Application of liquid-infused membranes to mitigate biofouling

The novel liquid-infused membranes have been shown to mitigate membrane biofouling. Here, the long-term stability of these membrane have been tested and analyzed using bacterial growth curve models.


Membrane characterization
The commercial PVDF membrane (HVHP00010) is characterized using scanning electron microscopy (SEM) (JEOL 5600 LV) and capillary flow porometer (Porolux-1000). The SEM images of top, bottom and cross section of the membrane are shown in Figure S1.
Capillary flow porometry measurement on the commercial PVDF membrane is done by pushing nitrogen gas through the membrane infused with a low surface tension liquid, i.e. Fluorinert FC-43, at different pressure values. The corresponding gas flow rate is measured simultaneously. Figure S2(a) shows the nitrogen gas flow rate as a function of pressure for the PVDF membrane. This measurement is conducted in two runs: in the first run, the so called wet curve, a sudden increase in gas flow rate is observed which corresponds to the pressure where the biggest pores are opened (first bubble point (FBP)). In the second run as the liquid has been already pushed out, a linear behaviour between flow and pressure is obtained (dry curve). The point where wet and dry curves meet corresponds to the smallest pore size. The half-dry curve is also plotted where the flow values are half of the flow values of the dry curve. The crossing point of this curve and wet curve determines the mean flow pore size (MFP). The Young-Laplace equation by considering total wetting (θ E =180°) is used to relate pressure to the pore size. In Equation (S1), r is the pore radius (m), γ is the interfacial tension (N/m) between permeating fluid and liquid, and θ E is the advancing contact angle (larger than 90°) of the permeating fluid with respect to the pore wall. Based on the results of this measurement, the pore size distribution of the membrane can be obtained which is shown in Figure  S2(b). As can be seen in Figure S2, the commercial PVDF membrane has a narrow pore size distribution with an average pore radius of 0.51 µm and size distribution of 0.043 µm (full width at half max/2).
The contact angle measurement on dry and liquid-infused membrane (K101-infused) is performed using contact angle Goniometer (Dataphysics OCA20). Static contact angle measurement is performed by dispensing a 2 µl water drop on the membrane surface. At least 6 independent static measurements are performed on different spots of the membrane surface. Dynamic measure-ments (advancing-receding contact angle (ARCA)) are performed within six cycles by placing the needle in the 2µl-drop (sessile drop needle-in mode) and continuously supplying or withdrawing water up to 6 µl at the rate of 0.5 µl/min. The delay time between each cycle (advancing and receding measurement) is 2 s. The average results of all the measurements results are shown in Table S1. A lower contact angle hysteresis and subsequently higher droplet mobility are observed for liquid-infused membrane compared to dry membrane. However, contact angle hysteresis of liquid-infused membrane is not < 5°which implies "slipperiness" 1 . This is possibly due to the presence of hydrophilic impurities in the PVDF membrane reported by the manufacturer.

Liquid-liquid displacement (LLD) analysis
In order to better understand the retention of the infusion liquid in the liquid-infused membrane after water is pushed through the membrane, liquid-liquid displacement (LLD) experiment is done. The schematic of the set-up is shown in Figure S3(a). A Bronkhorst mass flow controller (mini CORI-FLOW M14) and pressure meter (IN-PRESS P-502CI) which are connected using a control valve (COMBI-FLOW Mass flow C5I) are used. The LLD experiment is performed in four different cycles. Each cycle is carried out in a flux-increasing mode, which is done twice starting from zero up to a certain flux value. In each run, the flux is increased step-wise. At each step, flux is kept constant for 100 s and the pressure is reported for the last 40 s of each step 1 . The result is shown in Figure  S3(b).
In order to check for the presence of the infusion liquid in the membrane after the experiment, the obtained results are compared with the results of the pre-wet membrane (see Figure S3). To make the pre-wet membrane first the membrane was infused with 15.5 µl cm −2 ethanol. Then the ethanol-infused membrane was kept in a beaker with 200 ml of MQ water overnight. This is done to make sure that the ethanol in the membrane pores are replaced with water. The permeability of pre-wet as well as liquid-infused membranes is calculated using Darcy's law 2 Here and in the following, Q is the volumetric flow of the permeating fluid (in this case water) (m 3 /s), κ is the permeability (m 2 ), a is the total area of the membrane (m 2 ), µ is the viscosity S1 Electronic Supplementary Material (ESI) for Environmental Science: Water Research & Technology. This journal is © The Royal Society of Chemistry 2020    of the displacing fluid (Pa s), d p dx is the pressure gradient across the membrane thickness (Pa/m), r is the mean pore radius (m), and φ is porosity. A simple model is then used to relate permeability to porosity φ , namely 1 The calculated porosity is a measure of opened and active pores for water transport in the membrane. The results of the calculated permeability and the estimated fraction of the active pores are shown in Table S2 (membrane thickness and water viscosity are considered as 80 µm and 1 mPa s respectively). This fraction is the ratio between the calculated porosity for the liquid-infused membrane in each cycle and that of the pre-wet membrane. The permeability of the liquid-infused membrane increases in each cycle, revealing that new pores are opened for water transport. The lower permeability values of liquid-infused membrane (LIM) in comparison with pre-wet membrane suggests incomplete removal of the infusion liquid with around 39% retained infusion liquid in the membrane. For more information on this kind of analysis, we refer the reader to our other work 1 .

Pictures of feed and permeate spacers
Figures S4(a) and S4(b) show the pictures of the feed and permeate spacers respectively.

Results of feed pressure increase
The feed pressure increase during the bio-fouling experiment was also monitored. The results for both dry and liquid-infused membranes with the presence of the feed spacer in the membrane module is shown in Figure S5. Lower feed pressure increase at a certain time is observable for liquid-infused membrane compared to dry membrane. This further shows that less bacteria is formed on the surface of the liquid-infused membrane compared to that of the dry membrane due to the presence of the infusion liquid.

Effect of nutrient concentration
The effect of nutrient concentration on bacterial growth is investigated by increasing the nutrient concentration to 7.2 g CH 3 COONa, 1.1 g NaH 2 PO 4 .2H 2 O, and 2.6 g NaNo 3 . The results of TMP and feed pressure increase are shown in Figure S6. The lower increase in both TMP and feed pressure for liquid-infused membrane compared to dry membrane confirm improved perfor-  mance of liquid-infused membranes in mitigation of bio-fouling. The increase in both TMP and feed pressure of liquid-infused membrane in the presence of the feed spacer in the membrane monitor can be attributed to the effect of spacer in acceleration of bacterial formation and growth. This is explained more in the main paper. Figure S7 shows images obtained from z-stack of CLSM at different depths. Figures S7(a) and S7(b) demonstrate closest plane to the biofilm surface (feed water solution side). The closest plane to the membrane area is shown in Figures S7(c) and S7(d).

Modification of logistic model
The fitting parameters (a, b, and c) for both membranes with different cell configurations are shown in Table S3. Based on defini-tion of biological parameters (see main paper, section "Modeling of bacterial growth curve"), one can determine the modified logistic model accordingly.
The sigmoidal logistic model (Equation 1 in the main paper) can be rewritten as The first and second derivatives of Equation S4 are respectively and The inflection point is where the second derivative is zero, i.e. exp(b − ct) − 1 = 0. Therefore t i = b c and the corresponding y value at the inflection point using Equation S4 is equal to a 2 . The specific growth rate (µ m ) is then the first derivative (Equation S5) at the inflection point, i.e.
By knowing one point ( b c , a 2 ) and the slope of the tangent line ( ac 4 ), one can describe the tangent line as Lag period λ is defined as the t-axis intercept of the tangent line (Equation S8 = 0). Therefore λ is calculated as Asymptotic value A is reached when t→ ∞ in Equation S4. By considering that, The mathematical parameters a, b, and c can be calculated based on biological parameters, λ , µ m , and A using Equations S10, S9, and S7 respectively. By substituting these mathematical parameters in logistic model (Equation S4) one can define the modified logistic model (Equation 2 in the main paper).

Linear regression
The R 2 values of the linear fit to the exponential phase together with the root mean square error (RMSE) and summation of square error (SSE) are shown in Table S4 for different cell configurations. As it is evident a relatively good fit was obtained for all the results. The obtained duration of the lag phase, i.e. λ directly from the graph of ln( P P 0 ) as a function of time for different cell configurations is shown in Table S5.   ) as a function of time.
Membrane and cell configuration λ Dry-without spacer 2.001 Dry-with spacer 2.235 LIM-without spacer 9.004 LIM-with spacer 0.000