Electrostatic interaction governed solute transport in forward osmosis

Journal Pre-proof Electrostatic interaction governed solute transport in forward osmosis Guanglei Qiu, Gordon Kai Wai Wong, Yen-Peng Ting PII:

S0043-1354(20)30126-3

DOI:

https://doi.org/10.1016/j.watres.2020.115590

Reference:

WR 115590

To appear in:

Water Research

Received Date: 3 September 2019 Revised Date:

14 January 2020

Accepted Date: 3 February 2020

Please cite this article as: Qiu, G., Wai Wong, G.K., Ting, Y.-P., Electrostatic interaction governed solute transport in forward osmosis, Water Research (2020), doi: https://doi.org/10.1016/j.watres.2020.115590. 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. © 2020 Published by Elsevier Ltd.

1

2

Graphical abstract

1

Electrostatic interaction governed solute transport in forward osmosis

2

Guanglei Qiu 1,2,*, Gordon Kai Wai Wong 2, Yen-Peng Ting 2,*

3

1

4

China.

5

2

6

Engineering Drive 4, Singapore 117585, Singapore

7

*

8

*

School of Environment and Energy, South China University of Technology, Guangzhou 510006,

Department of Chemical and Biomolecular Engineering, National University of Singapore, 4

Corresponding author: [email protected] (G. Qiu); Corresponding author: [email protected] (Y.-P. Ting)

9 10

Abstract

11

Electrolytes are commonly employed as draw solutes in forward osmosis (FO). This work

12

demonstrates that electrostatic interactions play a key role in ion transport in the FO process. The

13

difference in diffusivity between the constituent ions of the draw electrolyte significantly impact the

14

forward transport of the feed ions. Draw electrolyte composed of low-diffusivity cations and high

15

diffusivity anions promoted forward transport of the feed anions and retarded that of the feed cation,

16

and vice versa. The effects were remarkable even for the most commonly used draw electrolytes

17

(NaCl or MgCl2), where the forward flux of NO3- and NO2- was found to increase by a few folds and

18

that of NH4+ was reduced by similar magnitudes than that observed in a nonelectrolyte draw solute

19

(glucose) system. More profound increase/reduction (up to 10 times) was observed for draw

20

electrolytes composed of highly asymmetric cations and anions. An analytical model is developed by

21

considering the electrostatic interaction between the draw and the feed ions, to predict its effect on

22

the forward transport of the feed ions. The normalized diffusivity difference (θD) between the 1

23

constituent ions of the draw electrolyte is found as a key factor that determines the transport

24

behaviors of the feed ions. These results may have important implications in enhancing our

25

understanding of bidirectional ion transport in FO. The findings may also be useful in the design and

26

development of FO processes for enhanced removal of charged pollutants via draw solute selection

27

and formulation.

28 29

Keywords

30

Forward osmosis; Bidirectional ion transport; Electrostatic interaction; Draw solute; Feed ions;

31

Modeling

32

2

33

1. Introduction

34

Forward osmosis (FO) as an emerging water and wastewater treatment technology has gained

35

increasing attention (Cath et al., 2006; Zhao et al., 2012; Chung et al., 2012; Shaffer et al., 2015; Zou

36

et al., 2019; Lee and Hsieh, 2019). In contrast with traditional hydraulic pressure driven membrane

37

processes, FO takes advantage of natural osmotic pressure for solute-water separation and shows

38

merits in reducing energy input, lowering membrane fouling and producing high quality product

39

water (Lutchmiah et al., 2014; McGovern et al., 2014; Awad et al., 2019). As a result, FO is

40

considered a promising alternative in brackish and sea water desalination, water purification and

41

energy recovery (Logan and Elimelech, 2012; Shaffer et al., 2015; Zou et al., 2019). In the area of

42

wastewater treatment, FO has been proposed for direct sewer mining (Xie et al., 2013; Zhang et al.,

43

2014), nutrient concentration and recovery (Xie et al., 2014; Qiu et al., 2015; Ansari et al., 2017;

44

Volpin et al., 2019), and water recovery from wastewaters for irrigation (Phuntsho et al., 2012;

45

Chekli et al., 2016; Phuntsho et al., 2016). FO has been also been shown to be an effective

46

technology in the removal of heavy metals (Cui et al., 2016; Ge et al., 2018) and emerging pollutants

47

(Coday et al., 2014; Holloway et al., 2014; Xie et al., 2018; Zheng et al., 2019). The combination of

48

FO and biological wastewater treatment has enabled the development of a forward osmosis

49

membrane bioreactor process (Achilli et al., 2009; Qiu et al., 2015; Wang et al., 2016), which show

50

unparalleled advantages in facilitated nutrient recovery and high through-put treatment of wastewater

51

(Qiu et al., 2016a; 2016b).

52

The numerous new features offered by the FO and FO-related processes largely result from the high

53

rejection properties of the FO membranes (Chung et al., 2012; Lutchmiah et al., 2014; Qiu et al.,

54

2015; 2016; Ansari et al., 2017). Like reverse osmosis, FO uses dense membranes, which allow 3

55

water molecule to penetrate but effectively reject solutes. However, unlike reverse osmosis (RO),

56

separation in FO relies on osmotic pressure, which is driven by a draw solution (Phillip et al., 2010;

57

Ge et al., 2013; Shaffer et al., 2015; Lee and Hsieh, 2019). Apart from the forward transport of solute

58

from the feed to the draw solution, draw solutes also inevitably leak from the draw solution into the

59

feed (Achilli et al., 2010; Hancock et al., 2011; Zou et al., 2019); this phenomenon is typically

60

termed as “bidirectional transport (or diffusion) of solutes” (Hancock et al., 2011; Lu et al., 2014).

61

When the feed and draw solutes are electrolytes, their interactions may mutually affect their transport

62

behaviors. Models have been developed to describe the bidirectional transport of electrolytes in the

63

FO system by ignoring their electrostatic interactions (Hancock et al., 2011; Manickam and

64

McCutcheon, 2017). Despite the strong agreements between the predicted and observed reverse

65

fluxes of draw ions, the observed feed ion fluxes deviated from the model (Hancock et al., 2011). For

66

systems containing NO3-, the deviation was more pronounced (Hancock et al., 2011; Irvine et al.,

67

2013). An ion-exchange mechanism was proposed to be responsible for these observations although

68

the underlying drive force is not yet understood (Irvine et al., 2013; Cheng et al., 2018). Similar

69

results were reported by Kong et al. (2018), where greatly overestimated NO3− rejection and

70

underestimated NH4+ rejection were observed with cellulose triacetate (CTA) membrane and NaCl as

71

draw solution. Asymmetric forward transport of Na+ and Cl- across a CTA membrane was also

72

observed with a draw solution composed of 1.8 M NH4HCO3 and 0.2 M NH4OH. Although the

73

phenomenon has been attributed to the higher reverse diffusion of NH4+ resulting from the higher

74

total ammonia concentration (2.0 M) than bicarbonate species (Lu et al., 2014). Yaroshchuk et al.

75

(2013) developed a Solution-Diffusion–Electro-Migration model to analyze the electrically coupled

76

transport of three different ions through membrane barrier layers. In FO using MgCl2 as a draw 4

77

solution and nanofiltration (NF)-like membranes, modeling revealed 3- to 4-fold enhancements in

78

Na+ rejection (i.e. reduction in the forward flux of Na+) relative to a pressure-driven process under

79

similar conditions. Although these results collectively suggest that reverse flux of draw electrolytes

80

affects the forward transport of the feed ions (Hancock et al., 2011; Irvine et al., 2013; Kong et al.,

81

2018), the way in which the draw electrolytes impact the feed ion fluxes remains unclear. Since a

82

major task of FO is membrane rejection of pollutants in the feed solution to achieve their removal, it

83

is essential to obtain an in-depth understanding of the impacts of draw solutes on the rejection of

84

feed ions and the governing mechanisms.

85

Research has revealed that coupled reverse transport of constituent ions of draw electrolyte occurs in

86

FO when DI water was used as a feed (Paul, 2004; Hancock et al., 2011). The driving force for this

87

coupled transport is the electrostatic attractions between the constituent ions (Cussler, 2009), which

88

modulate the diffusion of the cations and the anions to the same rate. The larger the difference in

89

their diffusivity, the greater the extent of electrostatic interactions between the constituent ions of the

90

draw electrolyte is expected.

91

Feed ions transport through the membrane are exposed to electrostatic interactions, where the

92

slow-moving draw ion would attract the oppositely charged feed ions towards the draw solution side,

93

and the fast-moving draw ion attracts the counter feed ions to the feed side. The transport of draw

94

ions may also be affected by the feed ions. However, since the draw electrolyte concentration is

95

typically much higher than that of the feed electrolyte in FO, the impact of feed electrolyte on the

96

transport of draw electrolyte are expected to be less significant. Based on the above reasoning, it may

97

be expected that (1) a difference in the diffusivities of the draw cation and anion potentially affects

98

the forward transport of the feed ions; (2) the larger difference, the higher the degree of impact may 5

99

be expected; and (3) by analyzing the electrostatic interactions between the draw ions within the FO

100

membrane, the impacts on the transport of the feed ions may be predicted.

101

The aim of this study is to understand the role of electrostatic interactions in ion transport in FO.

102

NH4+, NO2- and NO3- were used as model feed ions, due to their ubiquitous presence in water and

103

wastewater, and the removal of which is typically a major task in water and wastewater treatment.

104

The forward transport behavior of NH4+, NO2- and NO3- was analyzed with draw electrolytes

105

composed of cations and anions with different diffusivity (NaCl, MgCl2, KCl, Na2SO4, sodium

106

citrate, Tris-HCl, sodium polyacrylate (Ge et al., 2013) and poly diallyldimethylammonium chloride.

107

Glucose as a neutral draw solute was used to test the flux behaviors of the feed ions in the absence of

108

any electrostatic impact from the draw solute. A model was developed to describe the transport

109

behaviors of the feed ions by considering the electrostatic interactions between draw ions and the

110

subsequent effects on the transport of feed ions. This work provides fundamental knowledge of the

111

role of electrostatic interactions in ion transport in FO, which would benefit in improved

112

understanding and manipulation of the FO and related processes.

113

2. Material and Methods

114

2.1 FO setup

115

FO experiments were performed using a bench-scale setup (Supplementary Material Fig. S1). The

116

setup consists of a cross-flow FO cell, holding one piece of cellulose triacetate (CTA) membrane

117

(Hydration Technology Innovations, Albany, USA, effective area of 0.0003 m2), which separates the

118

cell into a feed solution chamber and a draw solution chamber. CTA membrane was used since it

119

contains negligible fixed charged groups (Irvine et al., 2013). Thus, the electrostatic interactions

120

between the draw or feed electrolytes and the membrane were minimized. Feed solution and draw 6

121

solution were continuously recycled using peristaltic pumps (Cole-Parmer, Barrington, USA) at a

122

flow rate of 200 ml/min, which resulted in a cross-follow viscosity of 13.1 cm/s in each chamber. All

123

the experiments were carried out at 23.5±0.5oC. The water flux was measured by continuously

124

monitoring changes in the weight of the feed solution.

125

2.2. Feed solution and draw solution

126

NaNO3, NaNO2 or NH4Cl at 1.0 mM were used singly as feed solutions. NaCl (0.5, 1.0, 2.0 and

127

4.0M), MgCl2 (0.5, 1.0, 2.0 and 4.0M), Na2SO4 (0.5, 1.0, 1.5 and 2.0 M), sodium citrate (Na3Cit) (0.5,

128

1.0 and 2.0 M), Tris-HCl (0.5, 1.0 and 2.0 M), sodium polyacrylate (PAANa, average M.W. of 5100,

129

at 100 and 250 g/L) and poly diallyldimethylammonium chloride (PDADMAC, average M.W. of

130

100,000, at 50 and 130 g/L) were used as draw solutes to represent electrolytes with dissimilar

131

difference in diffusivity between the constituent ions. Glucose (0.5, 0.75, 1.0 and 1.5 M) was used as

132

a non-electrolyte draw solute to analyze the transport behavior of feed ions without draw-feed

133

electrostatic interactions. Experiments were performed with the feed solution facing the active layer

134

(FO model). A new piece of FO membrane (cut off from the same membrane sheet) was used in each

135

experiment.

136

sides to remove any salts adsorbed, until the solution conductivity dropped below 0.25 µS. The water

137

permeability (A), the solute permeability (B) and the membrane structural parameter (S) were

138

determined according to procedures described by Tiraferri et al. (2013).

139

To further understand the electrostatic interactions between the feed and the draw electrolyte and the

140

effects of feed ions on the transport of the draw ions, FO experiments were performed with 10 mM

141

NH4NO3 as the feed solution and 1M NaCl, MgCl2, KCl, Na2SO4, Na3Cit or Tris-HCl as the draw

142

solution. The fluxes of the feed ions and the draw ions were measured by monitoring changes in the

Before use, the membrane was flushed in the FO setup with ultrapure water on both

7

143

concentration of draw ions in the feed, and that of the feed ions in the draw solution over time. All

144

the chemicals were acquired from Sigma-Aldrich (Merck, Darmstadt, Germany). The solutions were

145

prepared with ultra-pure water from a Milli-Q system (Merck, Darmstadt, Germany).

146

2.3 Chemical analysis

147

NO3-, NO2- and NH4+ were measured using Standard Methods (APHA, 1999). Cl- was determined

148

using mercuric thiocyanate colorimetric method. SO42- was measured using methylthymol blue

149

colorimetric method (APHA, 1999). Na+, Mg2+ and K+ were analyzed using an inductively coupled

150

plasma optical emission spectrometer (ICP-OES, Thermo, Cambridge, UK). The flux of the organic

151

ions was determined via TOC analysis using a TOC analyzer (Shimadzu, Kyoto, Japan).

152

2.4 Modeling of the ion transport considering electrostatic interactions

153

To describe the interaction and transport of multiple ionic species, extended Nernst–Planck equation

154

may be used (Schlögl, 1966; Dresner, 1972). However, for a system containing more than three ions,

155

an analytical solution of the equation does not exist (Dresner, 1972; Hancock et al., 2011; Yaroshchuk

156

et al., 2013). Since the draw solute concentration in FO is typically much higher than that of the feed

157

solute, we thus made the following theoretical derivation: (1) the electrostatic interactions between

158

the draw cation and anion result in their coupled transport (Cussler, 2009; Hancock and Cath, 2009;

159

Hancock et al., 2011). The extent of the electrostatic interactions between draw ions within the

160

membrane could be established using the extended Nernst–Planck equation. (2) The feed ions are

161

exposed to the electrostatic field which resulted from the different transport coefficients of the draw

162

ions when the feed ions pass through the FO membrane. (3) The feed ions do not substantially affect

163

the electrostatic interactions between draw ions due to their relatively low concentration. The above

164

assumptions would allow us to use the extended Nernst–Planck equation to analyze the electrostatic 8

165

interactions between draw ions and approximate its effects on the transport of the feed ions (Fig. 1).

166

As the first step, the feed and draw solute flux in the absence of electrostatic interactions was

167

considered, which may be used to describe the solute flux when the draw solute is a non-electrolyte

168

(e.g. glucose).

169

2.4.1 Feed and draw solute fluxes ignoring electrostatic interactions

170

A model has been developed to describe the bidirectional solute fluxes, ignoring the electrostatic

171

interactions among the constituent ions (Tan and Ng, 2008; Hancock and Cath, 2009; Hancock et al.,

172

2011; Manickam and McCutcheon, 2017). Based on solution-diffusion theory and a mass balance in

173

the external concentration polarization layer, the dense active layer, and the porous support layer

174

(Supplementary Material Fig. S2), the feed and draw solute fluxes may be expressed as:

175

176

=

=

/ /



/ /





(1)



(2)

177

where,

178

the solute permeability of the membrane for the draw solute, mol/m/s, which is defined as

179

(Hancock and Cath, 2009; Hancock et al., 2011; Manickam and McCutcheon, 2017), where

180 181 182

is the reverse flux of the draw solute, mol/m2/s;

is the water flux, m3/m2/s;

is

!

is

the diffusion coefficient of the draw solute in the active layer, m2/s, "! is the active layer thickness, m, #

is the partition coefficient of the draw solute in water and in the active layer (Hancock and

Cath, 2009); $ is the mass transfer coefficient in the external concentration polarization boundary

183

layer derived from film theory principles (Zydney, 1997; Hoek et al., 2002; McCutcheon and

184

is the structural parameter of the support

185

Elimelech, 2006; Manickam and McCutcheon, 2017); %

layer for the draw solute (Yip et al., 2010), which is defined as 9

&

'

, " is the thickness of the support

186 187 188

layer, m, and ( and ) are the porosity and tortuosity of the support layer, respectively (Hancock and Cath, 2009); *

and *

are the draw solute concentration in the bulk feed solution and the

bulk draw solution, respectively, mol/m3. All the variables in eq. 2 have the same meaning but are

189

defined for the feed solute. Detailed derivations of the equations have been reported (Hancock and

190

Cath, 2009; Hancock et al., 2011; Manickam and McCutcheon, 2017) and are provided in the

191

Supplementary Material.

192

According to previous studies (Loeb et al., 1997; McCutcheon and Elimelech, 2006; Tiraferri et al.,

193

2013; Manickam and McCutcheon, 2017), the water flux is determined by the osmotic pressure

194

difference between the feed and the draw solution and is influence by the internal concentration

195

polarization in the support layer and the external concentration polarization layer, which may be

196

calculated as in eq. 3

197

-

198 199

= +,

2

./0 3 4

1

-

./0

./0

1

5

(3)

where + is the water permeability of the FO membrane, m/s; 6

and 6

are the osmotic

pressure of the draw solution and the feed solution, respectively, Pa.

200

Thus, the draw solute flux, the feed solute flux and the water flux may be obtained using eq. 1-3

201

respectively.

202

2.4.2 Electrostatic interactions between draw ions in the membrane

203

For draw electrolytes composed of cations and anions with different diffusivity (e.g. NaCl or MgCl2,

204

etc.), the constituent ions tend to transport at the same rate (Fig. 1). The driving force for this coupled

205

transport of draw ions is the electrostatic attractions (Paul et al., 2004; Cussler, 2009; Hancock and

206

Cath, 2009; Hancock et al., 2011). The Nernst-Planck equation may be used to describe the 10

207 208 209 210 211 212 213

electrostatic coupling between the cation and the anion (Schlögl et al., 1966; Cussler, 2009). − −

=

89

=

89

where ;

;/

<

:

89

89

:

89

;

<

;/

;

C

;/

+ >89 *89

B

;ѱ

?@ ;/

+ >89 *89

(4a)

B

;ѱ

?@ ;/

(4b)

is the flux of the cation, mol/m2/s;

89

is the diffusion coefficient of the cation, m2/s;

is the concentration gradient of the cation, mol/m3/m; >89

is the ionic charge of the cation;

D is Faraday’s constant, C/mol; E is the gas constant, J/K/mol; F is the temperature, K; and

;ѱ ;/

is

the electrostatic potential gradient, showing the electrostatic attraction between the ions to maintain

214

their transport at the same flux-charge ratio, V/m. In eq. 4b, all the variables have the same meaning

215

but are now defined for the anion.

216

Since the system maintains electroneutrality at any point, thus

219

> >

220

Hancock et al., 2011):

217 218

221 222 223

226

=> =>

*

(5) (6)

From eq. 4a, 4b, 5 and 6, the flux of the draw electrolyte may be described as (Cussler, 2009; −

=:

<


C

<

G

<

G

CG

C

C

B

;

;/

(7)

Thus, the diffusion coefficient of the draw electrolyte may be expressed as the harmonic mean of these of the cation and anion (Cussler, 2009; Hancock et al., 2011):

224 225

*

;ѱ ;/

;ѱ ;/

=

<


C

<

G

<

G

CG

C C

(8)

may be solved from eq. 4a, 4b, 5 and 6 as:

=:


C

<

<

CG

C

B

;

;/

;ѱ ;/

?@

=H

;

;/

?@

(9)

227

From eq. 9, the direction of

228

two ions regardless of their charges. The term

229

indicates the extent of electrostatic interactions between draw ions. For conciseness, this parameter is

is determined by the difference in the diffusion co-efficient of the
11

C <

<

CG

C

is an important parameter which

230 231

defined as θ

, which represents the normalized difference in the diffusion coefficient of the draw

ions. ;ѱ ;/

232

Based on eq. 9, to understand the

233

concentration profile and the concentration gradient

234

which may be established using the solute flux model (Tan and Ng, 2008; Hancock et al., 2011;

235

Manickam and McCutcheon, 2017).

236

2.4.2.1 Active layer

237

Based on solution-diffusion theory, the draw solute flux through the active layer is only determined

238

by the diffusive flux (Hancock et al., 2011; Tiraferri et al., 2013). The reverse draw solute flux under

239

steady-state may be written as:

240 241 242

=

% J*

−*

,L

profile in the membrane, it is necessary to know the ;

;/

profile of the draw solute in each layer,

M

(10)

where * and * D,N are the draw solute concentration on the support layer side and feed solution side of the active layer, respectively, mol/m3.

243

From eq. 10, the draw solute concentration in the active layer has a linear profile with a constant

244

concentration gradient. Given that the thickness of the active layer is "! , m (Supplementary Material

245 246 247 248 249 250

Fig. S2), the concentration profile (* ) and the concentration gradient (

;

;/

)profile of the draw

solute in the active layer may be obtained as: ;

;/

*

=

=*

,L

+

,O

(11)

/

(12)

where P is the distance to the active layer and external boundary layer interface, m. with eq. 9, 11 and 12, the

;ѱ ;/

profile in the active layer may be obtained as:

12

251

;ѱ ;/

=H

,O

?@

4 3

,O

Q R

(13)

252

2.4.2.2 Support layer

253

The reverse draw solute flux in the support layer under steady-state may be expressed as (Hancock et

254

al., 2011; Tiraferri et al., 2013; Suh and Lee, 2013): =− *

255

+

;

;/

256

where

257

diffusion coefficient

258 259

262 263 264 265 266 267 268

is the apparent solute diffusion coefficient, m2/s, which is determined by the bulk , and the porosity (() and tortuosity ()) of the support layer, i.e.

(Yip et al., 2010; Hancock et al., 2011). %

which is defined as

260 261

(14)

&

'

%'

S

is the structural parameter of the support layer, m,

, where " is the support layer thickness, m. Thus

may expressed as

=

is equal to

, and

.

For eq. 14, the concentration gradient profile in support layer may be obtained as ;

;/

=

(15)

Integrating eq. 14 with the boundary conditions of the support layer: x=0, *89 =*89 ; x=" ; * =* . The concentration profile of draw solute in the support layer (* ) may be obtained as: *

= *

+

exp

%

T

T

%

: − 1B − P

%

(16)

T

where P is the distance to the active layer and support layer interface, m. By combining eq. 11, 14 and 15, the ;ѱ ;/

=

Y

:

:

4 4

4 4

B

B

4

4

Q R

Q R

;ѱ ;/

?@

4 4

profile in the external boundary layer may be expressed as:



(17) ;ѱ ;/

269

Although eq. 16 gives an accurate expression of

270

understanding the interactions. To simplify the equation, we consider that 13

in the support layer, it adds difficulties in *

is typically much

271

higher than

272

the support layer (this may be verified by plotting the

273 274

for the draw solutes, thus from eq. 15, a relatively constant

which is thus denoted as ∇ѱ% : ;ѱ ;/

≈H



?@

;ѱ ;/

;ѱ ;/

may be expected in

profile in the support layer using eq. 17),

=∇ѱ

(18) ;ѱ ;/

275

With eq. 13 and 18, the

276

As mentioned above,

277

anion.

278

To understand the effects of draw electrolyte on the feed solute, we considered that the feed ions are

279

subjected to the electrostatic potential gradient ( ;/ ) which results from the different diffusivity of the

280

;ѱ ;/

profile within the membrane may be obtained.

denotes the extent of electrostatic interactions between the draw cation and

;ѱ

draw ions, and allowed the feed ions to transport at their own rate (uncoupled from their counter ions)

281

(Yaroshchuk et al., 2013). Uncoupled transport of feed cation and anion under the effects from draw

282

solute in the bidirectional transport has been observed in previous studies (Hancock and Cath, 2009;

283

Hancock et al., 2011; Cheng et al., 2018).

284

2.4.3 Feed ions transport considering the electrostatic effects from draw ions

285

With the

286

of the feed ions in each layer of the membrane may be established.

287

2.4.3.1 Active layer

288

In the active layer, in addition to the diffusive flux component, an electrostatic interaction component

289

is considered.

290

−

291 292

,\]^

where

=

;ѱ ;/

!

profile of draw electrolyte and the extended Nernst-Planck equation, the forward flux

,\]^

,\]^

;

,_`a

;/

+

!

,\]^ >

,\]^ *

!

;ѱ ,\]^ ?@ ;/

(19)

is the forward flux of the feed ion, mol/m2/s;

!

,\]^

is the diffusion coefficient of

the feed ion in the active layer, m2/s; * ! ,\]^ is the concentration of feed ion in the active layer, 14

,\]^

293

mol; >

294

expression of which is give in eq. 13.

295

Since the solute permeability of the membrane

296 297

;ѱ ;/

is the charge of the feed ion; and

is the electrostatic potential gradient the

may be expressed as

, where

!

is diffusion

coefficient of the draw solute in the active layer, m2/s, "! is the active layer thickness, m, # is the partition co-efficiency of the solute in water and in the active layer, eq. 19 may be rewritten as:

298

−

299

where

300

proportional to the feed electrolyte permeability of the membrane (

301

Integrating eq. 20 based on the boundary conditions under a steady-state, i.e. x=0, c=*

302

x="! , c=*

303

be obtained:

304

*

307

=

,\]^ "! ,\]^

,bcd ,

where *

,L ,bcd

+

,_`a

;/

,\]^ "! >

,\]^ *

,\]^ ?@ H

,O

?@

,O

4 3

Q R

(20)

). ,L ,bcd

and,

the concentration profile and the forward flux of the feed ion in the active layer may

,\]^ = 1+> D%,ion H

= J1 + >

;

is the feed ion permeability of the membrane, mol/m/s, which is considered to be

D%,ion D% ,ion

,\]^

305

306

,\]^

P

%

D,N %* %

+

%

,\]^ H

%M

and *

,\]^

,\]^

−h

,

D%,ion

1+>D%,ion H

,_`a

3 4

D%,ion

D,N %* %

%

m ,O ,_`a ,O m ,O m

,O

m

%

− *D% i , D,N

,_`a H

n

,_`a H

n

%

%

5

P

R

+

D,N %* %

% D,N %* % %

>D%,jkl H

5

%

(21)

(22)

are the concentration of feed ion on the feed side and the support layer

side of the active layer, respectively, mol/m3.

,\]^

is the forward flux of the feed ion, mol/m2/s.

308

2.4.3.2 Support layer

309

Based on the Nernst-Planck equation, the feed ion flux in the support layer can also be derived using

310

a differential equation as in eq. 23.

311

−

,\]^

=− *

,\]^

+

,\]^

;

;/

<

−

,\]^ *

,\]^ >

,\]^ ?@ Δѱ

15

(23)

,\]^

312

where

313

may be expressed as

314

Integrating eq. 23 based on the boundary condition

315

concentration profile and the forward flux of the feed ion in the active layer may be obtained:

316

*

317

,\]^

= h*

,\]^

318

=:

=

319

*

320

where *

321 322

323

,\]^

is apparent diffusion co-efficient of feed solute ion in the support layer, m2/s, which

,\]^ +

+

,_`a

,_`a

,_`a R

,_`a

>

G

(Yip et al., 2010; Manickam and McCutcheon, 2017).

,_`a pqrѱ

,\]^ ?@ Δѱ 4

,_`a

B

,\]^

,_`a

s

,_`a

" 4 < D%+ % n ,_`a< pqtѱ %D% " 4 < D%+ % n ,_`a< pqtѱ %D% s v D%,jkl ,_`a

,_`a R

i exp h

−

4 <

G

,_`a pqrѱ

,_`a

s

n

/

n

,_`a R

,_`a pqtѱ

,_`a pqtѱ

,_`a

G

,_`a pqrѱ

uv

the

(24)

(25)

v 2

,_`a

,_`a

D%,jkl "% G %D%

: B% i −

,_`a R

4 <

,_`a R

x=0, * ,\]^ =* ,\]^ and x=" , * ,\]^ =* ,\]^ ,

,_`a pqrѱ

(24)

is the feed ion concentration in the draw solution, mol/m3, and x is the distance to the

active layer and support layer interface, m. Substituting eq. 24 into eq. 22, the feed ion flux may be obtained as:

,\]^

=

,_`a R

s

,_`a R

G

,_`a pqrѱ

G 3 4

,_`a pqrѱ

,

J2 G

,O m m ,O

,_`a Y w

n

M

,_`a

,_`a s

5 J2 Y

,_`a

G

,O ,_`a ,_`a M

s

,_`a R

4 <

,_`a v

s

4 <

n

,_`a pqtѱ

,_`a

,_`a R n

v

,_`a pqtѱ

,_`a

m

m

,O

n

,_`a w

v J2 G

v ,_`a Y

M

,_`a

(25)

324

Eq.25 appears in a similar form as the solute flux model which does not take into account

325

electrostatic interactions (eq. 2). Comparing the two equations, the effects of draw solute on the feed

326

ion flux is shown in the following aspects. In eq. 25, (1) an electrostatic force component was added

327

to the convective component, suggesting promoted/retarded transport of feed ion in the support layer;

328

), reflecting

329 330

(2) a weight factor J1 + >

,\]^ H

M was added to the salt permeability (

facilitated/hindered permeation of feed ions in the active layer; and (3) a weight factor ,O

G

,_`a Y

was applied to *

,L ,\]^

showing the concentration/dispersion effects on the feed 16

331

ions in the active layer.

332

3 Results and Discussion

333

3.1 Effects of draw electrolyte constituents on the feed ion flux

334

NO3- flux was measured at a feed NaNO3 concentration of 1mM but with different draw solutes at

335

different concentrations. For each draw solute, high draw solution concentration resulted in high

336

water flux (Fig. 2). There was a general trend that, for each draw solute, the NO3- flux increased with

337

the increase in the water flux, due to increased convection (Hancock and Cath, 2009; Hancock et al.,

338

2011) (Fig. 3a). As a non-electrolyte draw solute, glucose was expected to have minor electrostatic

339

interaction with NO3-. The non-electrostatic-interaction model (eq. 2) predicted the NO3- flux in the

340

glucose system well. This result also suggested that the CTA membrane was largely uncharged

341

(Hancock et al., 2011; Irvine et al., 2013). When electrolytes were used as draw solutes, the NO3-

342

flux patterns significantly deviated from the non-electrostatic-interaction model (and that in the case

343

of glucose). Higher NO3- flux was observed when NaCl, MgCl2, Tris-HCl or PDADMAC were used

344

as draw solutes. For all these draw solutes, the cations (Na+, Mg2+, TrisH+ or PDADMAn+) have

345

lower diffusion coefficient values (and larger hydrated radii, Nightingale, 1959; Zheng et al., 2019)

346

than that of Cl- (Supplementary Material Table S1) (Ng and Barry, 1995; Adamczyk et al., 2014).

347

Thus, the slow-moving cations tend to attract Cl- towards the draw solution side when transported

348

though the membrane. As an anion, NO3- receives the same attractive force by these cations towards

349

the draw solution side, thus resulting in higher forward fluxes. These results corroborate other studies,

350

where the NO3- flux was shown to be deviate significantly from the non-electrostatic-interaction

351

model when NaCl was used as a draw solute (Hancock et al., 2011; Irvine et al., 2013; Kong et al.,

352

2018). Additionally, it appeared that for these chloride salts, the lower the mobility of the cations, the 17

353

higher the impact on the NO3- flux (Fig. 3a). Even for the most commonly used draw solutes (i.e.

354

NaCl and MgCl2), the NO3- flux was significantly higher than the predictions of the

355

non-electrostatic-interaction models (1.8-2.0 times for NaCl and 2.3-2.7 times for MgCl2), implying

356

that electrostatic interactions played an important role on the flux of the feed ion, and must be

357

considered when evaluating membrane rejection of charged compounds.

358

In contrast, Na3Cit and PAANa generated significantly lower NO3- flux than that predicted by the

359

non-electrostatic-interaction model (0.54-0.57 times lower for Na3Cit and 0.32-0.35 times lower for

360

PAANa). Na3Cit and PAANa are weak electrolytes and are not completely dissociated at pH=7.

361

However, the diffusivity of the citrate ions and the PAA ions are much lower than that of Na+

362

(Supplementary Material Table S1) (Ng and Barry, 1995; Ge et al., 2012; Holloway et al., 2015). The

363

low diffusivity of these anions (and their large hydrated radii, Adamczyk et al., 2006; Thomasset et

364

al., 1986) results in an attraction of Na+ towards the draw solution side, and thus a negative

365

electrostatic field (eq. 9), which obstructed NO3- from passing through and repulsed it to the feed side.

366

As a result, significantly reduced forward fluxes of NO3- were observed. Similarly, the lower the

367

diffusivity of the draw anion, the higher the degree of reduction in the NO3- flux, thus showing that

368

, eq. 9 and 25) is a key

369

the difference in diffusivity between the draw cation and anion (or θ

factor that determines the effects of the draw solutes on the flux of feed ions.

370

As an anion, NO2- showed similar trends to that observed for NO3- (Fig. 3b). Glucose resulted in a

371

NO2- flux pattern close to that predicted by the non-electrostatic-interaction model (eq. 2), whereas

372

NaCl, MgCl2, Tris-HCl and PDADMAC resulted in significantly higher NO2- fluxes than the model

373

predictions (1.93-2.01, 2.6-3.1, 5.4-5.7 and 6.1-6.5 times higher for NaCl, MgCl2, Tris-HCl and

374

PDADMAC, respectively). The NO2- flux increased with the decrease in the cation diffusivity (and 18

375

the increase in the hydrated radius values of the cations, Supplementary Material Table S1). Na3Cit

376

and PAANa resulted in significantly retarded NO2- flux (0.43-0.57 and 0.27-0.28 of that predicated

377

by the non-electrostatic-interaction model) due to the higher diffusivity of the cation (Na+) than the

378

companion anions (citrate3- and PAAn-). The NO2- flux decreased with a decrease in the anion

379

diffusivity.

380

The transport of NH4+ showed an opposite trend as compared to NO3- and NO2-, where draw solutes

381

with the constitution of a slow-moving cation and a fast-moving anion (NaCl, MgCl2, Tris-HCl and

382

PDADMAC) resulted in NH4+ fluxes lower than that observed in the glucose system (Fig. 3c).

383

Conversely, in the system with draw solutes composed of fast-moving cations and slow-moving

384

anions, the forward transport of NH4+ was highly promoted. The resultant NH4+ fluxes in Na3Cit and

385

PAANa systems were 3.8-5.6 and 8.4-9.8 times higher than the predicted flux ignoring the

386

electrostatic interactions (and that in the glucose system).

387

Overall, these results (Fig. 3) demonstrated that the composition of the draw solute has significant

388

effects on the forward transport of the feed ions. The slow-moving constituent ion of the draw solute

389

attracts the counter-ion and repulses the co-ion, resulting in promoted forward fluxes of the

390

counter-ion and reduced forward fluxes of the co-ion. The higher degree of the difference in

391

diffusivity between the constituent ions of the draw solute, the higher was the impact observed on the

392

feed ion transport.

393

A one-way electrostatic model (eq. 25) was used to estimate the electrostatic impacts of the draw

394

electrolytes on the flux of the feed ions. The extent of the influence of each draw electrolyte was well

395

predicted (Fig. 3). The model was established based on the assumption that the draw ion

396

concentrations were much higher than that of the feed ions within the membrane matrix. This 19

397 398 399

assumption is valid within a major part of the membrane, even when the concentration of the draw solute in the feed solution is at low levels (where *

may be close to or lower than * ,

Supplementary Material Fig. S2), since within the active layer, the draw solute concentration

400

increases dramatically from the feed side to the draw side, while the concentration of the feed ion

401

sharply decreases in the same direction (eq. 12 and Supplementary Material Fig. S2). However, in

402

this case (i.e. when the concentration of the draw solute in the feed solution is at low levels), the

403

direct use of eq. 25 would overestimate the feed ion fluxes, since not all the feed ions may be

404

effectively affected by the draw ions when their concentrations were at similar levels. From eq. 25,

405

the extent of the electrostatic effects on the feed ion flux is affected by the concentration of the draw

406

electrolytes in the membrane, which decreases as the concentrations of the draw electrolytes at the

407

(feed side) surface of the active layer (*

408

ions affected by the draw ions would depend on the concentration ratio of the feed to the draw ions.

409

As the concentration of the draw ions at the surface of the active layer decreases, the proportion of

410

the feed ions affected by the draw ions would correspondingly decrease. In general, the electrostatic

411

effects would be expected to first increase and then decrease as the concentration of the draw solute

412

at the surface of the active layer increased (Supplementary Material Fig. S3). Thus, the feed ion

413 414

fluxes were approximated with *

,L

,L

) decrease. On the other hand, the proportion of the feed

(eq. 25) set to 20 and 50 mM (Fig. 3). Overall, it suggested that

the effects of the draw electrolyte on the flux of the feed ions may be predicted based on the model

415

developed considering the electrostatic interactions.

416

3.2 Role of electrostatic interactions

417

To better understand the electrostatic effects of the draw solute on the flux of the feed ions, the

418

concentration profile and the electrostatic potential gradient profile of the draw electrolyte within the 20

419

FO membrane was established based on eq. 11-13 and 15-17. Fig. 4 shows the use of MgCl2 as draw

420

solute. Since the diffusivity of Mg2+ is lower than Cl- (Supplementary Material Table S1), Mg2+ drags

421

Cl- when they transport through the membrane along the concentration gradient (eq. 11 and 15). The

422

electrostatic interactions between Mg2+ and Cl- ions results in the transport of Mg2+ and Cl- at the

423

same speed (eq. 8) (Ng et al., 2006; Cussler, 2009). The extent of the electrostatic interaction

424

between Mg2+ and Cl- is reflected in the calculated electrostatic potential gradient (

425

Higher

426

concentration gradient of MgCl2 in the active layer. The highest electrostatic potential gradient is

427

adjacent to the feed side interface, and is reduced gradually through the active layer (Fig.4a). A

428

relative constant electrostatic potential gradient was found within the support layer (Fig.4a), owing

429

largely to the same trends in the concentration and the concentration gradient profiles of MgCl2 in the

430

support layer (Fig.4a), which also supports the assumption of a constant electrostatic potential

431 432

;x ;/

;x ;/

, eq. 12 and 17).

values were observed in the active layer than in the support layer, owing to a high

gradient ∇ѱ% to simplify eq. 17 into eq. 18. The

;x ;/

profile (Fig. 4a) suggested that the draw

electrolytes are expected to show a more significant impact on the transport of feed ions in the active

433

layer than in the support layer.

434

Feed ions passing through the membrane are subjected to this electrostatic potential gradient. NO2-,

435

as an anion experiences the same electrostatic force as Cl- (i.e. attracted by Mg2+ toward the draw

436

solution side) and thus an increase in the forward flux. Fig. 4b shows the concentration profiles of

437

NO2- in the membrane with and without considering the electrostatic effects from the draw

438

electrolytes. With electrostatic effects (as according to eq. 21 and 24), significantly increased NO2-

439

concentrations was observed in the active layer, which resulted in a much higher NO2- concentration

440

at the active layer/support layer interface. In the support layer, NO2- continues to be attracted by the 21

441

Mg2+. As a result, the transport of NO2- was enhanced.

442

NH4+, as a cation, is expected to experience the same electrostatic force as did Mg2+ from Cl- (i.e.

443

toward the FS side). As a result, NH4+ shows significantly reduced forward flux and reduced

444

concentrations within the membrane (Fig. 4c). From the

445

and the concentration gradient profiles of NO2- (Fig. 4b) and NH4+(Fig. 4c), it is clear that the

446

electrostatic effects on the transport of feed ions occurred mainly in the active layer, especially in the

447

part close to the feed solution.

448

Although interactions occur between the constituent ions of the draw electrolyte within the

449

membrane matrix (as indicated by the Nernst-Planck equation, eq. 4a and 4b), these interactions

450

modulated the transport of the draw ions to the same rate. Since electroneutrality of the solution is

451

maintained at any point within the membrane, no explicit electrostatic potential is likely to be

452

generated across the membrane. During bidirectional transport, the electrostatic interactions among

453

the feed and draw ions results in re-partitioning of the feed and draw ions within the membrane

454

matrix (Fig. 4b and 4c). Overall, electroneutrality will still be maintained. As such, the solutions or

455

the membrane would not show any electrostatic potential externally.

456

3.3 Electroneutrality in bidirectional transport

457

To further understand the interactions between feed and draw solution and the effects of feed ions on

458

the reverse transport of draw ions, FO experiments was performed at an elevated feed electrolyte

459

concentration with 10mM NH4NO3 as a feed, and with different draw solutes at a concentration of

460

1M. The bidirectional transport behavior of the feed ions and the draw ions was evaluated.

461

Results showed that electrostatic interactions played a key role in the transport of the feed ions, even

462

with elevated feed ion concentrations (10mM, Fig. 4a). The trend was largely similar to that 22

;x ;/

profile (Fig. 4a) of the draw solution

463

observed at low feed ion concentrations (1mM, Fig. 2). In the glucose system, similar NH4+ and NO3-

464

fluxes were observed. Without electrostatic impacts from the draw solutes, the transport of NH4+ and

465

NO3- is coupled to maintain electrostatic neutrality in the system (Fig. 1a, eq. 7) (Cussler, 2009;

466

Hancock et al., 2011). while in other systems, the transport of NH4+ and NO3- was largely uncoupled.

467

Significantly promoted NO3- flux with highly reduced NH4+ flux was observed in systems with draw

468

solute composed of fast-moving anions and slow-moving cations (KCl, NaCl, MgCl2 and TrisHCl),

469

while the draw electrolyte with fast cation/slow anion combinations (Na2SO4 and Na3Cit) generated

470

significantly higher NH4+ flux then that of NO3-. The NH4+ flux/NO3- flux ratio show a strong

471

positive correlation with θD (eq. 9, Fig. 5a), suggesting that the flux behaviors of the feed ions were

472

largely determined by the diffusivity difference between the draw ions. θD (of the draw electrolyte)

473

is an effective indictor to denote the effects of draw electrolyte on the transport of feed ions.

474

Analyses of the reverse flux of the draw ions showed that the reverse transport of draw electrolytes is

475

largely coupled when the feed solution was ultra-pure water (Phillip et al., 2010) (Fig. 5c, Fig. 1a and

476

eq. 7). Uncoupled transport of the draw ions was observed when the feed solution was 10 mM

477

NH4NO3 (Fig.5c). Corresponding to the higher NO3- fluxes, increased reverse transport of Cl- was

478

observed for NaCl, MgCl and KCl, suggesting the effects of feed ions on the reverse transport of the

479

draw ions. This observation was in line with the ion-exchange phenomena reported by Irvine et al.

480

(2013). Similar evidences were observed in other studies with NaCl as a draw solute (Kong et al.,

481

2018). From this study, it seems clear that electrostatic interaction between draw and feed ions is a

482

key driving force of the ion-exchange phenomena. Contrasting the huge differences in the feed NH4+

483

and NO3- fluxes (Fig. 5a), lower differences were observed for the draw ions (Fig. 5c), owing to the

484

higher concentration of the draw ions than the feed ions. These results also suggested that the 23

485

electrostatic interactions (between draw and feed ions) has more remarkable impact on the transport

486

of the feed ions than on the draw ions (Hancock et al., 2011). Mass/charge balance evaluated showed

487

that despite the transport of draw and feed ions was affected in different extents, the mass/charge

488

difference generated due to the different flux of the feed ions was well compensated by that

489

generated due to the different flux of the draw ions in all systems (Fig.5d), which allowed both the

490

draw and the feed sides maintain an electroneutrality during the bidirectional transport of the feed

491

and the draw ions. These results again manifested that electrostatic interactions are the essential drive

492

force of the different bidirectional ions flux behaviors in different systems (Fig.5).

493

3.4 Discussion and implications

494

Using NO3-, NO2- and NH4+ salts as feed solutes, this study demonstrated that electrostatic

495

interaction plays a key role in the ion transport in the FO process. The composition of the draw

496

solute (specifically, the difference in the diffusion co-efficient between the draw anions and cations)

497

showed significant effects on the transport of the feed ions (i.e., the membrane rejection of the feed

498

ions). Draw solute composed of a slower cation (lower diffusion coefficient) and a faster anion

499

(higher diffusion coefficient) (e.g. NaCl, MgCl2, Tris-HCl or PDADMAC) significantly promoted the

500

forward transport of the feed anions (e.g. NO2- or NO3-) and retarded that of the feed cations (e.g.

501

NH4+). The opposite was true for draw solute composed of faster cations and slower anions (e.g.

502

Na3Cit or PAANa). The extent of the effects was determined by the normalized diffusivity difference

503

of the draw cation and anion (θD). The effects were remarkable even for the commonly used draw

504

solutes, such as NaCl and MgCl2, where the flux of the NO2- and NO3- was increased by a few times,

505

and the transport of NH4+ was retarded by a similar magnitude (Fig. 3 and 5). These results may

506

explain the commonly observed lower membrane (CTA FO membrane) rejection of NO2- and NO324

507

than NH4+ when NaCl or MgCl2 was used as draw solutes (Qiu et al., 2013; 2015; Wang et al., 2016;

508

Kong et al., 2018). The electrostatic interaction between draw and feed ions also provide a more

509

fundamental explanation of the ion-exchange phenomena observed in the FO process (Irvine et al.

510

2013; Kong et al., 2018; Cheng et al., 2018).

511

Draw solute composition significantly affects the membrane rejection of the feed ions (Fig. 3). These

512

results imply that the effects of draw solute may not be omitted when evaluating the performance of

513

FO processes and/or FO membranes. NaCl and MgCl2 are among the most commonly used draw

514

solute in FO (Achilli et al., 2010; Ge et al., 2013; Shaffer et al., 2015; Qiu et al., 2016a; 2016b; Awad

515

et al., 2019); the diffusivity difference between Cl- and Na+ or Mg2+ is high enough to show

516

significant effect on the forward transport of feed ions. Additionally, organic salts (Islam et al., 2019)

517

and some largely asymmetric electrolytes have been proposed as novel draw solutes (e.g.

518

Na10-phytate (Ge et al., 2018), PAANa (Ge et al., 2012), etc.) in FO due to their extremely low

519

leakage (Holloway et al., 2015; Cai and Hu, 2016; Zou et al., 2019). The electrostatic effects in FO

520

systems using these electrolytes are expected to be more significant. The effects of electrostatic

521

interaction on the removal of charged pollutants in these systems may need to be considered.

522

Additionally, the effects of the composition of the draw solute in amending the transport of feed ions

523

also suggested an opportunity to enhance the removal of specific charged pollutants in FO by

524

selecting appropriate draw solutes. To enhance the removal of negatively charged ions, a draw solute

525

composed of faster cations (high diffusivity or large hydrated radius) and slower anions (lower

526

diffusivity or small hydrated radius) are preferable. Conversely, a draw solute composed of slower

527

cations and faster anions would be expected to enhance the removal of positively charged pollutants.

528

The greater the difference in diffusivity between the ions in the draw solution (θD), the higher the 25

529

degree of effectiveness may be expected.

530

The electrostatic interactions between the feed and draw ions may be considered as a form of the

531

Donnan equilibrium in a more general sense (Donnan, 1924; Hancock et al., 2011), where it is not

532

non-diffusible ions or fixed charges in the membrane matrix that electrostatically excludes charged

533

ions (Lu et al., 2014), but the diffusivity difference between the constituent draw ions that altered the

534

transport behaviors of feed ions. The fluxes of the anion and the cation could differ by several folds

535

(e.g. the flux of NO3- was 36 times higher than NH4+ when 1M MgCl2 was used as a draw solution)

536

(Fig.5). These differences might be further enhanced by increasing the draw solute concentration or

537

using a highly asymmetrical draw solute (such as PAANa or PDADMAC as in this work). These

538

results suggest the potential to use FO for selective ion removal or concentration.

539

In general, electrostatic interaction is a key factor governing ion transport behaviors in FO. An

540

in-depth analysis of the effects of electrostatic interactions would result in improved understanding

541

of solute transport. This may lead to novel developments by manipulating the effects of electrostatic

542

interactions to enhance the removal of specific pollutants (such as heavy metals and/or charged trace

543

organic compounds).

544

4. Conclusion

545

Electrostatic interactions were shown to play a key role in ion transport in the FO process.

546

The composition of the draw electrolyte significantly impacts the forward transport of the feed

547

ions. Draw electrolyte composed of low-diffusivity cations and high-diffusivity anions promoted

548

the forward transport of the feed anions and retarded that of the feed cation. Conversely, the

549

forward transport of the feed anions was greatly reduced while that of the feed cation was

550

significantly enhanced, with draw electrolyte composed of high-mobility cations and 26

551

low-mobility anions.

552

The effects were remarkable even for the most commonly used draw electrolytes (NaCl or

553

MgCl2), where the forward fluxes of nutrient ions (NH4+, NO3- and NO2-) were

554

promoted/retarded by a few folds compared to that in a nonelectrolyte draw solute (glucose)

555

system. More profound increase/reduction (up to 10 times) was observed for highly asymmetric

556

draw electrolytes (PAANa or PDADMAC).

557

A mathematic model is developed by considering the electrostatic interaction between the draw

558

and the feed ions to predict the effect of electrostatic interactions on the forward transport of the

559

feed ions. The normalized diffusivity difference (θD) between the constituent ions of the draw

560

electrolyte is found as a key factor that determines the degree of the electrostatic effects on the

561

forward flux of the feed ions.

562

These results may have important implications in enhancing our understanding of bidirectional ion

563

transport in FO. The findings may be useful in the design and development of FO processes for

564

enhanced removal of charged pollutants via draw solute selection and formulation.

565

Acknowledgement

566

This research was funded by the Singapore National Research Foundation under its Competitive

567

Research Program (project No. R-279-000-338-281). Dr. Guanglei Qiu acknowledges the support of

568

National Natural Science Foundation of China (No. 51808297) and the Fundamental Research Funds

569

for the Central Universities, China (No. 2019ZD21).

570

References

571

Achilli, A., Cath, T.Y., Childress, A.E. 2010. Selection of inorganic-based draw solutions for forward

572

osmosis applications. J. Membr. Sci. 364 (1-2), 233–241 27

573 574

Achilli, A., Cath, T. Y., Marchand, E. A., Childress, A. E. 2009. The forward osmosis membrane bioreactor: a low fouling alternative to MBR processes. Desalination 239 (1−3), 10−21.

575

Adamczyk, Z., Bratek, A., Jachimska, B., Jasiński, T., Warszyński, P. 2006. Structure of Poly(acrylic

576

acid) in Electrolyte Solutions Determined from Simulations and Viscosity Measurements. J.

577

Phys. Chem. B 110, 22426–22435.

578

Adamczyk, Z., Jamrozy, K., Batys, P., Michna, A. 2014. Influence of ionic strength on

579

poly(diallyldimethylammonium chloride) macromolecule conformations in electrolyte solutions.

580

J. Colloid Interface Sci. 435, 182–190.

581 582

APHA. 1999. Standard Methods for the Examination of Water and Wastewater, 19th ed.; American Public Health Association. Inc.: Washington DC.

583

Ansari, A.J., Hai, F.I., Price, W.E., Drewes, J.E., Nghiem, L.D. 2017. Forward osmosis as a platform

584

for resource recovery from municipal wastewater - A critical assessment of the literature. J.

585

Membr. Sci. 529, 195–206.

586 587 588 589 590 591

Awad, A.M., Jalab, R., Minier-Matar, J., Adham, S., Nasser, M.S., Judd, S.J. 2019. The status of forward osmosis technology implementation. Desalination 461, 10–21. Cai, Y., Hu, X.M. 2016. A critical review on draw solutes development for forward osmosis. Desalination, 391, 16-29. Cath, T.Y., Childress, A.E., Elimelech, M. 2006. Forward osmosis: Principles, applications, and recent developments. J. Membr. Sci. 281, 70–87.

592

Chekli, L., Phuntsho, S., Kim, J.E., Kim, J., Choi, J.Y., Choi, J.S., Kim, S., Kim, J.H., Hong, S.,

593

Sohn, J., Shon, H.K. 2016. A comprehensive review of hybrid forward osmosis systems:

594

Performance, applications and future prospects. J. Membr. Sci. 497, 430–449. 28

595

Cheng, W., Lu, X., Yang, Y., Jiang, J., Ma, J. 2018. Influence of composition and concentration of

596

saline water on cation exchange behavior in forward osmosis desalination. Water Res. 137, 9-17.

597

Chung, T.S., Zhang, S., Wang, K.Y., Su, J., Ling, M.M. 2012. Forward osmosis processes: Yesterday,

598 599 600

today and tomorrow. Desalination 287, 78–81. Coday, B.D., Yaffe, B.G.M., Xu, P., Cath, T.Y. 2014. Rejection of trace organic compounds by forward osmosis membranes: A literature review. Environ. Sci. Technol. 48, 3612−3624.

601

Cui, Y., Liu, X.Y., Chung, T.S., Weber, M., Staudt, C., Maletzko, C. 2016. Removal of organic

602

micro-pollutants (phenol, aniline and nitrobenzene) via forward osmosis (FO) process:

603

Evaluation of FO as an alternative method to reverse osmosis (RO). Water Res. 91, 104−114.

604

Cussler, E.L. 2009. Diffusion mass transfer in fluid systems, 3rd ed.; University Press: Cambridge.

605

Donnan, F. G. 1924. The theory of membrane equilibria. Chem. Rev. 1 (1), 73–90.

606

Dresner, L. 1972. Some remarks on the integration of extended Nernst–Planck equation in the

607 608 609 610 611 612 613 614 615 616

hyperfiltration of multicomponent solutions. Desalination 10, 27–46. Ge, Q., Lau, C.H., Liu, M. 2018. A novel multi-charged draw solute that removes organic arsenicals from water in a hybrid membrane process. Environ. Sci. Technol. 52, 3812−3819. Ge, Q., Ling, M.M., Chung, T.S. 2013. Draw solutions for forward osmosis processes: Developments, challenges, and prospects for the future. J. Membr. Sci. 442, 225–237. Ge, Q., Su, J., Amy, G.L., Chung, T.S. 2012. Exploration of polyelectrolytes as draw solutes in forward osmosis processes. Water Res. 46, 1318−1326. Hancock N.T., Cath, T.Y. 2009. Solute coupled diffusion in osmotically driven membrane processes. Environ. Sci. Technol. 43, 6769–6775. Hancock, N.T., Phillip, W.A., Elimelech, M., Cath, T.Y. 2011. Bidirectional permeation of 29

617

electrolytes in osmotically driven membrane processes. Environ. Sci. Technol., 45, 10642–

618

10651.

619

Hoek, E.M.V., Kim, A.S., Elimelech, M. 2002. Influence of crossflow membrane filter geometry and

620

shear rate on colloidal fouling in reverse osmosis and nanofiltration separations. Environ. Eng.

621

Sci. 19, (6), 357–372.

622

Holloway, R.W., Regnery, J., Nghiem, L.D., Cath, T.Y. 2014. Removal of trace organic chemicals

623

and performance of a novel hybrid ultrafiltration-osmotic membrane bioreactor. Environ. Sci.

624

Technol. 48, 10859−10868.

625 626 627 628 629 630

Holloway, R.W., Maltos, R., Vanneste, J., Cath. T.Y. 2015. Mixed draw solutions for improved forward osmosis performance. J. Membr. Sci. 491, 121–131. Islam, M.S., Sultana, S., McCutcheon, J.R., Rahaman, M.S. 2019. Treatment of fracking wastewaters via forward osmosis: Evaluation of suitable organic draw solutions. Desalination 452, 149-158. Irvine, G.J., Rajesh, S., Georgiadis, M., Phillip, W.A., 2013. Ion selective permeation through cellulose acetate membranes in forward osmosis. Environ. Sci. Technol. 47, 13745–13753

631

Kong, F., Dong, L., Zhang, T., Chen, J., Guo, C. 2018. Effect of reverse permeation of draw solute

632

on the rejection of ionic nitrogen inorganics in forward osmosis: Comparison, prediction and

633

implications. Desalination 437, 144–153.

634 635 636 637 638

Lee, D.J., Hsieh, M.H. 2019. Forward osmosis membrane processes for wastewater bioremediation: Research needs. Bioresour. Technol. 290: 121795. Loeb, S., Titelman, L., Korngold, E., Freiman, J. 1997. Effect of porous support fabric on osmosis through a Loeb-Sourirajan type asymmetric membrane. J. Membr. Sci. 129, 243–249. Logan, B.E., Elimelech, M. 2012. Membrane-based processes for sustainable power generation using 30

639

water. Nature 488, 313−319.

640

Lu, X., Boo, C., Ma, J., Elimelech, M. 2014. Bidirectional diffusion of ammonium and sodium

641

cations in forward osmosis: Role of membrane active layer surface chemistry and charge.

642

Environ. Sci. Technol. 48, 14369−14376.

643 644

Lutchmiah, K., Verliefde, A.R.D., Roest, K., Rietveld, L.C., Cornelissen E.R. 2014. Forward osmosis for application in wastewater treatment: A review. Water Res. 58, 179–197.

645

Manickam, S.S., McCutcheon, J.R. 2017. Understanding mass transfer through asymmetric

646

membranes during forward osmosis: A historical perspective and critical review on measuring

647

structural parameter with semi-empirical models and characterization approaches. Desalination

648

421, 110–126.

649 650 651 652 653 654

McCutcheon, J. R., Elimelech, M. 2006. Influence of concentrative and dilutive internal concentration polarization on flux behavior in forward osmosis. J. Membr. Sci. 284, 237– 247. McCutcheon, J.R., McGinnis, R.L., Elimelech, M. 2005. A novel ammonia–carbon dioxide forward (direct) osmosis desalination process. Desalination 174, 1–11. McGovern, R.K., Lienhard V, J.H. 2014. On the potential of forward osmosis to energetically outperform reverse osmosis desalination. J. Membr. Sci. 469, 245–250.

655

Ng, B., Barry, P.H. 1995. The measurement of ionic conductivities and mobilities of certain less

656

common organic ions needed for junction potential corrections in electrophysiology. J. Neurosci.

657

Methods 56, 37–41.

658 659 660

Ng, H.Y., Tang, W., Wong, W. 2006. Performance of forward (direct) osmosis process: membrane structure and transport phenomenon. Environ. Sci. Technol. 40, 2408–2413. Nightingale, E.R. 1959. Phenomenological theory of ion solvation. Effective radii of hydrated ions. J. 31

661 662 663 664 665

Phys. Chem. 63, 1381–1387. Paul, D.R. 2004. Reformulation of the solution-diffusion theory of reverse osmosis. J. Membr. Sci. 241 (2), 371–386. Phillip, W.A., Yong, J.S., Elimelech, M. 2010. Reverse draw solute permeation in forward osmosis: modeling and experiments. Environ. Sci. Technol. 44 (13), 5170–5176.

666

Phuntsho, S., Shon, H.K., Majeed, T., Saliby, I.E., Vigneswaran, S., Kandasamy, J., Hong, S., Lee, S.

667

Blended fertilizers as draw solutions for fertilizer-drawn forward osmosis desalination. Environ.

668

Sci. Technol. 46, 4567−4575

669

Qiu, G., Law, Y.M., Subhabrata, D., Ting, Y.P. 2015. Direct and complete phosphorus recovery from

670

municipal wastewater using a hybrid microfiltration-forward osmosis membrane bioreactor

671

process with seawater brine as draw solution. Environ. Sci. Technol. 49, 6156–6163.

672

Qiu, G., Ting, Y.P. 2013. Osmotic membrane bioreactor for wastewater treatment and the effect of

673

salt accumulation on system performance and microbial community dynamics. Bioresour.

674

Technol. 150, 287–297.

675

Qiu, G., Zhang, S., Srinivasa Raghavan, D.S., Das, S., Ting, Y.P. 2016a. The potential of hybrid

676

forward osmosis membrane bioreactor (FOMBR) processes in achieving high throughput

677

treatment of municipal wastewater with enhanced phosphorus recovery. Water Res. 105,

678

370−382.

679

Qiu, G., Zhang, S., Srinivasa Raghavan, D.S., Das, S., Ting, Y.P. 2016b. Towards high through-put

680

biological treatment of municipal wastewater and enhanced phosphorus recovery using a hybrid

681

microfiltration-forward osmosis membrane bioreactor with hydraulic retention time in sub-hour

682

level. Bioresour. Technol. 219, 298-310. 32

683 684 685 686

Schlögl, R. 1966. Membrane permeation in system far from equilibrium. Berichte der Bunsengesellschaft Physik. Chem. 70, 400–414. Shaffer, D.L., Werber, J.R., Jaramillo, H., Lin, S., Elimelech, M. 2015. Forward osmosis: Where are we now? Desalination 356, 271–284.

687

Suh, C., Lee, S. 2013. Modeling reverse draw solute flux in forward osmosis with external

688

concentration polarization in both sides of the draw and feed solution. J. Membr. Sci. 427, 365–

689

374.

690

Tan, C.H., Ng, H.Y. 2008. Modified models to predict flux behavior in forward osmosis in

691

consideration of external and internal concentration polarizations. J. Membr. Sci. 324(1–2), 209–

692

219.

693

Thomasset, B., Friboulet, A., Barbotin, J.N., Thomas, D. 1986. Modulation by a high citrate

694

concentration of kinetic parameters and of functional stability of two immobilized thylakoid

695

systems. Biotechnol. Bioeng. 28(8), 1200-1205.

696

Tiraferri, A., Yip, N.Y., Straub, A.P., Castrillon, S. R.V., Elimelech, M. 2013. A method for the

697

simultaneous determination of transport and structural parameters of forward osmosis

698

membranes. J. Membr. Sci. 444, 523–538.

699 700

Vanysek, P. 2005. Ionic conductivity and diffusion at infinite dilution. In Lide, D.R. ed., CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL.

701

Volpin, F., Heo, H., Johir, M.A.H., Cho, J., Phuntsho, S., Shon, H.K. 2019. Techno-economic

702

feasibility of recovering phosphorus, nitrogen and water from dilute human urine via forward

703

osmosis. Water Res. 150, 47–55.

704

Wang, X., Chang, V.W.C., Tang, C.Y. 2016. Osmotic membrane bioreactor (OMBR) technology for 33

705

wastewater treatment and reclamation: advances, challenges, and prospects for the future. J.

706

Membr. Sci. 504, 113−132.

707

Xie, M., Luo, W., Guo, H., Nghiem, L.D., Tang, C.Y., Gray, S.R. 2018. Trace organic contaminant

708

rejection by aquaporin forward osmosis membrane: Transport mechanisms and membrane

709

stability. Water Res. 132, 90–98.

710 711

Xie, M., Nghiem, L.D., Price, W.E., Elimelech, M. 2012. Comparison of the removal of hydrophobic trace organic contaminants by forward osmosis and reverse osmosis. Water Res. 46, 2683–2692.

712

Xie, M., Nghiem, L.D., Price, W.E., Elimelech, M. 2013. A forward osmosis−membrane distillation

713

hybrid process for direct sewer mining: system performance and limitations. Environ. Sci.

714

Technol. 47, 13486−13493

715

Xie, M., Nghiem, L.D., Price, W.E., Elimelech, M. 2014. Toward resource recovery from wastewater:

716

extraction of phosphorus from digested sludge using a hybrid forward osmosis–membrane

717

distillation process. Environ. Sci. Technol. Lett. 1(2), 191–195.

718

Yaroshchuk, A., Bruening, M.L., Bernal, E.E.L. 2013. Solution-Diffusion–Electro-Migration model

719

and its uses for analysis of nanofiltration, pressure-retarded osmosis and forward osmosis in

720

multi-ionic solutions. J. Membr. Sci. 447, 463–476.

721

Yip, N.Y.; Tiraferri, A.; Phillip, W.A.; Schiffman, J.D.; Elimelech, M. 2010. High performance

722

thin-film composite forward osmosis membrane. Environ. Sci. Technol. 44 (10), 3812–3818.

723

Yong, J.S., Phillip, W.A., Elimelech, M. 2012 Coupled reverse draw solute permeation and water

724 725 726

flux in forward osmosis with neutral draw solutes. J. Membr. Sci. 392, 9–17. Zhao, S., Zou, L.C., Tang, Y., Mulcahy, D. 2012. Recent developments in forward osmosis: Opportunities and challenges. J. Membr. Sci. 396, 1–21. 34

727

Zhang, J., She, Q., Chang, V.W.C., Tang, C.Y., Webster, R.D. 2014. Mining nutrients (N, K, P) from

728

urban source-separated urine by forward osmosis dewatering. Environ. Sci. Technol. 48,

729

3386−3394.

730

Zheng, L., Price, W.E. McDonald, J., Khan, S.J., Fujioka, T., Nghiem, L.D. 2019. New insights into

731

the relationship between draw solution chemistry and trace organic rejection by forward

732

osmosis. J. Membr. Sci. 587: 117184.

733 734 735 736

Zou, S., Qin, M., He, Z. 2019. Tackle reverse solute flux in forward osmosis towards sustainable water recovery: reduction and perspectives. Water Res. 149, 362–374. Zydney, A.L. 1997. Stagnant film model for concentration polarization in membrane systems. J. Membr. Sci. 130, (1-2), 275–281.

35

1 2

Fig.1. Illustration of the potential electrostatic interaction among feed ions and draw ions. a. Forward

3

transport of feed electrolyte when the draw solute is a non-electrolyte. The feed cations and anions

4

are expected to transport at a harmonic flux to maintain electroneutrality; b. Reverse transport of

5

draw electrolyte composed of cations and anions having different diffusivity (the feed solution is

6

ultrapure water). The cations and anions are expected to transport at a harmonic flux to maintain

7

electroneutrality. The force harmonizing their transport is the electrostatic interactions, which may be

8

solved using the extended Nernst-Planck equation; c. Electrostatic interactions among feed ions and

9

draw ions when the draw solute is composed of cations and anions having different diffusivity. The

10

feed ions are exposed to the electrostatic potential gradient generated from the difference in

11

diffusivity of the draw cations and anions, where the cations or anions will either be

12

repulsed/attracted when they pass through the membrane, thus resulting in promoted/retarded flux.

22 20

Water flux, LMH

18 16 14

NaCl MgCl2

12

NaCl-Model MgCl2-Model

10

Na2SO4 8

Glucose Glucose-Model

6

Na2SO4-Model

4 0

1

0.5

1

1.5

2 2.5 DS concentration, M

3

3.5

4

4.5

4

4.5

a 150

Salt leakage, mmol/m2 /h

120

NaCl MgCl2 NaCl-Model

90

MgCl2-Model Na2SO4 Glucose Glucose-Model

60

Na2SO4-Model

30

0 0

2

b

0.5

1

1.5

2 2.5 DS concentration, M

3

3.5

0

DS concentration (NaPAA or PDMAC), g/L 100 150 200

50

250

300

16 Tris-HCl

Na3Cit

NaPAA

PDMAC

Water flux, mmol/m2/h

14

12

10

8

6

4 0

3

0.5

1 1.5 DS concentration (Na3Cit or Tris-HCl), M

2

2.5

c 0

DS concentration (NaPAA or PDMAC), g/L 100 150 200

50

250

300

30 Tris-HCl

Na3Cit

NaPAA

PDMAC

Salt leakage, mmol/m2 /h

25

20

15

10

5

0 0

0.5

1 1.5 DS concentration (Na3 Cit or Tris-HCl), M

2

2.5

4

d

5

Fig. 2. Water flux and reverse salt flux of each draw solution as a function of draw solution

6

concentration measured in the feed solution facing active layer mode with ultrapure water as the feed.

7

a. Water flux of NaCl, MgCl2, Na2SO4 and glucose. The dashed lines show the predicted values

8

based on eq.3; b. Reverse salt flux of NaCl, MgCl2, Na2SO4 and glucose. The dashed lines show the

9

predicted values based on eq.1; c. Water flux of Na3Cit, TrisHCl, PAANa and PDMAC; d. Salt

10

leakage of Na3Cit, TrisHCl, PAANa and PDMAC. Error bars indicate the standard deviation (S.D.)

11

of triplicate experiments.

12

9

Glucose NaCl

8

Na2SO4 MgCl2

7

NO3- flux, mmol/m2/h

PAANa Na3Cit

6

PDADMAC 5

TrisHCl NonE Model

4

NaCl E-model MgCl2 E-model

3

Na2SO4 E-model

2 1 0 0

1

5

a 8

20

25

10 15 Water flux, LMH

20

25

Glucose NaCl Na2SO4 MgCl2 PAANa Na3Cit PDADMAC TrisHCl NonE Model NaCl E-model MgCl2 E-model Na2SO4 E-model

7 6 NO2- flux, mmol/m2/h

10 15 Water flux, LMH

5 4 3 2 1 0 0

2

b

5

18

Glucose NaCl Na2SO4 MgCl2 PAANa Na3Cit PDADMAC TrisHCl NonE Model NaCl E-model MgCl2 E-model Na2SO4 E-model

16

NH4+ flux, mmo/m2/h

14 12 10 8 6 4 2 0 0

5

10 15 Water flux, LMH

20

25

3

c

4

Fig. 3. The (a) NO3-, (b) NO2- and (c) NH4+ flux patterns obtained with different draw solute at

5

different concentrations (NaCl: 0.5, 1.0, 2.0 and 4.0M; MgCl2: 0.5, 1.0, 2.0 and 4.0M; Na2SO4 0.5,

6

1.0 and 2.0 M; Na3Cit: 0.5, 1.0 and 2.0 M, Tris-HCl: 0.5, 1.0 and 2.0 M, PAANa: 100 and 250 g/L

7

and PDADMAC at 50 and 130 g/L). NaNO3 NaNO3 or NH4Cl at 1mM was used as feed solution in

8

each experiment. The solid line shows the predicted NO3-, NO2- or NH4+ flux patterns using the

9

non-electrostatic-interaction model (eq.2). The dash lines show NO3-, NO2- or NH4+ flux patterns for

10

each draw solute considering the electrostatic influence from the draw electrolyte (eq.25). Two dash

11

lines for each draw solute show NO3-, NO2- or NH4+ flux with

12

respectively (The setting is only used to approximate the effects of electrostatic effects using eq.25.).

13

Error bars indicate the S.D. of triplicate experiments.

,

set at 20 and 50 mM,

Support layer MgCl2 Concentration MgCl2 dψ/dx dc/dx

2500

2.5E+07

2000

2.0E+07

1500

1.5E+07

1000

1.0E+07

500

5.0E+06

0

0.0E+00

1

-5

0

5

10

a 2.50

Active layer

35

40

45

50

Support layer NO2NO 2

2.25 NO2- Concentration, mol/m3

15 20 25 30 Membrane thinkness, µm

5.0E+06

Concentration profile w/o electrostatic interaction 4.5E+06

NO2NO 2 Concentration profile with electrostatic interaction

2.00

NO2NO 2 Concentration gradient profile w/o electrostatic interaction

4.0E+06

1.75

NO2NO 2 Concentration gradient profile with electrostatic interaction

3.5E+06

1.50

3.0E+06

1.25

2.5E+06

1.00

2.0E+06

0.75

1.5E+06

0.50

1.0E+06

0.25

5.0E+05 0.0E+00

0.00 -10

2

-5

0

5

10

b Active layer

2.00

NH4+ Concentration, mol/m3

15 20 25 30 Membrane thinkness, µm

35

40

45

50

Support layer

4.0E+06

+ NH4+ NH 4 Concentration profile w/o electrostatic interaction NH4+ NH4+ Concentration profile with electrostatic interaction NH4+ NH4+ Concentration gradient profile w/o electrostatic interaction NH4+ Concentration gradient profile with electrostatic interaction NH4+

1.75 1.50

3.5E+06 3.0E+06

1.25

2.5E+06

1.00

2.0E+06

0.75

1.5E+06

0.50

1.0E+06

0.25

5.0E+05

0.00

0.0E+00 -10

3

c

Concentation gradient, mol/m3/m

-10

-5

0

5

10

15 20 25 30 Membrane thinkness, µm

35

40

45

50

Concentation gradient, mol/m3/m

dψ/dx, V/m Concentration, mol/m3

3.0E+07

Concentation gradient, mol/m3/m

Active layer

3000

4

Fig.4. a. Concentration profile, concentration gradient profile and the electrostatic potential gradient

5

profile within the FO membrane (1M MgCl2 as a draw solution and with

6

based on eq. 11, 12, 15 and 17, respectively. The external concentration polarization at the feed side

7

was determined based on Supplementary Material eq. S12. The

8

layer were reduced 10 times and the scale of the active layer was enlarged 10 times for a more

9

convenient representation.). b. The corresponding NO2- and c. NH4+ concentration and concentration

10

gradient profiles in the membrane with and without considering the electrostatic effects (established

11

based on eq. 2 and eq. 21 and 24, respectively, with a feed NO2- and NH4+ concentration of 1mM.

12

The external concentration polarization at the feed side was determined based on Supplementary

13

Material eq. S12. The scale of the active layer was enlarged 10 times for a more convenient

14

representation). The thickness of the support layer and the actively layer is set as 50 µm and 1.0 µm

15

(McCutcheon et al., 2005; Cath et al., 2006). A change in the setting of the thickness values of the

16

support layer and the actively layer does not alter the overall trend of each profile.

and

,

set at 50mM,

established

values in the actively

70.0

Feed ion flux, mmol/m2/h

60.0 NH4+ NH4+

NO3NO3-

50.0 40.0 30.0 20.0 10.0 0.0 NaCl

Glucose

a

Na Na2SO4 Na Na3Cit 2SO4 3Cit Draw solute

Tris HCl

KCl

100

0.8 JNO3-/JNH4+ JNO3-/JNH4+

θθD D

0.6

0.4

JNO3-/JNH4+

10

0.2

1

0

-0.2

-0.4

0.1 NaCl

2

b

MgCl2 MgCl2

Glucose

Na2SO4 Na2SO4

Na Na3Cit 3Cit

Draw solute

1

Tris HCl

KCl

θD

1

MgCl2 MgCl2

250

Reverse flux, mmol/m2/h

200

ClCl-

Cation

150

100

50

0 NaCl+UPH2O NaCl+UP H2O

MgCl22 MgCl

KCl+UPH2O KCl+UP H2O

KCl KCl

Draw solute

c

Amount of draw ion tansported to the feed, mmol

NH4+ NH4+

NO3NO3-

NH4+ NH4+

NO3NO3-

NO3NO3-

NH4+ NH4+

0.18

0.00

0.16

-0.02

0.14 0.12 0.10

-0.04 Mass of draw ion transported to the FS ∆ Feed ion mass Mass of feed ion transported to the DS ∆ Draw ion mass

-0.06 -0.08

0.08

-0.10

0.06

-0.12

0.04

-0.14

0.02

-0.16

0.00

-0.18 Cl Cl--

4

MgCl2+UPH2O MgCl 2+UP H2O

+ Na Na+

NaCl

d

ClCl-

ClCl-

Mg2+ Mg2+ MgCl2 MgCl2

Amount of feed ion tansported to the DS, mmol

3

NaCl NaCl

+ K+ K

KCl

5 6

Fig.5. a. Forward fluxes of feed ions (NO3- and NH4+, at a feed NH4NO3 concentration of 10mM)

7

with different draw solutes (at a concentration of 1M); b. Relationship between the feed cation-anion

8

flux ratio (

9

and anion (θD, eq. 9). c. Reverse fluxes of draw ions.

10

/

) and the normalized diffusion coefficient difference between the draw cation (The Cl- flux for MgCl2 was divided by 2 to

show a match with the Mg2+ flux); and d. A mass/charge balance evaluation of the bidirectional 2

11

transport of the feed and draw ions (the mass of Mg2+ was multiplied by its charge number, 2, to

12

evaluate the electrostatic neutrality). Error bars indicate the S.D. of triplicate experiments.

3

Highlights Electrostatic interactions play a major role in ion transport in the FO process; The nature of the DS significantly impacts the rejection of the feed ions; The forward fluxes of nutrient ions differ by a few folds with different DS; The diffusivity difference (θD) between the draw ions is a determining factor; Mathematical analysis allowed to approximate the electrostatic effects.

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. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: