Xuehui Zhao *,Yan Hu Yun Wu Hongwei Zhang

1 State Key Laboratory of Separation Membranes and Membrane Processes,Tianjin Polytechnic University,Tianjin 300387,China

2 School of Environment and Chemical Engineering,Tianjin Polytechnic University,Tianjin 300387,China

Keywords:Potassium permanganate Hollow fiber membrane Membrane fouling Chemical stability

A B S T R A C T The structure and performance of membrane materials are very important to the efficient and stable operation in membrane drinking water purification technology.Potassium permanganate(KMnO4),which can change the characteristics of organic matters and control membrane surface fouling,has been widely used as pre-oxidant in the front of membrane drinking water process.This study investigates the evolution of membrane surface structure and performance when polyvinylidene fluoride(PVDF)and polyethersulfone(PES)were exposed to 10,100 and 1000 mg·L-1KMnO4 solution for 6 and 12 d,respectively.The aged membrane physicochemical characteristics such as membrane surface morphology,chemical composition,hydrophilicity,porosity and zeta potential were evaluated by modern analytical and testing instruments.The anti-fouling property of membrane surface was also investigated by the filtration-backwash experiment.The results indicated that the different concentrations and exposure time of KMnO4 led to a different variation on PVDF and PES membrane surface structure and performance,which could further affect the membrane separation performance and the membrane fouling behaviors.The membrane surface pore size and porosity increased due to the dislodgment and degradation of membrane additive(PVP),which improved membrane permeability and enhanced the adsorption and deposition of pollutants in the membrane pores.With the increase of exposure time,the membrane surface pore size and porosity reduced for the reactions of chain scission and crosslinking on membrane materials,and the backwashing efficiency declined,leading to a more serious irreversible fouling.Compared with PVDF membranes,the formation of sulfonic group for PES membranes increased the negative charge on membrane surface due to the oxidation of KMnO4.The present study provides some new insights for the regulation of the pre-oxidant dose and the selection of the membrane materials in KMnO4 pre-oxidation combined with membrane filtration system.

1.Introduction

Membrane technology,as the third generation drinking water purification technology,has been paid more and more attention.However,membrane fouling is still a bottleneck in membrane technology,which impedes its further development[1–3].Many pretreatment technologies,including coagulation[3,4],oxidation[5]and adsorption[3,6]have been designed to mitigate membrane fouling and improve the quality of treated water.Among these pretreatment technologies,pre-oxidation technologies such as chlorine(Cl2),ozone(O3)and potassium permanganate(KMnO4)oxidation[7,8]play a crucial role in controlling membrane fouling.However,Cl2can react with natural organic matter(NOM)in the feed water to form more toxic disinfection by-products(DBPs)[9–11].O3oxidation increases the expenses and complexity of membrane filtration system due to the additional facilities[12].Consequently,KMnO4acted as a convenient and feasible oxidant has been widely applied in pre-oxidation process.Liang et al.[7]found that combined use of permanganate and chlorine could reduce the rate of ultrafiltration(UF)membrane fouling and improve the stability of UF membrane system.Lin et al.[13–15]showed that the use of KMnO4can significantly enhance the effluent water quality and mitigate the membrane fouling,due to the increased removal efficiency and the changed characteristics of NOM.Qu et al.[16]reported that in situ formed manganese dioxide particles changed the characteristics of the cells and exhibited a stronger ability in alleviating cell-related membrane fouling than KMnO4,which was the major mechanism of Microcystis cell fouling control by KMnO4pre-oxidation.Tian et al.[12]and Xie et al.[17]indicated that KMnO4pre-oxidation in combination with coagulation can not only improve the efficiency of coagulation,but also decrease the membrane fouling effectively.

The membrane surface physicochemical characteristics,such as pore diameter,porosity,zeta potential and hydrophilicity,have a significant effect on membrane performance.The enhancement of membrane hydrophilicity can improve water flux and increase the rejection of bovine serum albumin(BSA)solution,which also can mitigate membrane fouling due to the decrease of hydrophobic organic matters adsorbed on the membrane surface[18].The enlargement of membrane pore diameter can increase water flux and decrease the rejection of organics,which can adversely affect the quality of the produced water.Moreover,the changes of pore diameter may have an impact on the membrane fouling behaviors[19].The surface charge performance of membrane also can affect the rejection of organics and the anti-pollution ability.The increased surface negative charge can improve the electrostatic repulsion to the negative charged organic matters,and reduce the deposition of pollutants on membrane surface[20].

However,due to the characteristics of short reaction time in pre-oxidation immersed membrane filtration system,the direct contact of membrane material with KMnO4(overdose or incomplete reaction)can lead to a change of the membrane material structure and performance.Therefore,much attention should be focused on the stability of membrane material,which can impact not only the lifespan of membrane but also the quality of effluent.In previous studies,Xu et al.[10]found that the membrane tensile strength became weak and the membrane pore size became narrow by the pretreatment of chlorine,which could adversely affect the performance and operating life of membrane material.Lu et al.[15]reported that the KMnO4/UF system decreased the average membrane pore size,tensile strength and hydrophilicity in long term operation.Surawanvijit et al.[21]demonstrated that membrane exposed to chlorine experienced an increase in its surface roughness and hydrophilicity,which negatively affected the membrane integrity and performance.Nevertheless,how KMnO4affects membrane structure or surface characteristics under different conditions,such as exposure concentration and time,remains unclear.Hence,it is significant to investigate the effect of KMnO4on membrane material properties so that we can understand the influence mechanism of KMnO4on membrane lifetime.

The present study mainly focused on the effect of different KMnO4concentrations and exposure time on membrane structure and performance.We aim to investigate the mechanism how KMnO4affects the physicochemical characteristics of membrane surface.Both the polyvinylidene fluoride(PVDF)and polyethersulfone(PES)membranes were investigated to evaluate and compare their chemical stability after treatment with KMnO4solution.The effects of KMnO4on the characteristics of membrane,such as pore diameter,porosity,zeta potential and hydrophilicity were investigated.Furthermore,the membrane fouling behaviors were also discussed.

2.Experimental

2.1.Materials

PVDF( finger-like pores)and PES(sponge-like pores)hollow fiber membranes were purchased from a Membrane Technology(Tianjin)Co.,Ltd.The inner and outer diameter was 0.7 mm and 1.3 mm for PVDF fibers and was 0.8 mm and 1.4 mm for PES fibers,respectively.KMnO4was obtained from Tianjin Benchmark Chemical Reagent Co.,Ltd(Tianjin,China).Humic acids(HA)were purchased from Sigma-Aldrich,which was still stored in a freezer to avoid deterioration.HA was adopted to investigate membrane fouling and the concentration was 25 mg·L-1.Prepare the solution was filtered with 0.45-μm membrane by vacuum filtration to remove the insoluble substances before use.All solutions were prepared with deionized(DI)water produced from a Milli-Q water purification system(Millipore,USA).All reagents and chemicals were analytical grade.

2.2.Potassium permanganate treatment

In this study,the membranes were immersed in different concentrations of KMnO4for 6 and 12 d.During the exposure experiment,the equal numbers of PVDF and PES membranes with an effective filtration area of 2.45 m2were soaked in KMnO4solution.KMnO4solution was prepared in three different concentrations of 10,100 and 1000 mg·L-1and the pH value was adjusted to 7 by HCl and NaOH.The membranes were immersed in 5 L of beakers at room temperature and kept away from light to avoid deterioration.In order to keep the concentration of the KMnO4solution at the same level,the solution was changed every 48 h.After reaching to 6 and 12 d,part of membranes were took out and then thoroughly flushed with DI water.The membranes were soaked in DI water at least 24 h and then stored in DI water prior to testing.

2.3.Fouling and cleaning

All filtration experiments were performed in the dead-end mode with an out-inside type at room temperature.The pressure in the apparatus was controlled at 0.05 MPa by nitrogen gas as power supply.During the filtration,the permeate flux data was monitored in real time by an electronic scale,and the time was recorded by stopwatch.A schematic diagram of experimental apparatus is presented in Fig.1.The filtration experiment was mainly composed of the following steps.

(1)Each membrane was first compacted for 30 min at 0.08 MPa,and then the operating pressure was regulated at 0.05 MPa.The initial pure water flux was measured;

Fig.1.Schematic diagram of the experimental setup.(1,9-nitrogen;2,10-pneumatic setter;3,11-pressure gage;4-feed water tank;5-membrane module;6-permeate tank and balance;7-computer;8-drain;12-backwash water tank;13-backwash water tank and balance).

(2)Then the pure water was replaced by HA solution to obtain the relation curves that flux varies with time.Each period was 30 min,and the membrane flux data was collected every 15 min by an electronic balance;

(3)Hydraulic backwashing for the fouled membrane with DI water for 2 min(0.1 MPa)at the end of each cycle.

2.4.Membrane characterization methods

The morphology of PVDF and PES membranes were examined by a Hitachi S-4800 field emission scanning electron microscope(FESEM).The membrane porosity was acquired by the mass loss of wet membranes after drying.First,the membrane samples were soaked in DI water to fill the membrane space completely.Then,the wet membrane samples were measured by the analytical balance after removing the water absorbed on the membrane surface with blotting paper.After that,the membrane samples were dried in a vacuum drier and measured untila constantmass.The membrane porosity was calculated according to Eq.(1)

Fig.2.FESEM morphologies of the surface of PVDF membranes with different concentrations and exposure time(a)pristine membrane;(b)10 mg·L-1 for 6 d;(c)100 mg·L-1 for 6 d;(d)1000 mg·L-1 for 6 d;(e)10 mg·L-1 for 12 d;(f)100 mg·L-1 for 12 d;(g)1000 mg·L-1 for 12 d.

Attenuated Total Reflection-Fourier Transform Infrared(ATR-FTIR)was used to reflect the featured functional groups of PVDF and PES membranes.All spectra were recorded by summation of 16 scans set with 4 cm-1resolution between 450 and 5000 cm-1.The contact angle(DSA100m,KRUSS,Germany)of the membrane samples were performed by the sessile drop method to show membrane surface wet tability.At least 5 different points were chosen randomly to obtain the average values for each sample to minimize the error.The samples were dried in a vacuum drier at room temperature for at least 24 h prior to testing.The membrane surface charge was measured by a SurPASS electrokinetic analyzer(Anton Parr,Austria).The pH was automatically adjusted from 3 to 11 by the addition of NaOH and HCl.

3.Results and Discussion

3.1.Morphological characterization

The surface morphology of the virgin and treated membranes was examined by FESEM analysis.The FESEM images of the PVDF membrane's outer surface before and after immersion in KMnO4solution are shown in Fig.2.As presented in Fig.2(b)–(d),when PVDF membranes were exposed to 10,100 and 1000 mg·L-1KMnO4for 6 d,the apparent larger pore size could be observed on the membrane surface compared with virgin membrane.But interestingly,the numbers and size of the membrane pore decreased and narrowed noticeably when exposed to KMnO4for 12 d[Fig.2(e)–(g)].All the images suggested that exposure to KMnO4solution changed the morphology of membrane surface.The enlargement of membrane pore size might due to the dislodgment and degradation of polyvinylpyrrolidone(PVP)in the PVDF membrane surface[22].A reduction in the numbers and size of the membrane pore might be attributed to the alteration of the PVDF composition by chain scission and crosslinking reactions of the macromolecular chains.Fig.3 represents the FESEM images of the PES membrane's outer surface before and after immersion in KMnO4solution.The variation of PES membrane surface morphology was fundamentally consistent with that of PVDF membrane.The membrane pore size enlarged when exposed for 6 d and shrunk gradually when exposed for 12 d.The modification of membrane surface morphology had a great impact on the permeability and fouling behaviors.In addition,the hydrophilicity and zeta potential of membrane surface were closely related to the membrane surface morphology.These contents will be studied and discussed in the later.

Fig.3.FESEM morphologies of the surface of PES membranes with different concentrations and exposure time(a)pristine membrane;(b)10 mg·L-1 for 6 d;(c)100 mg·L-1 for 6 d;(d)1000 mg·L-1 for 6 d;(e)10 mg·L-1 for 12 d;(f)100 mg·L-1 for 12 d;(g)1000 mg·L-1 for 12 d.

3.2.ATR-FTIR spectroscopy

The ATR-FTIR spectra of PVDF and PES membranes before and after treated with KMnO4solution are presented in Fig.4.For PVDF membranes[Fig.4(a)and(b)],the band at 1675 cm-1can represent carbonyl group(C=O),which confirmed the presence of PVP in the membrane matrix[23].The intensity of the peak at 1675 cm-1for KMnO4-treated membranes reduced significantly as compared to the pristine membrane,indicating a weakening of the C=O bond.This decrease came with the appearance of two new bands at 1700 cm-1and 1770 cm-1when exposed to 1000 mg·L-1KMnO4solution,which could represent succinimide group that ascribed to PVP degradation products[18,24].It indicated that high concentration KMnO4solution not only impacted the PVP content,but it also induced PVP degradation.

For PES membranes[Fig.4(c)and(d)],the band at 1667 cm-1can attribute to the C=O bond of the PVP[25].The bands at 1700 cm-1and 1770 cm-1(assigned for succinimide group)ascribed to oxidation products of PVP.However,the new bands(1700/1770 cm-1)could be observed in spectra of PES membranes when exposed to KMnO4solution even at low concentrations(10 and 100 mg·L-1),indicating the PVP presented in the PES membrane matrix was more easily affected than PVDF.The observed different influences on PVP between PVDF and PES membranes could be explained by the different of membrane pore structure,the casting process,etc.Noted that the peak at 1045 cm-1could be assigned to the symmetric vibrations of SO3-[26],which was absent in pristine PES membrane.However,the band at 1045 cm-1(assigned for SO3-group)disappeared after treatment with KMnO4,indicating the dissolution of the SO3-group due to the oxidation reaction.Correspondingly,there was a weak new peak at 1034 cm-1[Fig.4(c)and(d)],which this peak was believed to be attributable to sulfonic group.The appearance of sulfonic group denoted the occurrence of oxidation degradation reaction on the treated PES membrane surface[27].It is worth to mention that the formation of sulfonic group can improve membrane hydrophilicity and negative charge[20].Based on these results,we concluded that PVDF and PES membranes treated with KMnO4led to a decrease in PVP content or a degradation of the PVP.

Fig.4.The ATR-FTIR spectra of PVDF and PES membranes with different exposure dose and time(a)PVDF-6 d;(b)PVDF-12 d;(c)PES-6 d;(d)PES-12 d.

3.3.Contact angle

The contact angle of pristine PVDF and PES membranes and of these membranes treated with 10,100 and 1000 mg·L-1KMnO4solution are shown in Fig.5.Compared with new membrane,the contact angle increased slightly for PVDF and PES membranes[Fig.5(b)]when treated with 10 mg·L-1KMnO4solution for 6 d,which could be due to the dislodgement of PVP in membrane surface.However,the contact angle for both two membranes decreased when treated with 100 and 1000 mg·L-1KMnO4solution,which indicated that surface hydrophilicity was improved.The main explanation was that the enhanced capillary effect due to enlarged membrane pore size,which could be responsible of spreading out of the drop by capillarity[20].Similar evidence also can be found in the literature[28],the contact angle tends to decrease when the pore size of glass capillary increases.For PES membranes,another possible explanation for the following decreased contact angle could attribute to the emerging of hydrophilic sulfonic group that it can lead to partial ionization of the membrane surface[29].It is worth mentioning that the effect of PVP on membrane surface hydrophilicity was the subordinate factor at this stage.The contact angle of these treated membranes increased gradually with the increase of KMnO4concentration when exposed for 12 d,and the value increased to 85.3°for PVDF membranes and 83.5°for PES membranes when treated with 1000 mg·L-1KMnO4solution.The reduction in hydrophilicity of processed membranes can be explained by the loss of PVP and the decrease of membrane pore size due to the alteration in the membrane structure or its composition.Based on these results,we believe that the impact of sulfonic group was not significant in comparison with other factors,though it can improve the hydrophilicity of PES membranes partly.It has to be pointed out that the increase in membrane surface hydrophilicity seems to improve the anti-pollution performance of membranes when exposed to 100 and 1000 mg·L-1KMnO4for 6 d,but in fact,the improved surface hydrophilicity was caused by the changes of membrane pore size at this stage.The hydrophilicity of membrane increased in this phase,but the membrane fouling would increase rather than decrease when compared with virgin membrane,which will be further discussed in the subsequent fouling experiment.

3.4.Membrane flux experiment

The pure water flux(J0)was measured at different pressure with outside-in mode.Usually the pure water flux of membrane can be described by the Hagen-Poiseuille Eq.(2),which is a linear relationship with trans-membrane pressure(TMP).

According to Eqs.(2)and(3),we can infer that the larger of the slope value(K),the larger of the porosity(ε)or pore size(d)of the membrane surface.Fig.6(a)shows the variations of PVDF membrane's pure water flux with TMP before and after treatment with KMnO4solution for 6 d.We can see that the slope value of virgin membrane was 2.35.After exposed to 10,100 and 1000 mg·L-1KMnO4solution for 6 d,the slope values reached 2.59,3.07 and 3.84,respectively.Obviously,the slope markedly increased with the increase of the KMnO4concentration,which indicated the porosity or pore diameter enlarged.However,the slope decreased gradually when the membranes exposed to KMnO4solution(apart from the concentration of 10 mg·L-1)for 12 d in Fig.6(b).It can be concluded that the porosity or pore diameter decreased when exposed for longer time.The enlarged porosity or pore diameter can be attributed to the dislodgment and degradation of PVP,and the impact of KMnO4oxidation was the main cause of the reduced porosity or pore diameter at a later stage.However,a different impact of KMnO4on PES membranes was found when compared with PVDF membranes in Fig.6(c).The slope value reached the maximum of 4.11 when exposed to 100 mg·L-1KMnO4solution for 6 d,which manifested the PVP in the PES matrix might be affected easily even at low concentration.But interestingly,the slope value decreased to 3.74 when exposed to 1000 mg·L-1KMnO4solution,indicating that the porosity or pore diameter dropped gradually due to the oxidation reaction between PES and KMnO4.As membrane exposure time increased to 12 d[Fig.6(d)],the slope values reduced to 2.74 and 2.42 for the exposure concentrations of 100 and 1000 mg·L-1,respectively,which showed that the porosity or pore diameter became lower than that of the original membrane.Further analysis of the results shows that the composition of the PES was more easily impacted by KMnO4than PVDF.

Fig.5.Contact angle of membranes with different KMnO4 exposure dose and time(a)PVDF membranes;(b)PES membranes.

Fig.6.Variations of pure water flux as a function of TMP(a)PVDF-6 d;(b)PVDF-12 d;(c)PES-6 d;(d)PES-12 d.

The porosity values of PVDF and PES membranes are presented in Table 1.For both two membranes,the membrane porosity increased with the increase of KMnO4concentration when exposed for 6 d.The increased porosity might be attributed to the dislodgment and degradation of PVP when exposed to KMnO4for 6 d,and the decreased porosity might be resulted from oxidation reaction by chain scission and crosslinking reactions when exposure time increased to 12 d.These results indicate that the membrane porosity and pore diameter were affected by KMnO4.

3.5.Zeta potential

Surface zeta potential is conducted to reflect the charge properties of membrane surface and demonstrates their relative changesupon chemical treatment.The zeta potential of pristine PVDF and PES membranes and the membranes after KMnO4exposure are shown in Fig.7.The decreased zeta potential with increasing of pH was caused by protonation or deprotonation of surface functional groups[21].As can be seen from Fig.7(a)and(b),it could be observed that there were no significantsurface charge modifications in the PVDF membrane outer surface after KMnO4treatment.It is confirmed that no charged functional groups generated or disappeared when treatment with KMnO4for PVDF membranes.As can be seen from Fig.7(c)and(d),the negative charge increased in sequence of PES(virgin)＜PES(10)＜PES(100)＜PES(1000),implying the effect of KMnO4on the surface compositions of PES membranes.This result could be explained by the formation of sulfonic group[29],which was in accordance with ATR-FTIR analysis.It is noteworthy that the negative charge became higher with the increase of exposure concentration and time,indicating that more sulfonic groups were formed as a result of the continuous oxidation.

Table 1Porosity(ε)of PVDF and PES membrane as a function of KMnO4 dose and exposure time

3.6.Membrane fouling and reversibility

Fig.7.Membrane surface zeta potential of the virgin and treated membranes with different KMnO4 exposure dose and time(a)PVDF-6 d;(b)PVDF-12 d;(c)PES-6 d;(d)PES-12 d.

Normalized flux values(J/J0)of the PVDF membranes when exposed to 10,100 and 1000 mg·L-1KMnO4solution for 6 and 12 d are shown in Fig.8(a)and(b).The virgin membrane flux declined to 88%and recovered to 95%after hydraulic backwash in the first period.Meanwhile the membrane flux after treatment with 10,100 and 1000 mg·L-1KMnO4solution decreased to 87%,85%and 84%and recovered to 93%,90%and 88%when exposed for 6 d,and the flux decreased to 84%,83%and 81%and recovered to 90%,87%and 85%when exposed for 12 d,respectively.When the filtration period was over(180 min),the virgin membrane flux recovered to 75%and the treated membranes recovered to 72%,71%and 69%for6 d and 71%,70%and 67%for12 d for the KMnO4concentrations of 10,100 and 1000 mg·L-1,respectively.Compared with the original membrane,the developing rate of fouling and degree of irreversible fouling of treated membranes were obviously increased.The reason was mainly due to the loss of the PVP which enhanced the hydrophobicity of membrane.Another reason could be the changes of the typical fouling models on account of the changes of the membrane porosity and pore diameter.The enlarged membrane pores may enable more organic matters to enter into pores and deposit on the pore walls,which reduced membrane pore volume and resulted in the increase of irreversible fouling.On the other hand,we assumed that the reduced membrane pores may also lead to a serious irreversible fouling.The pollutants would be harder to enter into smaller membrane pores,but the fouling absorbed into the pores was also hard to remove by backwashing at the same backwash pressure,which could be proved that the amount of backwashing water was far less than the pristine membrane when the membrane pore size decreased.The foulants continuously deposited on the membrane surface and in the membrane pores due to the cyclical filtration process,thus the membrane irreversible fouling increased.Furthermore,the membrane flux decreased with the increase of KMnO4concentration and exposure time,indicating that the membrane anti-pollution performance became worse.

For PES membranes,as shown in Fig.8(c)and(d),the pristine membrane flux decreased to 82%and recovered to 93%in the first period.Meanwhile the membrane flux after treatment with 10,100 and 1000 mg·L-1KMnO4solution decreased to 81%,79%and 78%and recovered to 91%,88%and 86%when exposed for 6 d,and the flux decreased to 79%,78%and 76%and recovered to 88%,86%and 83%when exposed for 12 d,respectively.When the filtration period was over(180 min),the virgin membrane flux recovered to 77%and the treated membranes recovered to 72%,71%and 68%for 6 d and 71%,69%and 64%for 12 d for the KMnO4concentrations of 10,100 and 1000 mg·L-1.This result showed that the developing rate of PES membrane fouling and degree of irreversible fouling were faster and higher than PVDF membrane,indicating that PES membranes exposed to KMnO4were impacted severely than PVDF membranes so that the anti-pollution ability was more vulnerable.

4.Conclusions

In this study,it can be confirmed that KMnO4solution had a significant impact on membrane surface morphology,hydrophilicity,porosity,zeta potential,permeation flux and membrane fouling behaviors for PVDF and PES membranes.In the early immersion,the membrane surface additive(PVP)was dissolved and degraded,and the membrane surface pore size and porosity increased.Moreover,the membrane surface hydrophilicity improved and the membrane permeation flux increased.With the increase of KMnO4exposure concentration and time,the membrane surface pore size and porosity reduced by chain scission and crosslinking reactions of the membrane materials.Furthermore,the membrane surface hydrophobicity enhanced and the membrane permeation flux decreased.For PVDF membranes,the membrane surface zeta potential remained unchanged.However,the membrane surface negative charge became higher due to the formation of sulfonic group for PES membranes after KMnO4treatment.

The membrane fouling experiment indicated that the micromolecular organics can deposit and absorb in the membrane pores more easily due to the enlarged pore size and porosity in the initial stage of immersion.With the increase of KMnO4exposure concentration and time,more organic matters can be retained on the membrane surface,and the backwashing strength and efficiency declined,resulting in a more serious irreversible fouling.Based on these results above,we can get some information in regard to the control of the pre-oxidant(KMnO4)dose and the selection of the membrane materials when considering the stability of membrane structure and performance in pre-oxidation combined with membrane filtration system.

Fig.8.Normalized flux declines of PVDF and PES membranes with different exposure time and dose at 0.05 MPa:(a)PVDF-6 d;(b)PVDF-12 d;(c)PES-6 d;(d)PES-12 d.

Nomenclature

d pore diameter,μm

L membrane thickness,mm

Δp trans-membrane pressure,MPa

Wwmass of wet state membrane,g

Wdmass of dry state membrane,g

ε surface porosity

η dynamic viscosity,m·s-1

ρmdensity of membrane,g·cm-3

ρwdensity of water,g·cm-3

τ pore tortuosity