Bio ﬁ lm compressibility in ultra ﬁ ltration: A relation between bio ﬁ lm morphology, mechanics and hydraulic resistance

Poroelastic ﬂ uid-structure interaction models were coupled to experimental data to determine the ef- fects of bio ﬁ lm spatial distribution of mechanical and hydraulic properties on the bio ﬁ lm hydraulic resistance and compressibility in membrane ﬁ ltration processes. Bio ﬁ lms were cultivated on ultra ﬁ l- tration membranes for 20 and 30 days under high (0.28 bar) and low (0.06 bar) transmembrane pressure (TMP), in dead-end ﬁ ltration mode. Subsequently, bio ﬁ lms were subjected to a compression/relaxation cycles by step-wise TMP changes. Structural deformation of bio ﬁ lms during compression was observed in-situ using optical coherence tomography. Experimental results show that the observed increase in the bio ﬁ lm hydraulic resistance during compression is not necessarily accompanied by a detectable bio ﬁ lm thickness reduction. A dual-layer bio ﬁ lm model with a dense base and porous top layer could explain these observed results. Because porosity controls indirectly the mechanical response of bio ﬁ lms under compression, results could be described without assuming a gradient in mechanical properties within the bio ﬁ lm. The bio ﬁ lm surface roughness did not signi ﬁ cantly in ﬂ uence the water ﬂ ux in this study. However, the fraction of bio ﬁ lm base layer directly exposed to bulk liquid could be a good indicator in the determination of water ﬂ ux. The main implications of this study for the design and operation of low-pressure membrane systems (e.g., MF and UF with fouling layer being the main ﬁ ltration resistance) lays in the selection of favorable operational TMP and bio ﬁ lm morphology. The


Introduction
Biofilm formation causes additional hydraulic resistance that adversely impacts water production in membrane systems (McDonogh et al., 1994;Radu et al., 2010). In membrane systems such as microfiltration (MF) and ultrafiltration (UF), biofilm resistance is the main filtration resistance (Dreszer et al., 2013;Ko and Pellegrino, 1992;Martin et al., 2014). Biofilms are often described as porous media consisting of several layers with different properties, such as density , porosity (Gao et al., 2011a;Okabe et al., 1998;Rosenthal et al., 2018) and elastic modulus (Aravas and Laspidou, 2008;Picioreanu et al., 2018). In general, biofilm porosity increases with the distance from substratum, whereas the biofilm elastic modulus (or rigidity) seems to have an opposite trend.
The spatial distribution of porosity and mechanical properties affect the biofilm permeability, as well as the structural responses under compressive forces. Biofilm compression has been often described as the main cause of changes in biofilm hydraulic resistance during water filtration (Derlon et al., 2016;Dreszer et al., 2013;Jorgensen et al., 2017;Poorasgari et al., 2016;Valladares Linares et al., 2015). Indeed, as biofilms are subjected to larger forces (e.g., higher transmembrane pressure, TMP) biofilms undergo a decrease in thickness and surface roughness (Derlon et al. , 2016Desmond et al., 2018c;Dreszer et al., 2014;Valladares Linares et al., 2015) leading to a reduction in biofilm porosity (Blauert et al., 2015) and permeability (Derlon et al., 2016;Desmond et al., 2018c). The magnitude of the increase in hydraulic resistance upon compression depends on biofilm composition (e.g., EPS concentration and composition) (Desmond et al., 2018a;Herzberg et al., 2009), growth conditions (e.g., operational TMP and growth time) (Derlon et al., 2016;Dreszer et al., 2014;Poorasgari et al., 2015) and operation mode (e.g., dead-end and cross flow). Poorasgari et al. (2015) reported an increased hydraulic resistance of the fouling layer under elevated TMP during dead-end filtration, without correlating this to the physical structure of the fouling layer. Dreszer et al. (2013) also reported that biofilm hydraulic resistance increases at higher permeate fluxes. However, Dreszer et al. (2013) calculated the biofilm thickness based on biofilm weight per specific area, meaning that compression effects on biofilm morphology could not be detected.
Later developments of in-situ imaging techniques such as optical coherence tomography (OCT) enabled researchers to study biofilm development (Wagner et al., 2010;Wang et al., 2017) and structural deformation in real-time during compression (Blauert et al., 2015;Desmond et al., 2018c). Biofilm thickness and hydraulic resistance were correlated using in-situ OCT imaging techniques during MF process (Dreszer et al., 2014). It was observed that the biofilm hydraulic resistances increased at larger permeate fluxes and the resistance returned almost to its original value as compression forces were released. However, in the study of Dreszer et al. (2014) the severe changes in resistance were only accompanied by a slight change in biofilm thickness. Valladares Linares et al. (2015) also related the change in hydraulic resistance of MF biofouling to the biofilm thickness and structural deformation through OCT imaging. Furthermore, Derlon et al. (2016) measured increased biofilm hydraulic resistance with increasing TMP during a dead-end UF system. The correlation between biofilm resistance, biofilm thickness and biofilm roughness was later studied by Desmond et al. (2018c) in a gravity-driven membrane (GDM) system. They observed that the increase in hydraulic resistance is accompanied by a reduction of biofilm relative roughness (based on OCT images) during compression of several model biofilms. Interestingly, they also reported that the increase in hydraulic resistance of a river water biofilm could not be correlated to changes in biofilm thickness and roughness. Recently, Jafari et al. (2018) proposed a fluid-structural model that can explain the structural and hydrological responses of a smooth surface biofilm to compression during water filtration in membrane systems. The numerical model enabled the quantification of mechanical and hydrological properties of different biofilms.
The relation between structural deformation and hydraulic resistance during compression of biofilms with different morphologies (e.g., surface roughness) is not still clear. Therefore, this study aims at evaluating membrane biofilm compressibility and the corresponding changes in biofilm hydraulic resistance as a function of: i) biofilm growth conditions (i.e., growth time and growth TMP); ii) spatial distribution of mechanical and hydrological properties in the biofilm, and iii) biofilm surface roughness. To this goal, a computational model was developed and supported by experimental results.

Biofilm cultivation and growth conditions
Biofilms were cultivated in a flow cell under dead-end ultrafiltration mode with the membrane effective area of 18.75 cm 2 . Biofilms developed from filtration of river water (Chriesbach river, Dübendorf, Switzerland) during winter, under growth conditions listed in Table 1. The detailed characteristics (Total organic carbon, dissolved organic carbon, assimilable organic carbon, etc.) of feed water used for biofilm growth can be found in (Derlon et al., 2013) and in supplementary information Table S1. In the first experiment, we evaluated the effect of biofilm age (20 and 30 days), when grown under constant transmembrane pressure (TMP ¼ 0.06 bar). In the second experiment, the effect of TMP (0.06 and 0.28 bar) during biofilm growth was studied. To evaluate data reproducibility, biofilms were grown in several parallel flow cells in each growth condition.

Biofilm compression experiments
The biofilms grown in parallel flow cells were subjected to the compression/relaxation tests consisting of gradual increase/ decrease of TMP to specific values, as defined in Fig. 1. Biofilms were subjected to an identical compression and relaxation cycle regardless of their growth TMP. The TMP range (between 0.06 and 0.5 bar) was selected based on practical implications and construction limitations GDM systems. Biofilms were discarded after one compression/relaxation test. All compression tests were done in a 20 C temperature-controlled room.

Hydraulic parameters
The permeate flux in [L/m 2 /h] was calculated from mass measurements of collected permeate. The biofilm hydraulic resistance R bio [m À1 ] resulted from the difference between the total hydraulic resistance R tot and membrane resistance R mem , as explained in Martin et al. (2014). The total filtration resistance was calculated through Darcy's law based on applied TMP and the measured permeate flux in the presence of biofilm (Jafari et al., 2018). The intrinsic membrane resistance, R mem , was measured with nanopure water for 24 h prior to fouling.

Biofilm morphology quantification
The morphological response of biofilms to compression forces was determined by means of optical coherence tomography (OCT) (Ganymede GAN210, Thorlabs GmbH, Dachau, Germany), light source center wavelength of 930 nm and refractive index of 1.33. In order to improve statistical certainty of biofilm morphological properties, at least 10 images were taken at random locations in each flow cell, at each pressure step. Mean biofilm thickness and surface roughness were quantified using a customized MATLAB routine (MathWorks, Natick, US). Mean absolute surface roughness (d abs ) shows biofilm thickness variability averaged for a number of image locations, according to eq. (1). Moreover, mean roughness coefficient (d rough ) was calculated, which indicates biofilm thickness distribution normalized to mean biofilm thickness based on eq. (2) (Murga et al., 1995) where n is the number of measurements, L f is biofilm local thickness and L f is the mean biofilm thickness.

Model geometry and physics
The mathematical model used to correlate the biofilm structural deformation with the corresponding changes in hydraulic resistance during compression was presented in details in (Jafari et al., 2018), therefore the model is here only briefly described. In this poroelastic model, fluid flow in the biofilm was reciprocally coupled to the structural mechanics of the biofilm. The gradient of liquid pressure in biofilm pores affects the effective stress in the biofilm and leads to structural deformation, while the deformation changes the permeability and consequently the pore pressure. Due to the dead-end filtration mode, the biofilm properties would change mainly in the direction of permeate flow (i.e., perpendicular to the membrane). However, a two-dimensional (2-D) model was developed to evaluate the effect of biofilm surface roughness on permeate flux and biofilm deformation (Fig. 2). Two different geometries were used to represent both smooth (cases 1 and 2) and rough surface biofilms (cases 3 to 6 in Table 2). Average biofilm thickness (L f ) and biofilm length (L x ) of the model biofilms were based on experimental results. The membrane was represented by an additional layer with thickness, L m . The biofilm base layer thickness L b and top layer thickness L t in the bi-layer model biofilm were constructed so that the sum (L b þ L t ) equals the average thickness (L f ). In case of smooth-surface biofilm (cases 1 and 2) the model could in principle be reduced to one-dimension (Jafari et al., 2018), however, for consistency, we kept the 2-D model geometry for all six cases. Finally, the biofilm depth in the third dimension (z) was considered to be large enough to apply the 2-D plane-strain simplification (Coussy, 2004).
The velocity and pressure fields for water flow through the biofilm were calculated from Darcy's law, with permeability K being related to biofilm porosity 4 by a linear relationship K ¼ A4 in which A is the biofilm permeability coefficient. Under compression, local biofilm porosity 4(x,y) is related to the porosity prior to compression, 4 0 , and biofilm displacement gradient in the compression direction (i.e., local strain in y-direction, ε y ) through equation (  . Liquid flow was calculated in all the domains while structural mechanics was applied only to U b and U t domains. G t : top layer boundary was set to constant pressure (0.5 bar); G b : base layer boundary conditions were set to zero deformation; G m : permeate side subjected to zero relative pressure so that the TMP matched the value used in the experiment and G l : symmetry conditions were applied to the lateral boundaries. The zoomed geometry shows part of the model geometry including one cluster with different domains.
The biofilm displacement tensor d resulted from the balance of momentum for a saturated porous material (Biot poroelasticity (Coussy, 2004),). The linear elastic response depends on the elastic modulus E and Poisson's ratio n of the biofilm. In case of bilayer biofilms, different hydraulic and/or mechanical properties were applied in each layer. Applied boundary conditions are presented in Fig. 2 and all model parameters are in Table 3.

Model cases and their structure
Six biofilm cases were selected based on their morphology (rough or smooth surfaces) and structures (mono-layer or bi-layer). Biofilms have different surface roughness properties and multilayer structure depending on their growth conditions, as reported by Desmond et al. (2018c). They also observed during dead-end filtration that biofilms developed under phosphate limitation had smooth surface and mono-layer structure as opposed of river water biofilms that had rough surface and bi-layer structure (Desmond et al., 2018b). Existence of base layer can be explained by biofilm stratification (densification) adjacent to the substratum (e.g., membrane) caused by different growth condition parameters such as hydrodynamic strengths, carbon sources, organic loading rate and culture time (Bishop et al., 1995;Derlon et al., 2008;Okabe et al., 1996). In addition, biofilm porosity and elastic modulus were selected as distinctive properties in determination of biofilm hydraulic and mechanical behaviour (Jafari et al., 2018). Thus, in this study we selected smooth surface (case 1 and 2) and rough surface biofilms (case 3 to 6). To evaluate the importance of the bilayer structure, four biofilm cases with different porosity and/or elastic modulus among the layers were set up (cases 2, 4, 5 and 6). Table 2 shows biofilm morphologies and specifications of the six chosen cases.

Model solution
The 2-D fluid-structure interaction model was solved in COM-SOL Multiphysics (v5.3.a, COMSOL Inc., Burlington, MA). The fluid flow in porous media was coupled with plane strain structural mechanics and computed through a stationary solver. Triangular mesh elements had a maximum size of 2 mm, to ensure the solution independency on mesh size.

Correlation between biofilm hydraulic resistance and the structural deformation
River water biofilms were cultivated in parallel flow cells, under three different conditions. Fig. 3 shows the biofilm mean thickness and hydraulic resistance measured during a compression and relaxation cycle. As expected, biofilms grown for longer time (30 days) were thicker (70 ± 10 mm, average thickness) than younger biofilms (40 ± 3 mm after 20 days), under the same growth TMP (0.06 bar) ( Fig. 3a and b). Furthermore, biofilms grown under high TMP (0.28 bar) were thinner (50 ± 3 mm, average thickness)  compared to the low TMP (0.06 bar) biofilms, at the same age (30 days) ( Fig. 3b and c). Interestingly, when subjected to compression and relaxation phases, the river water biofilms did not undergo a significant structural deformation (i.e., change in thickness and roughness) (Fig. 3aec). A relatively constant biofilm thickness is also observed in the time-lapse videos in Supplementary Information, SI-V1 and SI-V2, while the membrane displacement clearly indicates the applied pressure steps. However, biofilm hydraulic resistance increases significantly during compression over TMP range of 0.06e0.5 bar (Fig. 3def): from 3 Â 10 12 to 5 Â 10 12 m À1 for the biofilm grown at 0.06 bar for 20 days and from 3 Â 10 12 to 4 Â 10 12 m À1 for the biofilm developed for 30 days. Biofilms grown under high TMP (0.28 bar) showed greater hydraulic resistance change from 5 Â 10 12 to 8 Â 10 12 m À1 during compression tests. These measurements clearly confirm that biofilms grown under higher TMP were more compact (thinner) (Fig. 3b and c) and associated higher hydraulic resistance ( Fig. 3e and f).

Effect of growth conditions on biofilm surface morphology
Experiments in UF flow cells have shown that the growth conditions affect not only the biofilm thickness, but also the biofilm surface roughness. Fig. 4 displays biofilm surface morphology properties (i.e., mean absolute roughness and mean relative roughness coefficient) developed in different conditions. Clearly, the biofilms after 30 days of cultivation showed higher roughness coefficient (d rough ¼ 0.3 ± 0.05) than after 20 days (d rough ¼ 0.16 ± 0.05) when grown under TMP ¼ 0.06 bar (Fig. 4a). Moreover, the biofilms grown at larger pressure were smoother (d rough ¼ 0.11 ± 0.05) compared to biofilms grown at low pressures (Fig. 4a). Similar trend was observed in biofilm mean absolute roughness (Fig. 4b). However, change in the biofilm roughness measured during compression of river water biofilms did not follow any clear trend (as also reported in other studies, e.g. Desmond et al. (2018c)).

Selection of a fluid-structure biofilm model correlating thickness and resistance under compression
Experimental measurements of river water biofilms under compression showed a considerable increase in hydraulic resistance (up to~60%), while biofilm thickness only slightly changed. To explain the correlation between biofilm thickness and resistance during compression, we developed a fluid-structural model and evaluated several biofilm possible structures with different morphological, mechanical and hydrological properties (Table 2). Three main variables (mean biofilm displacement, change in hydraulic resistance and water flux) were calculated and compared with experimental results of biofilm grown for 20 days under TMP ¼ 0.06 bar (Fig. 5). The fitting parameters (Table 3) were selected for each model biofilm individually, so that the three measured variables are optimally represented.
The model results of mean biofilm displacement obtained by one-layer-rough (case 3), dual-porosity-rough (case 4) and dualporosity-elasticity-rough biofilm models (case 6) are in agreement with experimental results. However, the mean displacement in other model cases was still within range of experimental results (Fig. 5a). Furthermore, the measured water flux was around 20e35 L/m 2 /h, which is compatible with the calculated flux for onelayer-flat (case 1), dual-porosity-elasticity-flat (case 2), dualporosity-rough (case 4) and dual-porosity-elasticity-rough biofilm models (case 6), Fig. 5b. Finally, Fig. 5c indicates that dual-porosityelasticity-flat (case 2), dual-porosity-rough (case 4) and dualporosity-elasticity-rough (case 6) biofilm models could explain a significant increase in hydraulic resistance (40e60%) during compression. Considering all three criteria, the dual-layer rough biofilms (Cases 4 and 6) are the most suitable to explain the experimental results. The difference between cases 4 (constant mechanical properties across the biofilm) and 6 (layers of different elasticity) shows that a gradient of initial biofilm porosity is more important than a gradient of mechanical properties in determination of biofilm deformation and hydraulic resistance during compression. Therefore, case 4 (dual-porosity-rough) was selected to further evaluate biofilm local properties during compression, due less model parameters required compared with case 6.

Model calibration and parameters estimation
All the model cases were calibrated with experimental results of biofilms grown for 20 days under TMP ¼ 0.06 bar. Model parameters used in this study are shown in Table 3. Geometric parameters (i.e., biofilm average thickness, base and top layers thickness and top layer coverage area) were selected based on OCT images and biofilm morphological properties of the specific biofilm. Initial porosity of top and base layers (if applicable) were chosen with the assumption that porosity of base layer is lower than top layer porosity prior to compression (Gao et al., 2011b). The porosity values and distribution in biofilms were in accordance with the observations reported by (Blauert et al., 2015;Gao et al., 2011b;Wagner et al., 2010). In the model calibration procedure, initial biofilm porosity of both layers (if applicable) was kept constant and only fitting parameters (permeability coefficient, elastic modulus) were changed to calibrate the models. Moreover, during model selection procedure (Fig. 5), a model was considered acceptable only if the model results were within the range of experimental data (considering experimental deviations). For example, in Fig. 5a all the models were acceptable for biofilm deformation due to the large spreading of data in the experiments. Sensitivity analysis of the proposed fluid-structure model to different parameters has been presented in our previous work (Jafari et al., 2018).

Local biofilm properties during compression
Computed 2-D distributions of the main model variables during compression (TMP ¼ 0.5 bar) are presented in Fig. 6. The water flows at higher velocity through the thin biofilm sections (~14 mm/ s), while the water velocity in the thicker parts (i.e., top layer) is much lower (~2 mm/s) (Fig. 6a). As expected, lower biofilm thickness results in lower hydraulic resistance and higher fluxes. The biofilm experiences the highest stress (2500 N/m 2 , Von Mises stress) near the membrane, compared to the top layer (570 N/m 2 ), as shown in Fig. 6b. In addition, due to large pressure drop, the stress is higher in the thick biofilm parts. Considering the relation of stress and strain, thus, greater local strain is observed in the biofilm next to the membrane (Fig. 6c). The top biofilm layer displaces more (13 mm) than the base layer (1 mm), due to the cumulative effect of strain on displacement (Fig. 6d). Higher local strain leads to lower biofilm porosity (Fig. 6e) based on eq. (3) and, consequently,  to reduced permeability (Fig. 6f). Although the biofilm top layer porosity remains almost constant (4 ¼ 0.8), the base layer undergoes a significant reduction of porosity after compression (4 ¼ 0.3 to 0.15). Similarly, biofilm permeability in top layer remained around 14 Â 10 À18 m 2 after compression, while the permeability decreased to~1 Â 10 À18 m 2 in the base layer.
Spatial distributions of biofilm porosity, permeability and physical structure (i.e., thickness) along the membrane surface cause heterogeneity of water flux along the membrane. Fig. 7a shows a pronounced difference in the calculated water flux at the biofilm base along the flow cell (~15e50 L/m 2 /h), whereas the flux is homogenized by flow through the membrane (37e41 L/m 2 /h). This considerable difference in flux distribution between biofilm and membrane boundaries (Fig. 7a) is correlated to flux homogenization in membrane domain, caused by lower membrane resistance and greater thickness compared to the biofilm).
A more detailed analysis demonstrates that due to distinct biofilm properties in the top and base layers, porosity and permeability undergo different behaviors during compression. Fig. 7b shows biofilm strain in the compression direction, ε y , across the biofilm depth, after compression at TMP ¼ 0.5 bar. The strain decreases from 0.7 at the membrane side to zero at the liquid side. The small change in strain gradient at the base layer/top layer interface is caused by the difference in porosity of the two layers. Fig. 7c demonstrates that the top layer porosity remains almost constant after compression, while biofilm porosity in base layer drastically decreases from its initial value (0.5) to 0.3 in top of base layer and 0.15 at the membrane surface.

Evaluation of flux and deformation from OCT biofilm images
Exact biofilm surface geometries (initial and after compression) were extracted from OCT images and the water flux and biofilm deformation were calculated on these geometries using the dualporosity-rough model (case 4). Fig. 8a and b shows OCT images of the biofilm under transmembrane pressure of 0.06 and 0.5 bar, respectively. Fig. 8a  The numerical model developed for the Case 4 (dual-porosityrough biofilm) was also used to evaluate the effect of biofilm surface roughness on the hydraulics and structural response of the biofilm to the same compression conditions (TMP ¼ 0.5 bar). To ensure that the area of base layer in contact with the liquid remained constant, the roughness was increased by changing the half-circular colonies into half-ellipses with increasing semi-major axes (four structures, shown in Fig. 9a).
Increasing the biofilm surface roughness from 20 to 80 mm (i.e., peaks 50e200 mm high) resulted in a total deformation from 8 to 13 mm, respectively. Fig. 9b shows that the total biofilm average displacement is mainly determined by the top layer (displaced 10e16 mm), while the base layer is less compressed (4 mm). However, more biofilm surface roughness just slightly decreases water flux during compression, from 34 L/m 2 /h (d abs ¼ 20 mm) to 32 L/m 2 / h (d abs ¼ 80 mm). Water flux approached a constant value as the surface roughness increased above 35 mm, which implies that the contribution of top sections to the water flux becomes negligible at high roughness.

Fraction of exposed base layer
Since the biofilm roughness does not significantly impact the permeate flux accordingly to our model results, we also evaluated other potential morphological parameters. The permeate flux during compression was calculated for three biofilm geometries with different morphologies (Table 4). Biofilm geometries were selected in which have identical average thickness and roughness values, but different fractions of base layer exposed to bulk liquid. To satisfy the mentioned criteria, different top/base layers thickness values were chosen. Fraction of exposed base layer was defined as area of biofilm base layer divided by the total biofilm surface area. The dual-porosity-rough model (Case 4) was applied and permeate fluxes were calculated under TMP ¼ 0.5 bar. Model results clearly demonstrate that configurations with higher fraction of exposed base layer (i.e., 0.71 for config. II) allow higher water flux (27.4 L/m 2 / h) compared to 10 and 20.7 L/m 2 /h for config. I and config. III, respectively (Table 4).

Discussion
Biofilm hydraulic resistance and structural deformation. Biofilms grown under high TMP showed higher hydraulic resistance and lower thickness compared to biofilms developed under low TMP (Fig. 3). In addition, biofilms grown under high TMP showed lower roughness values compared to biofilm developed under low TMP (identical growth time) (Fig. 4). This could be explained by higher drag force (induced by higher flux) and consolidation effect caused by the long-term continuous compression under high TMP. These results agree with other reported observations (Casey, 2007;Derlon et al., 2016;Le on Ohl et al., 2004). Biofilms developed under high TMP are likely more compact (i.e., lower porosity), which reduces the biofilm permeability and ultimately increases its hydraulic resistance. In this study we consistently observed that the increase in biofilm hydraulic resistance during compression was accompanied by limited biofilm deformation ( Fig. 3 and Supplementary Information, SI-V1 to SI-V2). A similar trend was also reported previously (Desmond et al., 2018a;Dreszer et al., 2014). One possible explanation for the increased hydraulic resistance would be a reorganization of the biofilm material (McCarthy et al., 2002) at a scale lower than the OCT resolution (thus not observable by OCT), while the biofilm thickness remains approximatively constant. Other authors related the larger hydraulic resistance during compression to the collapse of the mushroom-like biofilm structure (Valladares Linares et al., 2015) and the corresponding loss in macro-porosity , with a significant reduction in biofilm thickness. In our study, due to the small measured deformation during compression, we propose that the hydraulic resistance increase was caused by pore/particle reorganization at a scale lower than the OCT detectable threshold. In addition, simulation results confirm that in case of the base layer deformation equal to OCT detectable threshold (~3 mm), biofilm hydraulic resistance would rise by 110%, in agreement with the observed  results.
The biofilm model selection. A bi-layer morphology with a porous layer on top of a thin and dense base layer was observed by Derlon et al. (2016) and Desmond et al. (2018b) for biofilms developed under dead-end GDM. In order to explain the observed trend in biofilm structural deformation and the corresponding hydraulic resistance, several biofilm models were evaluated. The poroelastic numerical model proposed in Jafari et al. (2018) for smooth surface biofilms was extended here to include rough surface with duallayer properties. Fig. 5 confirms that only cases 4 and 6 (i.e., rough and double-layer biofilm, as observed in experimental results from Fig. 5) could explain the small total biofilm deformation associated with significant rise of hydraulic resistance under compression.
The gradient of porosity across the biofilm is more important than the gradient of elastic modulus for fluid-structural models. Gradients in biofilm porosity (Blauert et al., 2015;Okabe et al., 1998; or biofouling layer porosity (Gao et al., 2011a) were reported, with generally a dense base layer and more porous top layer. In this study, both model cases 4 and 6 can explain the observed trends in biofilm compressibility (Fig. 5). However, the model case 4 (i.e., same elastic modulus across both layers) would be preferable as it contains less parameters and thus it is simpler ( Table 2). The comparison between model cases shows that the biofilm deformation is mainly a result of pore compression, and the variable mechanical properties can be achieved by a gradient in porosity. This observation can further be used to simplify development of fluid-structure models. However, one should note that when water is not forced through the biofilm (e.g., biofilm developed on pipe walls) a gradient in elastic modulus could be important for the mechanical response (as permeate flux and porosity are not relevant) .
Biofilm local properties. Water permeates mostly through the thin parts of the biofilm due to lower hydraulic resistance (Figs. 6a, 7a and 8). This is in accordance with the computations by Martin et al. (2014) for model biofilm in GDM. Fortunato et al. (2017) reported unusual calculation results in which the permeate flux through biofilm peaks is larger than the flux through the thinner parts (biofilm cavities), in a submerged membrane biofilm reactor. They claimed this observation is due to the effect of liquid vortices in biofilm cavities leading to lower pressure gradient. However, their result is physically unrealistic because small axial velocities would only lead to negligible pressure drop compared to the transmembrane pressure gradient.
During compression, the biofilm porosity decreases mainly in the base layer (near the membrane) (Figs. 6e and 7c), which is in

Table 4
Three model biofilm configurations (geometries) with similar morphological properties (average thickness and surface roughness). Biofilms with greater fraction of exposed base layer lead to higher permeate flux. Results are based on dual-porosity-rough model (Case 4 parameters) and compression under TMP ¼ 0.5 bar.

Configuration
Model  Radu et al. (2015) for soft porous materials under deformation. Thus, during compression of the fouling layer, the base layer permeability decreases much more than in the top layer (due to local porosity reduction). Therefore, the base layer becomes even more important in the determination of water flux. However, not all biofilms may display this bi-layered structure. Desmond et al. (2018b) observed that for biofilms with smooth surface (i.e., synthetic biofilm developed under phosphate-limiting conditions), biofilm hydraulic resistance is determined by the whole biofilm structure and not by a dense base layer.
Effect of biofilm surface roughness on permeate flux. Although biofilm surface roughness affected the structural response during compression, its impact on the total permeate flux was not significant (Fig. 9). Again, this could be explained by the fact that the magnitude of the permeate flux is mainly dictated by the base layer. Derlon et al. (2012) reported that predation by eukaryotic microorganisms leads to heterogeneous biofilm structure with larger surface roughness accompanied by lower membrane coverage. The reduced membrane coverage caused higher values of the measured permeate flux at greater biofilm surface roughness. Fraction of exposed base layer. Although biofilm surface properties, such as roughness coefficient and thickness, are generally useful when characterizing biofilm morphology (Li et al., 2016;, these measures are not adequate when water flux is concerned. Biofilms with identical roughness and thickness might lead to different water fluxes during compression ( Table 4). Fraction of exposed base layer proves to be a better indicator to correlate permeate flux and biofilm surface morphology in membrane systems. A greater fraction of exposed base layer would result in a higher permeate flux through the biofilm.

Conclusions
An increased biofilm hydraulic resistance during compression is not necessarily accompanied by large structural deformation (i.e., not observable by OCT). The rise in resistance could be explained by micro-scale particle/pore reorganization of biofilms under pressure; Hydraulic resistance of membrane biofilm formed from river water is mainly governed by properties of their base layer (i.e., density, porosity and fraction of base layer exposed to bulk liquid), while deformation is governed by biofilm roughness; A poroelastic fluid-structural model was proposed to explain various biofilm behaviors under compression. The dual-layer biofilm with a porous top layer and a dense base layer can explain the observed increase in hydraulic resistance coupled with minor structural deformation; Model simulations indicate that, when developing fluidstructural models for membrane systems, considering a gradient in biofilm initial porosity is more important than a gradient in the elastic modulus. This allows to reduce complexity of poroelastic models; Biofilm surface roughness alone does not impact significantly water permeate flux under compression. The fraction of exposed base layer could be a better biofilm morphology indicator in determination of permeate flux.

Declaration of interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.