resulting water ux through the active layer by in uencing the di usion of the draw solutes through the pores. This is visible in Fig.3b and d, showing the ICP pro le within the porous support and the resulting water ux, respectively. In Fig.3b, the x axis is reporting the distance from the AL (x = 0) with an overall thickness of the pore equal to 150 m. Interestingly, a slight variation of the ICP pro le was observed comparing the porous curve shape ( Oin 135 Fig.3) to the a straight channel ( in Fig.3). This variation can be ascribed to the di erence in tortuosity between the two shapes. This result suggest that, in the presence of a fabricated membrane with a porous curve support structure characterized by a xed (i) porous support thickness and (ii) homogeneous pore diameter, the actual water ux may be compared with the simulated water ux through an ideal membrane with straight pore channels, thus deriving the tortuosity and hence the structural parameter of the fabricated 140 membrane. On the other hand, opening or reducing the internal pore section induce a less or more pronounced 4 Figure 2: a) Porous Model represented by a single pore geometry. Blue and orange arrows represent the water and the reverse salt uxes through the AL, respectively. The gure is reporting the curved shape, indicated with Owithin the text. Alternative shapes were investigated and indicated as follows: straight , narrowing cone M, widening cone 3, concave cone and convex coneD. b) Resolution of the Defect Model in the vicinity of the defect in the AL. The arrows indicate the local cross ow of water within the feed channel and the convective ow through the defect. resolution poor.a small part of the membrane vicinity, indicating local cross ow and ow through a defect in the active layer. ICP pro le ( andDin Fig.3), with a consequent increase or decrease of the resulting water ux through the AL, respectively (Fig.3d). However, the larger in uence on FO membrane behaviour was observed by performing the CFD simulations while narrowing or widening the shape of the pore channel ( Mand3in Fig.3). In comparison with the straight pore case, the di usion of the draw solute can be strongly enhanced 145 or reduced by widening or narrowing the shape of the pore, respectively. A wider pore can induce a two times higher water ux occurring at the AL, compared to the equivalent narrower pore structure (Fig.3d). This is ascribed to the di erence osmotic pressure resulting at the AL-draw solution interface and it may be explained considering that a large opening section at the porous-DS channel interface would increase the solute mass transfer, counterbalanced through an increase of the water ux through the AL at the steady 150 state. In uence of DS parameters: cross- ow velocity and reverse salt ux . Cross- ow velocity and reverse salt ux may be considered as the main DS parameters potentially a ecting the FO membrane permeation. While the cross- ow velocity is an operating parameter of the FO ltration, the reverse salt ux strongly depends upon the choice of the draw solute. For instance, it is well known that the reverse salt ux 155 through the same thin- lm composite (TFC) membrane can be strongly reduced by choosing inorganic salts composed of multivalent ions instead of deploying more di usive monovalent compounds such as sodium and chloride [26, 27, 28]. Figure 3c and 3d show the e ect of the DS cross- ow velocity and reverse salt ux on water ux through the membrane, respectively. To observe the e ect of the reverse salt ux, NaCl was simulated as draw solute and used as boundary conditions in the CFD simulations. Unexpectedly, results 160 suggest that a change in cross- ow velocity or the loss of NaCl ascribed to the reverse salt ux a ects marginally the resulting water ux at the active layer. Interestingly, this is true for each of the pore shapes investigated, suggesting that (i) the reverse salt ux has no signi cant in uence on ICP at the pore scale and that (ii) the driving force ascribed to the DS concentration gradient at the AL is mainly exerted through the di usive motion of the solute within the porous support. In other words, no signi cant e ects on water 165 permeation through the AL can be associated with the convective motion induced by the change in the DS 5 (a) 0 50 100 150 2000.30.40.50.60.70.80.91.0ICP profile Distance from AL ( µm)(b) 0.05 0.10 0.15 0.20 0.25 0.306.0E-68.0E-61.0E-51.2E-51.4E-51.6E-51.8E-5Water Flux, JW (m/s) DS cross flow vel. (m/s)(c) 0.0E+03.0E-66.0E-69.0E-61.2E-51.5E-51.8E-5 w/o JSWater Flux, JW (m/s)(d) w/ JSIFigure 3: In uence of porous support structure and DS operating parameter on ICP and water ux in FO membrane. Investi- gation performed on a) di erent porous support geometries presenting the resulting b) ICP pro le and c) water ux, the latter reported as function of the cross ow velocity variation. In uence of reverse salt ux B on water ux is presented in d) as function of the di erent porous support geometries. cross- ow velocity or the loss of NaCl during ltration, regardless the type of pore shape characterizing the PSS. Overall, the results suggest that the DS cross ow velocity and the reverse salt ux of the draw solute does not represent critical parameters when designing new porous support structures for classical TFC FO membranes. However, it is worth noting that these parameters may a ect the correct operation of the FO 170 membrane, when placed in modules for real applications. For instance, depending on the membrane module con guration and operation (e.g., hollow ber operated in counter-current) a signi cant variation of cross- ow velocity may be observed along the membrane area (both on the draw and feed side), potentially a ecting the water recovery rate achieved [29]. On the other side, the reverse salt ux may represent a detrimental factor in real FO operation, such as in the Food and Beverage industry [30], responsible for the increase 175 in the operational and environmental cost of the ltration system due potential contamination of the nal products. 6 -60 -40 -20 0 20 40 603.0E-66.0E-69.0E-61.2E-51.5E-51.8E-52.1E-5Water Flux, JW(m/s) ϕ( )75 µm 100 µm 150 µm 200 µm 300 µm(a) +𝜑 JW−𝜑 JW(b)Figure 4: In uence of porous support (i) geometry and (ii) thickness on water ux through the membrane. Results of the CFD simulations are reported in a) showing the water ux J Was function of a sensitivity analysis performed to investigate b) widening/narrowing conical pore geometries while varying the thickness of the porous support. , ,M,Oand,3refer to di erent porous support thicknesses and not to the pore shape as reported in previous gures . 3.2. A more in-depth analysis of the PSS: in uence of widening and narrowing conical pore shapes on the resulting FO water ux Based on the results presented above, widening/narrowing the conical pore shape of the porous support is 180 representing the geometrical factor, which most signi cantly a ect the membrane permeability, i.e. geometries and4in Fig. 3. To further investigate this e ect, speci c CFD simulations were performed through the PM by narrowing/widening simultaneously the conical pore in relation with the porous support thickness. The results of the simulations are reported in Fig.4. Each point in Fig.4a is representative of a CFD simulation, performed by changing (i) the thickness of the porous support (reported in the legend of the gure), as 185 well as (ii) its narrowing/widening conical shape as described by Fig. 4b through the angle associated with the amplitude of the pore. Values for the porous thickness were chosen accordingly to what is reported in literature [31, 32, 33]. As expected, a lower thickness of the porous support entails an increase in the water ux through the membrane. This result is in accordance with what expressed in literature [34, 35]. Moreover, the structural parameter S is linearly proportional to the thickness of the support layer. Therefore, 190 a lower support thickness would entail a decrease in the structural parameter, inducing larger water ux through the AL as reported in 4a. Practically, shortening the support thickness would reduce the ICP, ascribed to the reduction of the length of the pathway that the draw solute needs to be covered via di usive motion prior to reach the AL. For this reason, during the last decades, research has been focused on new membrane materials and innovative fabrication procedures able to minimize the structural parameters of FO 195 membranes [36, 37, 38, 39]. However, the results presented in Fig.4a suggest that a modi cation of porous support geometry towards a wider conical pore would strongly reduce the negative e ect on FO membrane performances ascribed to a larger support thickness. The results indicate that similar water uxes would be achieved by increasing the widening of the pore ( 'positive) regardless the thickness of the support layer. On the other hand, to fabricate a more permeable FO membrane, a reduction of the porous support thickness is 200 strongly suggested in the presence of narrower conical pores. These ndings may have a substantial impact on future research development: new and high-performance FO membranes can be obtained by tailoring the shape of the porous support towards wider conical pores, without compromising on membrane thickness and mechanical stability fabricating thinner membranes. This would represent a great advantage in innovative 7 FO membrane application, such as in pressure retarded osmosis or pressure assisted forward osmosis, where 205 the mechanical stability is an essential parameter for correct membrane operation. [40, 41]. 3.3. In uence of defects in AL The previous sections focused on uid dynamics studies aim at understanding the in uence of PSS and DS parameters on FO membrane behaviour, while simulating a perfect semi-permeable AL. However, AL may presents imperfections which can potentially a ect the membrane ltration properties. To characterize the 210 e ects of the presence of defects within the AL in FO membranes operated in cross- ow ltration mode, the DM was developed. A schematic overview of the simulation is reported in Fig. 2b, where a defect (i.e., a hole) has been incorporated in the AL while reporting the local cross ow of water within the feed channel and the possible convective ow through the defect. The DM quanti es the defect velocity Udas the mean velocity passing through the defect. To characterize Ud, we can derive the following assumptions and mathematical 215 relations. With reference to Fig. 2b, it is assumed that the feed velocity pro le in the membrane vicinity is approximately parabolic. Speci cally, the parabolic pro le is a function of the bulk cross ow velocity Uf and the channel width w. The local cross ow at a speci c distance yfrom the AL of the membrane can be de ned as: 220 Uf(w;y) =3 2Ufwyy2 w2(1) Based on this feed ow pro le, a series of simulations were performed through the DM by changing the defect lengths ldin combination with the bulk cross ow velocity Uf. The results are reported in Figure 5a. The data obtained from the simulations are represented as disks and crosses. The percentage of defected area is an indirect parameter referring to ld, over a xed length of the AL. Through the series of simulations described above , a similarity relation for the defect ow can be de ned as follow: 225 Ud Uf(ld)= 1:77ld 1mp 2 (2) Figure 5a plots the relative defect ow Ud=Uf(w;ld) against the absolute boundary ow Uf(w;ld), which relates to equation (1). For a given value of ld, all data points lie on a horizontal line, i.e. the defect ow Ud is proportional to the bulk ow at distance ld,Uf(w;ld). Furthermore, the results show that the data points are organized in constant plateaus, which only depend on the defect length ld, i.e. the data seems to follow a scaling law. The entire data follows the scaling law in equation (2. The results show a good agreement 230 between the simulations and the similarity relation, regardless the size of the boundary limits imposed in the simulations (i.e., the width of the cross- ow channel w). This suggests that a mathematical equation can be used to describe the imperfections of the AL when expressed as holes Combining these two equations, and under the assumption of ld w, the defect ow can be expressed as a function of the bulk cross ow velocity and the defect width. 235 Ud(Uf;ld)2:66Ufld wld 1mp 2 (3) This is what reported in Figure 5b, where the defected ux (i.e., the convective water ow through the defect) is reported as function of the size of the defect incorporated in the AL (expressed as percentage of defected area). The graph is thus reporting a visual overview of what is expressed through eq. 2, showing that the defected ux is not only proportionally increasing with the size of the AL imperfection, but it is also exponentially a ected by the increase of the cross- ow velocity applied within the feed channel. It is worth 240 noting that the model does not include voluntarily the possible external concentration polarization (ECP) which may derive from the presence of dissolved species in the feed solution. The defected ux indeed would not be a ected by ECP, since the water ow through the defect is driven by convective and not di usive motion. However, dissolved or dispersed species in solution may be transported convectively through the AL imperfection, thus resulting in contamination of the draw solution. 245 8 0.0E+0 8.0E-6 1.6E-5 2.4E-5 3.2E-502468101214 3% defected area6% defected area9% defected area12% defected area17% defected area21% defected area750 µm 1500 µm (a) 0 4 8 12 16 20 240.0E+08.0E-51.6E-42.4E-43.2E-44.0E-4Defect Flux (m/s) Defect Area (%)0.075 0.0625 0.05 0.0375 0.025 0.0125 (b)Figure 5: a) Relation of relative defect ow and near-wall cross ow and its dependence on the defect area. b) Defect ux against defect area: Defect ux is one order of magnitude greater than osmotic ux. 3.4. Understanding the in uence of the defects within the AL in FO membrane performances The output of the DM was incorporated in PM with the aim to investigate the e ect of the presence of defects in the AL on ICP, water ux and membrane selectivity. The simulations were performed by modelling the straight pore channel, thus avoiding any coupling e ect due to a di erent pore geometry. The results are reported in Figure 6. Figure 6a presents the water uxes trends through the AL as function of the percentage 250 of defected area, accounting for both the defected and total ux through the AL. While the defected ux is associated with the water leakage from the feed to the draw side due to the presence of defects, the total ux through the AL is considering both the defected ux and the water passage through the remaining intact section of the membrane via solution-di usion. The defected ux is almost linearly increasing with the increase of the percentage of defected area, as in agreement with what expressed by the DM and the derived 255 defect ux equation (2). On the contrary, the total water ux shows an exponential trend with the increase of the percentage of defected area. Interestingly, no signi cant e ect was observed on total water ux for a defected area <3%. This may be ascribed to the low fraction of feed water passing through the defected area, which is insucient to a ect the overall water ux. On the contrary, when the percentage of defected area is>3%, the convective water passage is responsible for a larger dilution factor of the draw solute within 260 the pore support, thus a ecting the ICP as described in Fig.6b with evident e ects on the total water ux (Fig.6a). The results presented above (Fig.3c) imply that the draw solute and water transport within the porous support of a FO membrane is mainly governed by di usion, while no signi cant e ect is associated with the convective transport of solute through the water from the DS bulk. The presence of defects in AL 265 would potentially lead to a convective mass transport of water and contaminants from the feed to the draw site. Since this would potentially a ect the membrane performances via a reduction of the real membrane selectivity, a sensitivity analysis was carried out to assess the membrane rejection in the case of the presence of defects in the AL. The well known equation for calculating the membrane rejection R (eq.4) was taken into account, where cpis representing the concentration of the contaminant in the product water (i.e., in the 270 draw solution in FO case) and cfthe bulk concentration of contaminant in the feed solution. Without loosing generality, we assume a 0% rejection to contaminant within the defected area while the nominal rejection was varied from 0 to 100% for AL, thus representing the possible variation of the selectivity against di erent 9 pollutants depending on the characteristics of the membrane involved. Pollutants were modelled as inorganic ions dissolved in water and mass balances of water and solutes were carried out at the AL-solutions interface, 275 accounting for the water uxes trends obtained from the CFD simulations (Fig.6a). Results are reported in Fig.6b and c, where contour plots are deployed to show the e ective selectivity of an FO membrane characterized by a nominal rejection (y axis) and a percentage of defected area. R= 1cp cf(4) Defect Area Defect Area Figure 6: In uence of the presence of defects on the AL on membrane performances. Results present a) the water ux through the membrane as function of the increase of the defected area in AL. Water ux is distinguished between defected and total ux, thus incorporating both the convective ux through the defected area and the water passage through the AL, via solution-di usion. The related ICP pro le is reported in b), as function of the distance from the active layer. Counter-plots c) and d) report the real rejection of a TFC-FO membrane while varying its nominal selectivity (e.g., declared by the membrane manufacturer) as function of the possible presents of defects on the AL. 10 4. Conclusion & Outlook This study reports a comprehensive modeling analysis of classical TFC membranes designed for Forward 280 Osmosis applications (i.e., with the active layer facing the feed solution and the porous support structure facing the draw solution). Speci cally, the study aims at understanding the in uence of the pore support structure of the TFC membrane and the potential presence of defects within its active layer on water perme- ation and contaminants removal. An in-depth CFD analysis was performed by implementing two separate models in OpenFoam, namely Porous Model (PM) and Defect Model (DM). 285 The PM was used to investigate (i) the porous support structure and (ii) the draw solution operating parameters on membrane productivity. The CFD simulations were performed on fundamental pore geome- tries, tailored to investigate the aspects of tortuosity and varying cross sectional areas. Results suggest that a geometrical variation of the porous support structure may strongly a ect the resulting water ux through the active layer by in uencing the di usion of the draw solutes through the pores. In particular: 290 •Opening or reducing the internal pore section induces a less or more pronounced ICP pro le, with a consequent increase or decrease of the resulting water ux through the AL, respectively. •Compared with a classical straight pore channel, the di usion of the draw solute can be strongly enhanced or reduced by widening or narrowing the shape of the pore, respectively. •A modi cation of the porous support geometry towards a wider conical pore would strongly reduce the 295 negative e ect on FO membrane performances ascribed to a larger support thickness, thus resulting in an increase of the water ux through the AL even in the presence of thicker membranes. This may potentially pave the way to future research development, aiming at developing suitable FO membranes for innovative applications, such as pressure retarded osmosis or pressure assisted forward osmosis where the mechanical stability of the membrane (i.e., membrane thickness) is a crucial parameter for correct 300 operation. •No signi cant e ect on water permeation through the AL can be associated with the convective motion induced by the change in the DS cross- ow velocity or the loss of draw solute during ltration, regardless the type of pore shape characterizing the PSS. In other words, the DS cross ow velocity and the reverse salt ux of the draw solute does not represent critical parameters when designing pore support structures 305 for new TFC membranes for FO applications. However, these parameters cannot be disregarded while instead, they may represent key parameters for scaling up promising FO membranes to pilot and real scale applications. The DM was used to investigate the e ect of the presence of defects within the AL in TFC membranes when operated in cross- ow mode. A new mathematical correlation was derived from the CFD results, where 310 the defected ux (i.e., the convective water ow through the defected area) is reported as function of the size of the defect incorporated in the AL. Under the assumption of having the ld w(defect length much smaller than the channel width) , the mathematical correlation is valid for any type of defects, regardless their geometry. The results suggest that the defected ux is not only proportionally increasing with the size of the AL imperfection, but it is also exponentially a ected by the increase of the cross- ow velocity applied 315 within the feed channel. The model does not include the ECP. However, dissolved or dispersed species in solution may be trans- ported convectively through the AL imperfection, thus resulting in contamination of the draw solution. To understand the e ect of the presence of defects within the AL to the nal membrane selectivity, the math- ematical correlation developed was included in the PM for further CFD simulations. The resulting water 320 ux through the membrane (accounting both the di usive motion through the AL and the convective motion through the defected area) showed an exponential trend with the increase of the percentage of defected area, suggesting the presence of a threshold (3% of defected area) below which the convective passage of con- taminated water ux through the defect is not a ecting the membrane productivity. Finally, the sensitivity analysis performed to study the membrane selectivity resulting from the incorporation of defects within the 325 11 AL suggests, as expected, that the convective passage of contaminants from the feed to the draw side may strongly a ect the quality of the water produced. However, the presence of defects may not be a detrimental factor for membrane operating with high nominal rejection ( >90%) and low percentage of defected area (<1%), thus suggesting that even a non-perfect membrane can perform a valuable ltration when operated in cross- ow mode. 330 Acknowledgments M.G., B.T., W.Z. and C.H.N. thank the Department of Environmental and Resource Engineering at the Technical University of Denmark. F.A. thanks the Department of Mathematical Sciences at Aalborg University, Denmark. 12