hydrophilic dual-layer membranes for direct contact membrane distillation

Journal Pre-proof Theoretical guidance for fabricating higher flux hydrophobic/hydrophilic dual-layer membranes for direct contact membrane distillation Lihua Zhao, Chunrui Wu, Xiaolong Lu, Derrick Ng, Yen Bach Truong, Jianhua Zhang, Zongli Xie PII:

S0376-7388(18)31711-3

DOI:

https://doi.org/10.1016/j.memsci.2019.117608

Reference:

MEMSCI 117608

To appear in:

Journal of Membrane Science

Received Date: 21 June 2018 Revised Date:

18 September 2019

Accepted Date: 23 October 2019

Please cite this article as: L. Zhao, C. Wu, X. Lu, D. Ng, Y.B. Truong, J. Zhang, Z. Xie, Theoretical guidance for fabricating higher flux hydrophobic/hydrophilic dual-layer membranes for direct contact membrane distillation, Journal of Membrane Science (2019), doi: https://doi.org/10.1016/ j.memsci.2019.117608. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Graphical Abstract

1

Theoretical guidance for fabricating higher flux hydrophobic/hydrophilic

2

dual-layer membranes for direct contact membrane distillation

3

Lihua Zhaoa,b,c, Chunrui Wub, Xiaolong Lu b*, Derrick Ngc, Yen Bach Truongc, Jianhua Zhangd,

4

Zongli Xiec*

5

a

Shenzhen Key Laboratory of Environmental Chemistry and Ecological Remediation, College of

6

Chemistry and Environmental Engineering, Shenzhen University, Shenzhen 518060, PR China

7

b

8

International Joint Research on Separation Membranes, Institute of Biological and Chemical

9

Engineering, School of Material Science and Engineering, Tianjin Polytechnic University, Tianjin

State Key Laboratory of Separation Membranes and Membrane Processes/ National Center for

10

300387, PR China

11

c

CSIRO Manufacturing, Private bag 10, Clayton South MDC, VIC 3169, Australia

12

d

Institute for Sustainability and Innovation, Victoria University, P.O. Box 14428, Melbourne, VIC

13

8001, Australia

14

*Corresponding authors. Tel./fax: +86 22 83955169 (X. Lu), +61 3 9545 2938 (Z. Xie).

15

E-mail addresses: [email protected] (X. Lu), [email protected] (Z. Xie).

16

Abstract

17

In this study, a new simultaneous heat and mass transfer theoretical model of the

18

membrane distillation process operating under direct contact membrane distillation

19

(DCMD) mode has been developed for the hydrophobic/hydrophilic dual-layer

20

composite membranes. Using the proposed model, a criterion parameter ( β ) was

21

derived to determine whether the flux will be increased for the prepared

22

M hydrophobic/hydrophilic composite membranes. A flux ratio ( γ DL/SL ) of dual-layer to

23

single-layer membrane was also developed to predict the DCMD flux performance of

24

the composite membranes. To validate the theoretical model, three sets of dual-layer

1

25

hydrophobic/hydrophilic composite membranes and single-layer hydrophobic

26

membranes with defined total thicknesses (240µm, 260µm, and 285µm) and different

27

thickness ratios ( δ δ o = 3.69, 2.48 and 2.19) were purposefully fabricated using

28

electrospinning technique. Theoretical modelling results were compared with the

29

experimental data in terms of DCMD flux ratio. The experimental data of flux ratios

30

E for the three sets of fabricated membranes at 60℃, γ DL/SL , are 2.75, 1.97 and 1.80,

31

respectively, which fit well with the model prediction values ( γ DL/SL = 2.96, 2.18, and

32

1.97) within high agreement level at a relative standard deviation of 9.6%.

33

Furthermore, the flux ratio of DL2 to SL2 membranes (dual-layer and single-layer

34

membranes with 260µm total thicknesses and δ δ o = 2.48 thickness ratio) at different

35

feed inlet temperatures still maintain a high degree of consistency with model values.

36

Overall, the results show the experimental data agree well with the theoretical model

37

prediction for the flux ratio within relative standard deviation of 10.1%, thereby

38

confirming the validity of the proposed model. Additionally, a critical value of the

39

thickness ratio ( χ ) was calculated, χ =1+ 1

40

guidance to design a highly efficient hydrophobic/hydrophilic dual-layer composite

41

membrane for DCMD applications in the future work.

42

Keywords: Theoretical modelling; Hydrophobic/hydrophilic; Dual-layer membranes;

43

Flux enhancement; Membrane distillation

44

1. Introduction

45

M

β , this value could provide useful

As an emerging membrane technology, membrane distillation (MD) possesses 2

46

some unique advantages over the conventional membrane processes, being its

47

theoretically complete rejection of non-volatile species, the potential to use the

48

low-grade waste heat and/or alternative energy sources such as solar and geothermal

49

energy, and operations can be carried out at low pressures and less strict requirements

50

in terms of mechanical strength of the membranes used [1-4]. It has great potential for

51

application in seawater desalination, waste water treatment and concentration of

52

temperature sensitive materials [5-6].

53

Despite its great potential, MD process hasn't been commercialized for industrial

54

application. One major limitation is that there is no membrane specifically designed

55

for MD process as yet. The currently used MD membranes are generally designed for

56

microfiltration (MF) purpose. Thus, there is a strong need to improve the MD

57

membrane design and structure for a better MD performance [7]. In contrast to

58

conventional pressure driven membrane separation processes such as microfiltration,

59

ultrafiltration (UF) and nanofiltration (NF), MD involves a coupled mass and heat

60

transfer phenomena which is especially obvious in direct contact membrane

61

distillation (DCMD). Awareness of the coupling effect is essential in designing

62

membranes for the MD process, thus both mass and heat transfer need to be

63

considered simultaneously in order to design an ultimate membrane for MD process.

64

Theoretically, a high-performance membrane in MD applications should exhibit: (1)

65

low vapor transfer resistance for higher flux, (2) low thermal conductivity to prevent

66

heat loss across the membrane, and (3) good mechanical durability and stability for

3

67

long term use [8]. To get higher flux, a common approach is to fabricate thinner

68

membranes, since the thinner membranes are expected to exhibit a higher vapor flux

69

due to the lower mass transfer resistance. However, membrane with such thin wall

70

thickness often becomes fragile and has low mechanical strength that fails to

71

withstand the hydraulic pressures from feed and/or permeate side. In addition, in the

72

process of DCMD, a thinner membrane increases the conductive heat loss through the

73

membrane matrix which translates into a lower temperature gradient across membrane,

74

leading to a decrease of the driving force and reduction of the permeate flux [9].

75

Several approaches have been investigated by different research groups to enhance

76

the properties and performance of MD membranes, which include: (a) incorporation

77

of nanoparticles into polymeric matrix [10-12]; (b) fabrication of electrospun

78

nanofiber membranes (ENMs) [13-16]; and (c) fabrication of dual-layer or triple-layer

79

membranes [17-23]. Among these, hydrophobic/hydrophilic dual-layer membrane

80

seemed to be an effective way to solve the membrane thickness problem and showed

81

promising positive improvement as the thicker hydrophilic layer can mechanically

82

support the brittle thin hydrophobic layer while the thin hydrophobic layer reduces the

83

mass transfer resistance and generates a higher vapor flux [24].

84

In the hydrophobic/hydrophilic membranes, vapor condensation occurs at the

85

interface of hydrophobic/hydrophilic layer, the existence of hydrophilic layer may

86

greatly reduce the mass transfer resistance between the evaporation side and the

87

condensation side comparing with mere hydrophobic membrane of the same thickness.

4

88

However, the thinner hydrophobic layer increases conductive heat loss and the

89

hydrophilic layer introduces an additional heat transfer resistance that amplifies the

90

undesirable temperature polarization which will reduce the flux instead. To address

91

this problem, Bonyadi and Chung [24] calculated the overall heat transfer coefficient

92

in permeate side and pointed out that in order to minimize the heat transfer resistance

93

induced by the fixed hydrophilic layer thickness, one possible way is to fabricate the

94

hydrophilic layer as porous as possible. In addition, their following study [25]

95

investigated the effect of hydrophilic layer’s thermal conductivity on vapor flux. They

96

found that the thermal conductivity of the hydrophilic layer is a key factor affecting

97

the flux. The results showed a greater improvement in vapor flux by importing fillers

98

with high thermal conductivity in the hydrophilic layer. However, there was no flux

99

comparison with single-layer hydrophobic membranes of the same total thickness.

100

Although previous studies [26-29] have demonstrated the concept of hydrophobic/

101

hydrophilic composite membranes as high flux MD membranes, suggesting that a

102

thinner hydrophobic layer combined with a thick hydrophilic layer will increase the

103

flux, however, there are still questions to be explored: 1) When compared with

104

single-layer hydrophobic membrane with same thickness, could the flux enhancement

105

be expected from the dual-layer composite membrane? 2) What is the relationship

106

between the flux enhancement of dual-layer membrane and the thickness ratio of each

107

layer? So far, researches and practical understanding on this topic remain scarce.

108

In a new research, Chew et al. [30] developed an MD model for a hydrophobic

5

109

microporous membrane that having a hydrophilic macromolecular- or bio-fouling

110

(MMBF) layer on the feed side. In their study, the effect of hydrophilic fouling layer

111

was incorporated into the model and developed an experimental protocol for assessing

112

whether the Kelvin effect is operative or not. Normalized flux equation ( N /N 0 ) was

113

also derivated and used to predict the flux decline resulting from the presence of

114

hydrophilic MMBF layer. Inspired by the above work, the main objective of this

115

research is to investigate the effect of an additional hydrophilic layer on flux

116

performance of the hydrophobic/hydrophilic dual-layer membrane. A theoretical

117

model based on the heat and mass transfer mechanisms was developed for the

118

hydrophobic/hydrophilic dual-layer membrane. The model synthetically combined the

119

effect of the following factors on DCMD flux: thinner hydrophobic layer will increase

120

the flux since the reduced mass transfer resistance; on the other hand, flux will be

121

decreased due to the fact that thinner hydrophobic layer increases conductive heat loss

122

and the thicker hydrophilic layer introduces an additional heat transfer resistance that

123

amplifies the undesirable temperature polarization which will reduce the flux instead.

124

Taking comprehensive account of above factors into the model, the flux performance

125

of hydrophobic/hydrophilic dual-layer membrane was systematically studied. A

126

criterion parameter ( β ) was also derived to determine whether the flux will be

127

increased for the prepared hydrophobic/hydrophilic membrane. Moreover, the

128

relationship between the flux enhancement of dual-layer membranes and the thickness

129

ratio of each layer were also investigated. Further, a novel hydrophobic/hydrophilic

130

dual-layer membrane was specifically fabricated via electrospinning with controlled

6

131

thickness to allow for experimental validation of the theoretical model.

132

Electrospinning technique was adopted here since it is a versatile method that can

133

meet the requirements of forming a uniform nanofiber layer with controlled thickness

134

on the support surface. MD performance tests were conducted for the fabricated

135

membranes under DCMD mode to verify the theoretical model validity. To the best

136

knowledge of the present authors, this is the first time to systematically study the flux

137

performance of a hydrophobic/hydrophilic dual-layer membrane versus single-layer

138

hydrophobic membrane with same total thickness from both theoretical modelling and

139

experimental validation approaches.

140

2. Experimental

141

2.1. Materials

142

Polyvinylidene fluoride-co-hexafluoropropylene (PVDF-HFP, Mw = 400,000

143

g/mol), N, N-dimethylformamide (DMF), acetone, sodium chloride (NaCl), and

144

lithium chloride (LiCl) were purchased from Sigma-Aldrich. All chemicals were used

145

as received. In addition, a commercial hydrophilic Biodyne-A Nylon 6,6 membrane

146

(water contact angle < 40°) was sourced from Pall corporation and used as the

147

hydrophilic substrate (support layer) of the dual-layer membrane.

148

2.2. Membrane preparation

149

PVDF-HFP solution was prepared by dissolving 15 wt.% PVDF-HFP polymer

150

pellets in a mixed solvent composed of DMF and acetone (4:1 by wt.%) through 7

151

overnight stirring at room temperature. A small amount of LiCl (0.005 wt.%) was

152

added into the PVDF-HFP solution to improve its electrospinnability [31]. Table 1

153

shows the composition of the dope solution used in this study. Table 1 Composition of the electrospinning dope solution.

154

Materials

PVDF-HFP

DMF

acetone

LiCl

Content (wt. %)

15

68

17

0.005

155

Fig.1 shows a schematic drawing of the electrospinning set-up. To fabricate the

156

dual-layer hydrophobic/hydrophilic membrane, the commercial hydrophilic Nylon 6,6

157

membrane was first fixed onto the surface of rotating drum collector, followed by

158

electrospinning hydrophobic PVDF-HFP nanofibers on top of the Nylon 6,6

159

membrane substrate. For comparison, a control single-layer hydrophobic PVDF-HFP

160

membrane with same total thickness was also fabricated by electrospinning

161

PVDF-HFP nanofibers directly to the rotating drum collector covered with an

162

aluminum foil.

163 164

Fig.1. Schematic diagram of the electrospinning equipment.

8

165

3 sets of dual-layer hydrophobic/hydrophilic membranes and single-layer

166

hydrophobic membranes of different total thicknesses and thickness ratios were

167

fabricated by manipulating the electrospinning time while keeping all the other

168

operating conditions unchanged. The electrospinning operating conditions are

169

summarized in Table 2. After electrospinning, the fabricated membranes were dried in

170

an oven at 60 ℃ for 24 h to remove the residual solvents. Table 2 Operating conditions of the electrospinning.

171

172

173

Spinning conditions

Value

High voltage (kV) Feed flow rate (ml/h) Tip-to-collector distance (cm) Chamber humidity (%) Chamber temperature (℃)

20 1.0 15 30-40 23-25

2.3 Membrane characterization

All the membranes used in the present study were characterized by the

174

measurement of total thickness ( δ ), hydrophobic layer ( δ o ) and hydrophilic layer ( δ i )

175

thickness, hydrophobic layer mean pore diameter ( do ), hydrophobic layer ( ε o ) and

176

hydrophilic layer ( ε i ) porosity and hydrophobic surface water contact angle ( θ ).

177

Details of the experiments are presented in the supplementary information. Table 3

178

shows membranes characterization results for the single-layer hydrophobic and

179

dual-layer hydrophobic/hydrophilic membranes. These characterization results are

180

used for theoretical calculation and experimental verification in the following

181

sections.

9

Table 3 Characterized physical properties of the electrospun membranes.

182

Membrane

δ

δo

δi

Code

(µm)

(µm)

(µm)

SL-1

240±1.8

240±1.8

0

DL-1

240±2.1

65±0.7

175±1.5

SL-2

260±2.2

260±2.2

0

DL-2

260±2.5

105±1.0

155±1.2

SL-3

285±2.7

285±2.7

0

DL-3

285±2.3

130±1.2

155±1.2

δ δo 3.69

2.48

2.19

εo

εi

do

θ

(%)

(%)

(µm)

(°)

89.5±1.8

-

1.472±0.060

146.8±0.8

90.6±1.2

70.3±1.2

1.515±0.103

146.7±1.1

89.1±1.7

-

1.313±0.099

144.4±1.0

90.3±2.1

71.1±0.8

1.467±0.055

144.3±1.3

89.7±1.8

-

1.286±0.126

147.3±0.9

90.3±0.8

71.1±0.8

1.419±0.007

146.5±0.4

183

Note: SL and DL represent single-layer, dual-layer membranes, respectively.

184

2.4 DCMD test

185 186

Fig.2. Schematic of the experimental setup used for DCMD test.

187

DCMD experimental set-up in a counter-flow current (as depicted in Fig.2) was

188

used to test the MD performance of the fabricated membranes. The effective

189

membrane area of the membrane cell is 75 cm2. 1.5-mm-thick polypropylene

190

mesh-like spacers were used on both feed and permeate sides to mechanically support

191

the membrane while promoting the fluid mixing conditions. A saline solution of 3.5

192

wt.% NaCl and deionized (DI) water were used as the feed and permeate solutions.

193

DCMD experiments were carried out for the fabricated membranes at different feed 10

194

temperatures ranged from 40 to 80℃. The permeate conductivity was automatically

195

recorded every 30s by using a conductivity meter (CON110, Oakton), and the

196

quantity of the permeate was periodically recorded by using a digital balance

197

(GF-6000, AND) throughout the duration of the test. DCMD flux ( J ) was calculated

198

from the following equation:

J=

199

∆m S ⋅ ∆t

(1)

200

where ∆m is the weight gain of the permeate over a predetermined time, kg; S is

201

the effective membrane area of the membrane cell, m2; and ∆t is the time interval, h.

202

3. Theory

203

In DCMD operating mode, the hydrophobic side of the dual-layer membrane is

204

brought into contact with a constant flow of hot feed solution, and the membrane

205

hydrophilic layer is kept in contact with a cold-water stream on the permeate side.

206

Cold-water would penetrate into the pores of the hydrophilic layer and wet the

207

hydrophilic layer of the membrane.

208

During DCMD process, water transport can be described in following steps: 1)

209

water from the bulk feed solution transports and evaporates at the interface of the

210

feed/membrane; 2) water vapor transports through the pores of the hydrophobic layer;

211

3) the water vapor transported across the hydrophobic layer condenses at the interface

212

of the hydrophobic/hydrophilic layers followed by wicking through the hydrophilic

213

layer in liquid state [24]. Unlike the commonly used single-layer hydrophobic 11

214

membranes, for the hydrophobic/hydrophilic dual-layer membranes, liquid/vapor

215

interfaces are formed only at both ends of the hydrophobic layer and there is no phase

216

change at the interface of permeate/hydrophilic layer (Fig.3). Heat and mass transfer

217

occur simultaneously across both hydrophobic and hydrophilic layer of the membrane.

218

The heat and mass transfer models for hydrophobic/hydrophilic dual-layer membrane

219

were derived based on the well-known MD model of single-layer hydrophobic

220

membrane developed by Schofield et al. [32].

221 222 223 224

225

Fig.3. Schematic of heat and mass transfer profiles in DCMD of water transportation through dual-layer hydrophobic/hydrophilic membrane(left) and single-layer hydrophobic membrane(right).

3.1. Heat transfer

226

In the DCMD process, heat transfer includes the heat transferred through the

227

boundaries of the feed side ( qf ) and permeate side ( qp ), and through the membrane

228

hydrophobic layer ( qo ) and hydrophilic layer ( qi ) and can be represented as:

229

qf = hf (T b,f − T m,f )

(2)

230

qo = ho (T m,f − T'm,p ) + Jw∆HV

(3)

12

231

qi = hi (T'm,p − Tm,p )

(4)

232

qp = hp(Tm,p − Tb,p)

(5)

233

In the equations above, T is the absolute temperature, h is the heat transfer

234

coefficient, ∆HV is the latent heat of water vaporization and Jw is the vapor permeation

235

flux. The subscripts b, f, p, m, o and i refer to the bulk solution, feed, permeate,

236

membrane, hydrophobic and hydrophilic layers of the membrane, respectively.

237

At the steady state condition, the overall heat transfer flux through the entire

238

thickness of membrane, qm , is equal to the amounts of heat transfer in the hydrophobic

239

layer ( qo ) and hydrophilic layer ( qi ). Therefore, the overall heat transfer coefficient

240

( hm ) of the entire membrane thickness may be written as:

241

242

243 244

245

hm =

qm 1 1 =( + )−1 Tm,f − Tm,p ho+( Jw∆HV (Tm,f − T'm,p)) hi

(6)

3.2. Mass transfer

The vapor permeation flux ( Jw ) in DCMD process is assumed to be proportional to the trans-membrane vapor pressure difference as follows:

Jw = Bm ( pm,f − p'm,p )

(7)

246

where Bm is the mass transfer coefficient of membrane hydrophobic layer; pm,f

247

and p'm,p are the water vapor partial pressures at the hot feed side and interface of

248

the hydrophobic/hydrophilic layers.

13

249

Since the vapor pressures at the hot feed side and interface cannot be directly

250

measurable, it would be more convenient to express Eq. (7) in terms of temperatures

251

as following equation as suggested by Schofield et al. [32]: Cm

252

Jw =

253

C m = B mδ o (

δo

(Tm,f − T'm,p )

(8)

dp )T m dT

(9)

dp )Tm can be calculated from the Clausius-Clapeyron equation [33] and Tm dT

254

where (

255

is the mean temperature in membrane hydrophobic layer.

256

Eq.(8) is accurate for dilute solutions, but it must be modified for more

257

concentrated solutions to account for the vapor pressure depression caused by the

258

presence of nonvolatile solutes in feed solution [32]: Cm

259

Jw =

260

Since vapor pressure deviation between the 3.5% NaCl solution (feed solutions in

261

this study) and pure water is less than 2% [34], Eq. (8) is still used for the following

262

calculation, Eq. (10) would only be important for the concentrated feed solutions or in

263

the presence of significant concentration polarization.

264

3.3. Theoretical modelling of the dual-layer composite membrane permeate flux

δo

(Tm,f − T'm,p − ∆Tth )(1 − xm )

(10)

265

To better understand the performance of dual-layer hydrophobic/hydrophilic

266

composite membrane, it is very important to develop a valid theoretical model from

14

267

theoretical view to enable predicting the DCMD flux of these new composite

268

membranes and facilitating the optimization of membrane fabrication.

269

270

271

Substitute the Jw with Eq. (8), Eq. (3) can be rewritten as:

qo =

k o'

δo

(T m,f − T'm,p ) + J w ∆ H V =

expressed as:

273

Jw =

275

(T m,f − T'm,p )

(11)

C m (Tm,f − Tm,p ) Cm (Tm,f − Tm,p) = ' '  1 1  δ o+(ko +Cm∆HV) δ i ki ( ko' +Cm∆HV)  ' + '   (k o + C m ∆ HV ) δ o ( k i δ i ) 

(12)

A constant total thickness value δ is assumed for the hydrophobic/hydrophilic composite membrane, substituting δ o=δ -δ i into Eq. (12) and further rearrangement:

276

Jw =

277

where

278

β=

279

δo

By rearranging Eq. (11) and substituting Tm,f − T'm,p into Eq. (8), the Jw can be

272

274

k o' + C m ∆ H V

C m (T m,f − T m,p ) δ + δ i ( β − 1)

(13)

ko' +Cm∆HV ki'

(14)

3.3.1. Flux enhancement criterion condition

280

According to Eq. (13), we can deduce that if the constant β is smaller than 1, an

281

increase in the hydrophilic layer thickness, δ i ，of the composite membrane would

282

enhance the DCMD flux. Accordingly, utilizing the dual-layer membrane would

15

283

achieve higher flux when compared to the single-layer hydrophobic membrane with

284

the same total thickness. Moreover, the smaller the β value, the more significantly the

285

flux can be improved. Since β is obviously a positive value, the criteria for the flux

286

increase is therefore,

287

0＜β＜1

288

In Eq. (9), the value 2405.55 kJ/kg was used for the latent heat of water

289

vaporization ( ∆HV ) [26], and the value of Cm is infinitesimally small (~10-9 -10-7),

290

thus the influence of latter term in numerator in Eq. (14), Cm∆HV , can be neglected

291

because it has a very small magnitude (~10-6-10-4) compared to the ko' (~10-2).

292

Therefore, the Eq. (14) can be simplified as:

293

β≈

(15)

ko' kaε o + ko(1 − ε o) = ki' kwε i + ki(1 − ε i)

(16)

294

From Eq. (16), the value of β is approximately equal to the ratio of the thermal

295

conductivities of hydrophobic layer to the hydrophilic layer. Generally speaking, the

296

thermal conductivity of the hydrophobic layer will be less than that of hydrophilic

297

layer. This is due to the fact that most of the membrane polymers have similar thermal

298

conductivities ( k =0.1-0.3 W/(m·K)) [24], while the void volume in the hydrophobic

299

layer would be occupied by the less thermal conductive air molecules ( k a = 0.0269

300

W/(m·K))[26], on the other hand, the hydrophilic layer would be occupied by the

301

more conductive liquid water ( k w = 0.626 W/(m·K))[26] during the DCMD operation.

302

In this case, the value of β is always smaller than 1, therefore the flux of the

16

303

hydrophobic/hydrophilic composite membrane will be higher than that of single-layer

304

hydrophobic membrane with same total thickness. However, the flux would not

305

increase infinitely based on Eq. (13), since the minimal value of β is ka/kw = 0.04

306

(as ε o = ε i = 1 in Eq. (16)).

307

3.3.2. Flux enhancement ratio

308

Further rearrangement of Eq. (13) yields:

309

Jw =

310

In ideal circumstances, the thermal conductivity of hydrophilic layer is infinite,

311

which means that there is no heat transfer resistance in hydrophilic layer, and the

312

thermal conductivity in hydrophobic layer is almost close to zero. According to Eq.

313

(16), β =0 , and the flux will be,

C m (T m,f − T m,p ) δo = B m ( p m,f − p m,p ) δ + δ i ( β − 1) δ o + βδ i

(17)

314

J w = B m ( p m,f − p m,p )

315

By comparing the above two equations, we can deduce that, flux reduction

316

proportion, φ , due to the conductive heat loss in both hydrophilic layer and

317

hydrophobic layer, can be derived using the following equation:

(18)

δo βδ i = δ o + βδ i δ o + βδ i

318

φ = 1-

319

Under the good flow conditions, temperatures on the membrane surface at both

320

sides are very close to that of bulk solutions, therefore, the flux ( J wDL ) of hydrophobic/

321

hydrophilic dual-layer membrane can be approximated as:

(19)

17

δo δo BmDL ( p m,f − p m,p ) ≈ B DL ( p b,f − p b,p ) δ o + βδ i δ o + βδ i m

322

J wDL =

323

For the single-layer hydrophobic membrane, δ i=0 and then δ o=δ , the flux

324

( J wSL )

(20)

can be expressed as follows:

325

J wSL = B mSL ( p m,f − p m,p ) ≈ BmSL ( p b,f − p b,p )

326

Under the same DCMD experimental operating conditions (feed and permeate

327

temperatures, flow rates, feed solution concentrations), the flux ratio ( γ

(21)

M DL/SL

) of

328

dual-layer to single-layer membrane with same total thickness can be derived from the

329

above two equations and expressed as following:

J wDL δ o BmDL = J wSL δ o+βδ i BmSL

330

γ

331

For a homogeneous membrane, such as one fabricated using electrospinning

332

method, its membrane structures and properties (pore diameter do , porosity ε o , and

333

pore tortuosity τ o ) only have slight change with membrane thickness δ o (see

334

membrane properties data in Table 3 and membrane structure images in Fig.6).

335

According to the Eqs. in Table S1, the mass transfer coefficient ratio of dual-layer to

336

single-layer membrane, BmDL BmSL , is inversely proportional to their hydrophobic layer

337

thickness ratio. Therefore, Eq. (22) can be written as:

338

γ

M

= DL/SL

(22)

δo B δo δ δ = = δ o+βδ i B δ o+βδ i δ o δ o+βδ i DL

M

= DL/SL

m

SL

(23)

m

339

According to Eq. (23), if there is infinite thermal conductivity in hydrophilic layer

18

340

and ignore the conductive heat loss in hydrophobic layer, β =0 according to Eq. (16),

341

M the flux ratio will be equal to the thickness ratio ( γ DL/SL = δ δ o ). However, in the

342

non-ideal real situation, conductive heat loss does exist in the hydrophilic layer and

343

thinner hydrophobic layer, therefore, using mere thickness ratio ( δ δ o ) to estimate the

344

flux ratio is unsound. Therefore, it is important to calculate the theoretically flux ratio

345

346

M ( γ DL/SL =

δ ) to enable prediction of the flux enhancement of the δ o+βδ i

hydrophobic/hydrophilic dual-layer membrane more scientifically and accurately.

347

From Eq. (23), the flux ratio could be estimated based on the calculated β value

348

and the known hydrophobic layer thickness ( δ o ), hydrophilic layer thickness ( δ i ) and

349

total thickness ( δ ). Table 4 shows the calculated thermal conductivities in

350

hydrophobic layer ( ko' ) and hydrophilic layer ( ki' ), β values and theoretical flux

351

ratios ( γ DL/SL ) for the three sets of dual-layer membranes with different total

352

thicknesses and thickness ratios ( δ δ o ).

353

M

Table 4 Summary of thermal conductivities, β values and theoretical calculated flux ratios.

γ

Membrane code

ko' (W/m·K)

ki' (W/m·K)

β

DL-1

0.0452

0.497

0.091

2.97

DL-2

0.0459

0.499

0.092

2.18

DL-3

0.0459

0.499

0.092

1.98

M DL/SL

354

M Note: γ DL/SL is the flux ratio of dual-layer to single-layer membranes obtained from theoretical model calculation

355

E and similarly, γ DL/SL is the flux ratio of experimental results in the following part.

19

356

3.3.3. Guidance for higher flux enhancement

357

In order to find a critical value of the thickness ratio and provide useful guidance

358

to design a highly efficient hydrophobic/hydrophilic dual-layer composite membrane

359

for DCMD applications in the future work, the relationship between flux ratio ( γ

360

M DL/SL

)

and thickness ratios ( δ δ o ) was further explored.

361

Assume that χ = δ δ o , therefore, Eqs. (19) and (23) can be simplified as:

362

φ=

βδ i β (δ − δ o ) β ( χ − 1) = = δ o + βδ i δ o + β (δ − δ o ) β ( χ − 1) + 1

363

γ

=

364

Obviously, δ ≥ δ o , and then χ ≥ 1 . For a constant β , with the increase of χ , the

365

M values of γ DL/SL and φ increase gradually, and converge to 1 β and 1, respectively.

366

Theoretical simulation was conducted at various β values ranging from 0.1 to 0.5.

367

The results of the calculation are depicted in Fig.4.

M DL/SL

(24)

δ δ χ = = δ o+βδ i δ o+β (δ − δ o) β (χ −1)+1

(25)

12 β = 0.10

10

β = 0.12

8

γ

β = 0.15 M

6 DL/SL

β = 0.20

4

β = 0.30 β = 0.50

2 (1,1)

0

0

50

100

χ

150

200

368 369

Fig.4. The relationship between

γ

M DL/SL

and thickness ratios at different

20

β

values.

370

M M Apparently, when δ o=δ , χ =1 , γ DL/SL identically equal to 1. γ DL/SL increases

371

gradually with the increase of χ , but as χ increases to a certain value, the flux

372

M ratio γ DL/SL remains stagnant and approaches to an asymptotic value, 1 β . This

373

indicates that the contribution to the flux enhancement due to the decreasing of

374

hydrophobic layer thickness is getting smaller and smaller. As shown in Fig. 3, the

375

dual-layer membrane exhibits different mechanisms in mass and heat transfer

376

compared to conventional single-layer hydrophobic membrane. In DCMD, the water

377

vapor transports through the hydrophobic layer of the dual-layer membrane and then

378

condenses at the interface of hydrophobic/hydrophilic layers followed by transporting

379

through the hydrophilic layer in liquid state. For the same total membrane thickness,

380

the increasing of χ indicates the increasing thickness of hydrophilic layer. The

381

thicker hydrophilic layer will add an additional heat transfer resistance from the

382

membrane interface to the bulky permeate layer. This will lead to an increase of the

383

temperature at the vapor-liquid interface of the hydrophobic/hydrophilic layers due to

384

the temperature polarization effect in the hydrophilic layer across the bulk permeate.

385

As a result, the temperature difference across the hydrophobic layer will be reduced,

386

and consequently reduces the driving force and water flux in MD. This will offset the

387

increased water flux due to the low mass transfer resistance with thin hydrophobic

388

layer, resulting in the diminishing effect of the increasing χ as observed in Fig. 4. In

389

a recent study by Liu et al. [35], they also reported the trend of water flux vs total

390

membrane thickness does not follow a linear relationship. While keeping the

391

hydrophobic layer thickness constant, with the increasing the hydrophilic layer

21

392

thickness, the water flux gradually decreased.

393

Based on Fig. 4, it will be important to identify the critical thickness ratio beyond

394

which there is no significant improvement in flux. When the flux reduction ratio

395

φ = 0.5 , which means half of the positive effect of thickness reduction of the

396

hydrophobic layer (flux enhancement associated with the reduction of the membrane

397

mass transfer resistance) will be counteracted by the negative effect (flux decline

398

associated with the reduction of the membrane conduction heat transfer resistance in

399

hydrophobic layer and an additional resistance induced by the hydrophilic layer).

400

Beyond this value, more than half of the positive effects of thickness reduction were

401

counteracted by the negative effects, and the flux enhancement reach diminishing

402

returns rapidly. Thus, the χ values at this point, χ =1+ 1 , would be the critical

403

value of the thickness ratio beyond which there is no significant improvement in flux.

404

This value could provide useful guidance to design a highly efficient hydrophobic/

405

hydrophilic dual-layer membrane for DCMD applications in the future work.

β

406

In addition, it can be also seen from Fig.4 that the smaller the β value, the flux

407

can be significantly improved. If one can decrease the β value and make it infinite

408

small and approaches to zero, the flux enhancement would be even more dramatic.

409

From Eq.(16), it is obvious that when β value approaches zero, indicating an

410

increase in either the hydrophobic or hydrophilic layer porosities ( ε o , ε i ) and/or an

411

increase in the hydrophilic layer thermal conductivity, which would eventually

412

decrease the mass and heat transfer resistances through the membrane. This

22

413

speculation is consistent with previous researches [24-26]. Thus, for a high

414

performance hydrophobic/hydrophilic dual-layer membrane, the heat transfer

415

resistance in hydrophobic layer should be as high as possible to reduce the heat loss

416

and build a larger temperature difference between both sides of the hydrophobic layer;

417

while for the hydrophilic layer, the heat transfer resistance should be as low as

418

possible to reduce the temperature polarization in hydrophilic layer. Both

419

requirements are conducive to increase the flux for the hydrophobic/hydrophilic

420

dual-layer membranes.

421

4. Experimental validation

422

To validate the theoretical model, three sets of dual-layer hydrophobic/hydrophilic

423

composite membranes and single-layer hydrophobic membranes with defined total

424

thicknesses and different thickness ratios were purposefully fabricated using the

425

electrospinning technique.

426

4.1. Membrane chracterization

(a)

(d)

(g)

(b)

(e)

(h)

427

428 23

(c)

(f)

(i)

429 430 431

Fig.5. Cross section images of (a) SL-1; (b) SL-2; (c) SL-3; (d) DL-1; (e) DL-2; (f) DL-3, and thickness measurement of (g) DL-1; (h) DL-2; (i) DL-3.

432

Fig.5 shows the cross-section images for the three sets of lab-fabricated

433

single-layer and dual-layer membranes. The double layer structure is obviously

434

observed and the hydrophobic PVDF-HFP nanofibers are nicely adhered to the Nylon

435

support layer forming good interfacial connection. This unique design enables the

436

dual-layer membrane to achieve higher flux while maintaining mechanical properties

437

due to the strong mechanical strength of the hydrophilic Nylon 6,6 membrane. In

438

addition, SEM images confirm that all three sets of membranes have same controlled

439

total thickness of about 240µm, 260µm and 285µm, respectively (Fig.5g-4i). The

440

thickness of hydrophobic active layer of dual-layer membranes are 65µm, 105µm and

441

130µm, respectively. The thickness ratio of total thickness to hydrophobic layer ( δ δ o )

442

of dual-layer membranes are 3.69, 2.48 and 2.19, respectively.

443

In order to illustrate the homogeneous structure of the electrospun membranes, top

444

surface and enlarged cross section images of the single-layer membrane and the

445

hydrophobic layer of dual-layer membrane were also observed. The top hydrophobic

446

layer was carefully peeled off from the dual-layer membrane and fractured by liquid

447

nitrogen. The top surface and enlarged cross section SEM images of the SL-2 and

24

448

hydrophobic layer of DL-2 membrane are shown in Fig.6.

449

Top surface

Enlarged cross section

(a)

(b)

(c)

(d)

450

451 452

Fig.6. Top surface and cross section images of (a), (b) hydrophobic layer of DL-2; (c), (d) SL-2.

453

From Fig.6, it can be seen that the hydrophobic layer of the dual-layer membrane

454

(DL-2) have similar top surface and cross section morphologies with the single-layer

455

membrane (SL-2). Fig.7 shows the pore size distribution of the fabricated single-layer

456

and dual-layer membranes. All the membranes show sharp distribution of pore size.

457

The mean pore sizes of the single-layer and dual-layer membranes are similar. It

458

should be noted that, in the electrospinning process, nanofibers were stacked layer by

459

layer. At the same spinning conditions and use same dope solutions, the spinning time

460

only change the membrane thickness rather than affect the membrane structures and

461

other properties. Therefore, the hydrophobic layer of the dual-layer membrane have

462

same membrane structure and similar membrane properties (pore diameter, porosity,

463

and pore tortuosity), as confirmed by the membrane characterization results in Table3.

25

5 SL-1 SL-2 SL-3 DL-1 DL-2 DL-3

Diff Flow (%)

4 3 2 1 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Pore Size (µm) 464 465

466

Fig.7. Pore size distribution of the lab-fabricated single-layer and dual-layer membranes.

4.2. Experiment validation of the flux enhancement

DCMD flux (kg/m2h)

60 48 36 2.75 1.97

24

1.80

12 0

467 468

Dual-layer Membranes Single-layer Membranes

SL1 DL1

SL2 DL2

SL3 DL3

Fig.8. DCMD flux comparison of three sets of dual-layer and single-layer membranes at 60℃.

469

Fig.8 shows the DCMD flux at 60℃ for the three sets of dual-layer and single-layer

470

membranes with different total thickness and thickness ratios ( δ δ o ). Results showed

471

that, all the three dual-layer membranes achieved higher flux than the single-layer

26

472

membranes regardless the component and thicknesses (i.e. δ , δ o and δ i ). This is

473

consistent with speculation from the previous part where the calculated β values

474

(see in Table 4) satisfy the criterion condition given by Eq. (15). The experimental

475

flux ratios ( γ DL/SL ) of dual-layer to single-layer membranes are 2.75 ( δ δ o = 3.69), 1.97

476

( δ δ o = 2.48) and 1.80 ( δ δ o = 2.19), respectively. The comparison between

477

experimental flux ratio ( γ DL/SL ), model prediction ( γ DL/SL ) and thickness ratio ( δ δ o )

478

was depicted in Fig.9.

E

E

M

5 δ δo

Specific value

4

γ γ

3

M DL/SL E DL/SL

2 1 0

479 480

1.0

1.5

2.0

2.5

3.0

3.5

4.0

δ δο Fig.9. Comparison of thickness ratio, experimental flux ratio and theoretical values.

481

From Fig.9, it can be seen that the increased conductive heat loss induced by the

482

thicker hydrophilic layer and thinner hydrophobic layer, as mentioned in Section 3.3.2,

483

make the experimental flux ratios ( γ DL/SL ) is no longer equal to the thickness ratio

484

( δ δ o ) but fits well with the model prediction ( γ DL/SL ). It is obvious that the gap

485

E between δ δ o and γ DL/SL values is further enlarged with the increase of thickness

486

E M ratio ( δ δ o ). Apparently, when δ i=0 δ o=δ , γ DL/SL , γ DL/SL and δ δ o identically

487

equal to 1. As the δ δ o increases, which means that the hydrophilic layer gets

E

M

27

488

E thicker and the hydrophobic layer becomes thinner, the increase of flux ratio γ DL/SL

489

becomes slower, and gradually skews from the thickness ratio ( δ δ o ). This result can

490

also be reflected from the φ value. According to Eq. (19), the flux reduction

491

proportions ( φ ) are 9.9%, 12.0% and 19.7%, respectively. This value is almost

492

doubled when δ δ o increases from 2.19 to 3.69. Nevertheless, experimental data

493

γ

494

( δ δ o = 1~3.69 ), within high agreement level at a relative standard deviation of 9.6%,

495

which confirms the validity of the theoretical model.

E DL/SL

M remains its fit well with the model prediction γ DL/SL in the experimental range

496

In order to better illustrate the accuracy of model prediction, DL2 and SL2

497

membranes were tested at different feed inlet temperatures ranged from 40 to 80℃.

498

The resultant DCMD flux as a function of the feed inlet temperature is presented in

499

Fig. 10.

DCMD flux (kg/m2h)

70 SL2 Membrane DL2 Membrane

56 42 28 14 0

40

50

60

70

80

Feed Temperature (℃ ) 500 501

Fig.10. DCMD flux of DL2 and SL2 membranes at different feed inlet temperatures.

28

502

The general trend where the DCMD flux increases exponentially with increasing

503

feed inlet temperature is observed. This is due to the fact that the water vapor pressure

504

increases exponentially with increasing temperature, resulting in an increment of

505

driving force for water vapor transport. Compare the DCMD flux of DL2 and SL2 at

506

E different feed inlet temperatures varied between 40 and 80℃, the flux ratio ( γ DL/SL )

507

values ranged from 1.96 to 2.08 and maintains a high degree of consistency with

508

model value at a relative standard deviation of 10.1%. Despite Eq. (8) is used to

509

calculate the flux of small trans-membrane temperature differences, the model still

510

predicts the experimental results at high level of confidence in the experiment

511

conditions.

512

It is worth mentioning that all the electrospun membranes showed superior salt

513

rejection (>99.9%) during all the DCMD operation in this study and no leakage was

514

detected or observed throughout the duration of the test. This is mainly attributed to

515

the excellent hydrophobicity and minimal pore size characteristics of the electrospun

516

nanofiber membranes. While for a systematic and comprehensive study, membrane

517

fouling, pore-wetting and long-term performance will be studied in the future work.

518

5. Conclusions

519

This work developed a mathematical model that comprehensive analysed the

520

performance of hydrophobic/hydrophilic composite membrane from a theoretical

521

view point. To validate the model, three sets of dual-layer hydrophobic/hydrophilic

522

nanofiber composite membranes and single-layer hydrophobic membranes with 29

523

defined thicknesses were purposefully fabricated using electrospinning technique. The

524

membranes were tested by the DCMD experiment and results showed that

525

experimental data are in good agreement with theoretical values, showing differences

526

of less than 10.1% relative standard deviation, validating the reliability of the model.

527

This model would provide useful guidance to predict the composite membrane

528

DCMD performance and aids to design a highly efficient hydrophobic/hydrophilic

529

DCMD membranes. However, it should be mentioned that this study is only a

530

preliminary research, there are many deficiencies in this paper that need to be further

531

studied, such as effect of operating conditions (feed salinity, flow velocity, feed

532

temperature, temperature difference over the membrane), membrane fouling,

533

pore-wetting and long term performance, all of these need to be discussed elaborately

534

in the following study.

535

Acknowledgments

536

The authors would like to acknowledge the financial support from CSIRO

537

Manufacturing, the National Natural Science Foundation of China (nos. 21576210

538

and 51578376), as well as the China Postdoctoral Science Foundation (no.

539

2018M643192). Lihua Zhao gratefully acknowledge the scholarship from China

540

Scholarship Council. Vinod Kadam and Mark Greaves from CSIRO Manufacturing

541

are also greatly acknowledged for the help in electrospinning and SEM training.

30

Nomenclature Bm

mass transfer coefficient of membrane hydrophobic layer (kg/m2·h·Pa)

Cm h

membrane permeability defined in Eq. (9) (kg/m·h·K) heat transfer coefficient (W/m2·K)

hm △Hv

overall heat transfer coefficient of entire membrane (W/m2·K) latent heat of water vaporization (kJ/kg)

J Jw

experimental DCMD flux (kg/m2·h) DCMD vapor permeation flux (kg/m2·h)

k

thermal conductivity (W/m·K)

ki'

hydrophilic-layer thermal conductivity (W/m·K)

ko'

hydrophobic-layer thermal conductivity (W/m·K)

p

water vapor partial pressures (Pa)

q T

heat transfer flux (W/m2) absolute temperature (K)

Tm

mean absolute temperature in hydrophobic-layer (K)

Greek letters

β

γ

factor defined in Eq. (14) flux ratio of dual-layer to single-layer membranes

δ δi

total membrane thickness hydrophilic-layer thickness

δo εi εo τ

hydrophobic-layer thickness hydrophilic-layer porosity

θ

water contact angle

φ

flux reduced proportion

hydrophobic-layer porosity pore tortuosity

Subscripts a b

air bulk

f i

feed hydrophilic layer

m m,f

membrane membrane hydrophobic surface at the feed side

m,p

membrane hydrophilic surface at the permeate side 31

o

hydrophobic layer

p w

pore water

Superscripts E experimental result M DL

model calculation value dual-layer membrane

SL

single-layer membrane

542

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Research highlights: Dual-layer nanofiber membranes were fabricated by electrospinning for DCMD. The membrane was composed of PVDF-HFP nanofibers and Nylon 6,6 membrane substrate. A mathematical model was developed to predict the flux of dual-layer membranes. The theoretical model was tested and validated by the experimental results. The experimental data resemble well with the theoretically calculated values.

Conflict of interest statement The authors declared that they have no conflicts of interest to this work. We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.