Forward Osmosis Membranes under Null-Pressure Condition: Do

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Forward Osmosis Membranes under Null-pressure Condition: Do Hydraulic and Osmotic Pressures Have Identical Nature? Seungho Kook, Chivukula D. Swetha, Jangho Lee, Chulmin Lee, Tony Fane, and In S. Kim Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b05265 • Publication Date (Web): 21 Feb 2018 Downloaded from http://pubs.acs.org on February 25, 2018

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Environmental Science & Technology

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Forward Osmosis Membranes under Null-pressure Condition: Do Hydraulic and Osmotic

2

Pressures Have Identical Nature?

3 4

Seungho Kooka, Chivukula D. Swethaa, Jangho Leea, Chulmin Leea, Tony Faneb, and In S.

5

Kima,c,*

6 7

a

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Technology (GIST), 123 Cheomdangwagi-ro, Buk-gu, Gwangju 61005, South Korea

9

b

School of Earth Sciences and Environmental Engineering, Gwangju Institute of Science and

UNESCO Centre for Membrane Science & Technology, School of Chemical Engineering,

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University of New South Wales, Sydney NSW 2052, Australia

11

c

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123 Cheomdanwagi-ro, Buk-gu, Gwangju 61005, South Korea

Global Desalination Research Center, Gwangju Institute of Science and Technology (GIST),

13 14 15

Corresponding Author

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In S. Kim ([email protected], +82-62-715-2436)

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#310, School of Earth Sciences and Environmental Engineering, Gwangju Institute of Science

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and Technology (GIST), 123 Cheomdangwagi-ro, Buk-gu, Gwangju 61005, South Korea

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1 ACS Paragon Plus Environment


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TOC/Abstract Graphic

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ABSTRACT

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Forward osmosis (FO) membranes fall into the category of non-porous membranes, based on the

27

assumption that water and solute transport occur solely based on diffusion. The solution-

28

diffusion (S-D) model has been widely used in predicting their performances in the co-existence

29

of hydraulic and osmotic driving forces, a model that postulates the hydraulic and osmotic

30

driving forces have identical nature. It was suggested, however, such membranes may have pores

31

and mass transport could occur both by convection (i.e. volumetric flow) as well as by diffusion

32

assuming that the dense active layer of the membranes is composed of a non-porous structure

33

with defects which induce volumetric flow through the membranes. In addition, the positron

34

annihilation technique has revealed that the active layers can involve relatively uniform porous

35

structures. As such, the assumption of a non-porous active layer in association with hydraulic

36

pressure is questionable. To validate this assumption, we have tested FO membranes under the

37

conditions where hydraulic and osmotic pressures are equivalent yet in opposite directions for

38

water transport, namely the null-pressure condition. We have also established a practically valid

39

characterization method which quantifies the vulnerability of the FO membranes to hydraulic

40

pressure.

41 42

Keywords: null-pressure; hydraulic pressure; osmotic pressure; forward osmosis; membrane

43

characterization

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45

Introduction

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Exploitation of seawater as a freshwater source has been globally conducted to meet the

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increasing water demand 1. Though technological advancement in reverse osmosis (RO)

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desalination has enabled a significant reduction in production cost, in the last few decades the

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practical hurdle of marginal cost reduction has been faced 2. A technological breakthrough

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seemed plausible when the forward osmosis (FO) process was reintroduced in the early 2000s as

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one of the potential future desalination means. FO utilizes osmotic pressure as major driving

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force by employing a semi-permeable membrane between the seawater and a draw solution,

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which exhibits higher osmotic pressure than seawater, to efficiently reject salts whilst

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maximizing water transport through the membrane 3. Nevertheless, a recent thermodynamic

55

assessment has concluded that the FO unit process itself can outperform RO in terms of energy

56

cost

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higher energy to recover freshwater out of the diluted draw stream than from seawater. However,

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the hybridized version of the two processes, namely the FO-RO hybrid process has promise.

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Here FO functions as pre-treatment for RO employing wastewater of low osmotic pressure as

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feed and seawater of high osmotic pressure as draw and thereby provides the following RO with

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diluted seawater, yielding significantly lower energy demand than the conventional RO process 5,

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6

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membrane elements

64

observed which implies the performance of the membrane element, in practical terms, is

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dependent on both hydraulic and osmotic pressures. Up until now, most FO membranes have

66

been considered non-porous, so that the two driving forces affect the membrane performances

67

with an equal identity. This assumption, however, is questionable since hydraulic pressure is

4

but with a fundamental thermodynamic flaw that the post-treatment of FO requires even

. There are a number of pilot-scale studies reporting the performances of spiral-would FO 7-10

and, without exception, pressure drop between the inlet and outlet was


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defined at a macroscopic level while osmotic pressure is a driving force derived solely based on

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thermodynamic assumptions. The scope of this study is to deepen the understanding of mass

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transport in FO membranes.

71 72

Theoretical background. It is worth re-visiting earlier versions of transport models to see how

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such postulation came about. On the basis of Onsager’s theory of irreversible processes (i.e.

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Onsager reciprocal theorem

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complete set of irreversible transport models estimating the mass transports (i.e. water and solute

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transport) through a cell membrane

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dependent on concentration

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osmotic pressure to hydraulic pressure (i.e. Staverman reflection coefficient, σ) assuming the

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identical solute concentration across a cell membrane at equilibrium state

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by K-K. The pioneering work of Spiegler and Kedem (abbreviated to S-K from this point) was

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later devoted to the commencement of understanding the mass transport through RO membranes

82

16

11, 12

14

), Kedem and Katchalsky (abbreviated to K-K) established a

13

yet with a limitation that permeability coefficients are

. Prior to K-K, Staverman introduced the concept of reflection of

15

which was relayed

.

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The Achilles’ heel of the irreversible thermodynamic models is the fact that transport

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mechanisms cannot be envisioned in regards to membrane structure and properties. These

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models consider membranes as black boxes, which has been examined by Dickson

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that mass transports can only be predicted based on the phenomenological coefficients

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this regard, Lonsdale suggested the mass transports occur only by diffusion following Fick’s law

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and Henry’s law, namely the solution-diffusion (abbreviated to S-D) model

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important assumptions: 1) completely non-porous and homogeneous membrane, 2) uncoupled

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solvent and solute transports (i.e. no interactions among species), 3) no solvent-solute-membrane


19

17

, meaning 14, 18

. In

. There are 4


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interactions and 4) mass transport occurs only by diffusion following the respective

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concentration gradients and diffusivities. However, the membrane performance could not be

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accurately predicted due to numerous unknown factors such as degree of imperfection (defects)

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of the membrane structure leading to pore flow associated with hydraulic pressure

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the positron annihilation technique has revealed that the active layers can embrace relatively

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uniform porous structures 21 and this may induce the participation of convective transport. There

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have been attempts to accommodate the potential convective transport due to hydraulic pressure

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(i.e. denying the second assumption). For example, the solution-diffusion-imperfection (S-D-I in

99

short) model

22

20

. Recently

was suggested to accommodate potential convective transport and pressure

100

dependence of the chemical potential of solutes was incorporated by the extended solution-

101

diffusion (abbreviated to E-S-D) model

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require phenomenological coefficients that must be determined by experiments and non-linear

103

regression.

23

. Nevertheless, these two modified S-D models also

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Loeb and Sourirajan initiated the era of the asymmetric membrane in the early 1960s with

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the application of the first cellulose-based commercial RO membrane, namely the Loeb-

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Sourirajan type membrane. It is composed of two layers: a dense active layer, also known as

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selective or skin layer, that plays a pivotal role in rejecting salts and a porous support layer which

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offers physical strength to the membrane

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water transport possible, asymmetric membranes have been improved by developing thinner and

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denser active layers along with thinner, more rigid and more porous support layers to maximize

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salt rejection and minimize structural resistance to water transport.

24

. To efficiently reject salts while achieving fastest

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Meanwhile, assuming the membrane is completely non-porous, Loeb and his colleagues

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conducted a set of forward osmosis experiments (i.e. osmotic pressure as sole driving force)


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using one of the Loeb-Sourirajan type membranes (i.e. Toray CA-3000, cellulose acetate

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asymmetric RO membrane with woven fabric support) and made an excellent discussion on

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internal concentration polarization (ICP) inside the porous fabric support using MgCl2 solutions

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in both chambers separated by the membrane

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work of Loeb by testing a commercial cellulose triacetate FO membrane from Hydration

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Technology Innovations Inc. (Albany, OR, USA), the same membrane (i.e. CTA-ES) tested in

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our study, using 0.05 to 2 M NaCl as feed and 1.1 to 6 M NH4HCO3 as draw

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permeability coefficient obtained from the FO experiments was equivalent to that obtained from

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RO experiments, and it was concluded that the water permeability is independent of NaCl

123

concentration in the feed. The water permeability from the FO experiments was obtained

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incorporating the effect of ICP and external concentration polarization (ECP) that occurs on the

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active layer surface induced by the presence of water flux. In their work, however, there are two

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important logical segments missing: 1) derivation of solute resistivity for the multicomponent

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system (i.e. water as solvent, NaCl as solute for feed and NH4HCO3 as solute for draw)

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considering the fact that MgCl2 solutions were employed in both chambers (i.e. the solute

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resistivity of MgCl2 in the fabric support) in the work of Loeb, and 2) the degree of membrane

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deformation due to hydraulic pressure and flux in the RO experiments. Regarding the first

131

missing segment, concentration at the active-support interface cannot be computed without the

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solute resistivity. If they were obtained using the bulk osmotic pressures of the feed and draw, the

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ICP was not properly taken into account since diffusion coefficients of NaCl and NH4HCO3 in

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water are different and the impact of convection to solute mass balance in the fabric support was

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neglected, thus the data presented in 26 may not be reliable. Significantly higher osmotic pressure

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of the NH4HCO3 solution only corresponds to the unjustifiable solute resistivity of NaCl in the

25

. McCutcheon and his colleagues expanded the


26

. The water


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feed solution in their analyses. For the second segment, the membrane was assumed to be

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asymmetric, thus the porosity of the membrane can be reduced if compacted under the effect of

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pressure (i.e. denser membrane potentially leading to increased resistance to water transport). To

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clarify the effect of hydraulic pressure it is suggested that it can cause compaction in two ways,

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(1) due to volumetric compression of the solid regions of the membrane, and (2) due to the shear

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stress imposed by transmembrane pressure (TMP) gradient directly related to water flux. The

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relative magnitudes of these effects will depend on the imposed pressures and fluxes and

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membrane material. Based on the above arguments, it cannot be clearly stated that the water

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permeability is independent of NaCl concentration. Most importantly, the membranes tested in

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the two previous works are assumed to be completely non-porous (i.e. σ = 1) whereas, in the real

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case, it might not be.

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ICP has been widely accepted as the major cause of osmotic driving force loss primarily

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due to the convective water transport inside the support layer 3, 26, 27. There are studies that report

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the impact of ECP alongside the ICP, stating that ECP is determined by the shear stress caused by

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the crossflow in the membrane’s vicinity 28, 29. The combined effect of ICP and ECP is generally

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known to deteriorate the membrane performance; in fact, it is a resultant of mass balance

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determined by the intrinsic membrane parameters. A recent study by Tiraferri et al. reported a

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clear experimental validation of water and solute permeability coefficients obtained from a four-

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stage FO experiments without employing hydraulic pressure

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permeability coefficients obtained from osmosis-based method can accurately predict the FO

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performance. Nevertheless, their work is valid only when the presence of CP can be accurately

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projected into the simulation. In addition, the presence of CP has yet to be experimentally

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proven. The fact that the assumption on the presence of CP is valid, when osmotic pressure is the


30

. This indicates the use of the

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only driving force, does not necessarily applicable to the cases when hydraulic and osmotic

161

pressures co-exist. Hydraulic pressure is a physical force that affects structural integrity of

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membranes. To a more important note, adopting these coefficients to the actual field FO

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applications may not be a viable option. It is because of the hydraulic pressure dependence of the

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FO process in real life which primarily affects the two important coefficients (i.e. pressure build-

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ups and pressure drops causing variations of permeability coefficients within the feed and draw

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channels in the pilot scale), thereby altering the estimation.

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Thoroughly considering the conventional S-D model and the two modified S-D models,

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this leads to the analogy that the water and solute permeability coefficients can be dependent on

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hydraulic and osmotic pressures and thus the membrane performance can be case specific. In this

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context, though the irreversible thermodynamic theory cannot offer any insights into transport

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mechanisms, it enables a more thorough assessment on what is genuinely taking place in the

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black box membranes by analyzing the relationships among the coefficients associated with

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overall transport behaviors.

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For an ideal membrane, with no effect of CP and constant osmotic pressure difference

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across the membrane assumed, one can draw a completely straight line in a 2-D domain

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representing the relationship between the resultant water flux and the hydraulic pressure

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difference across this ideal membrane and the flux reversal point (FRP) (i.e. equivalent hydraulic

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and osmotic pressures with opposite directions for water transport) was defined by Lee et al. 31.

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This imaginary plot has been adopted for FO in

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pressure-assisted osmosis (PAO) (i.e. identical direction of hydraulic and osmotic pressures for

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water transport) (Figure 1) 32.

182

3

and has been further expanded to embrace

Analyzing the FRP provides a fundamental basis for understanding the true performance



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of FO membranes in association with the coexistence of hydraulic and osmotic pressures, since

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hydraulic pressure is a physical force that can be defined in macroscopic terms upon

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compressibility whereas osmotic pressure, according to S-K, is a resultant of a thought

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experiment due to the unknown presence of perfectly ideal membrane (i.e. no solute transport) 16.

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However, both forms of driving force can lead to flux and shear stress that can also compress the

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membrane. In addition, the nature of the membranes is also questionable because the presence of

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a perfectly non-porous membrane is arguably currently impossible. Thus, should FO membranes

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be categorized as non-porous membranes with inborn flaws when manufactured, an

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understanding the FRP could enable us to quantify the flawlessness (i.e. degree of being non-

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porous) under variations of hydraulic and osmotic pressures in practice.

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Figure 1. Water transport directions in regards of hydraulic pressure in accordance with osmotic

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pressure in an ideally non-porous membrane (adopted and modified from 31, 32)

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Scope. In early studies, the Staverman reflection coefficients of several RO membranes were

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measured under a fixed concentration (i.e. 3.5wt% NaCl) and a fixed hydraulic pressure (i.e.

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1,200 psi or 82.74 bar)

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fabrication in the last decades this should provide improved flawlessness of non-porous

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membranes. Therefore, mapping the vulnerability of recent membranes to hydraulic pressure in

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association with osmotic pressure variations is of due importance in both scientific and practical

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terms. This study accepts the non-porous assumption when no hydraulic pressure is present. The

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responses of FO membranes under the co-presence of the two pressures were critically analyzed.

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The objectives of this study are to 1) validate the theoretical assumptions on the hydraulic and

31

. However considering the technological advancement in membrane



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osmotic pressures postulated to exhibit identical nature and 2) quantify the vulnerability of FO

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membranes to hydraulic pressure in association with osmotic pressure considering the

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membranes as black boxes. It can be hypothesized that, if no water transport is achieved at null-

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pressure condition (i.e. no convective transport and negligible CP), higher solute flux would be

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observed due to higher effective osmotic pressure assuming the membranes are completely non-

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porous according to the fourth assumption of the S-D model and the characteristic diffusion of

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each species (Figure 2). Two cases are specified in our study: Case-I - osmotic pressure as the

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only driving force for water transport when the active layer is facing the feed solution (i.e. NaCl

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solution) and the support layer is facing the DI water, and Case-II - the null-pressure condition

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where osmotic and hydraulic pressures are acting in opposite directions with identical membrane

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configuration in regards of the two solutions. This study is devoted to offer counter-evidence of

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the first and fourth assumptions of the conventional S-D model based on the assumptions that the

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solvent and solute transports are coupled and no CP is present. Based on the validation results of

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the assumptions, a novel membrane characterization method was proposed to quantitatively

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measure the vulnerability of membranes to hydraulic pressure. This work thoroughly considered

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important assumptions of both irreversible thermodynamic models and the conventional S-D

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model to set-up the hypothesis.

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Figure 2. Active layer facing NaCl solution and support layer facing DI water, for which (a)

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Case-I: osmotic pressure difference (∆π) as the only driving force for water transport and (b)

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Case-II : hydraulic pressure (∆P) acting on the opposite direction for water transport against ∆π

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Materials and Methods

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Membranes. CTA-ES membrane was purchased from Hydration Technology Innovations Inc.

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(Albany, OR, USA). The membrane is composed of cellulose triacetate with embedded polyester

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support mesh enveloped by cellulose triacetate. One side of the membrane is thermally treated to

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form active layer when cured. PA-TFC membrane was supplied by Toray Chemical Korea Inc.

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(Seoul, South Korea). The membrane consists of three layers: 1) active layer - polyamide

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coating, 2) intermediate layer – polysulfone and 3) support layer - an embedded polyester

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support mesh embraced by polysulfone.

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Water permeability measurement. The temperature of DI water was controlled at 20°C. A

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single membrane coupon was tested throughout the hydraulic pressure range specified above to

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obtain a set of water permeability coefficients by gradually increasing the hydraulic pressure and

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not exceeding the respective pressure value. The membrane specimen was compacted for 2 h

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using DI water under each designated hydraulic pressure condition (Figure S2). The pressure was

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immediately lowered to one fifth of each designated pressure and volumetric change was

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recorded for 5 minutes and the next higher pressure condition was tested by gradually increasing

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at the identical interval (Figures S3 and S4). In addition, to crosscheck the impact of membrane

250

compaction, initial pressure conditions of the previous tests were inserted (i.e. red dots in Figures

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S3 and S4) within the range of the following measurement (Figure S5). The detailed protocol is

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given in Table S2.

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Results and Discussion

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Water Transport in Case-I. Figure S1 shows the impact of osmotic pressure on water flux in

256

Case-I. CTA-ES membrane yielded relatively linear correlation with osmotic pressure whereas

257

PA-TFC membrane showed a severe non-linearity. The results indicate more severe CP occurred

258

in the PA-TFC membrane above approximately 10 bar of osmotic pressure but not significant

259

enough water flux to cause the non-linearity for the CTA-ES membrane. According to the

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assumptions on the S-D model for completely non-porous asymmetric FO membranes, mass

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transports are governed by the apparent parameters (i.e. water and solute permeability

262

coefficients, namely A and B values). Assuming isothermal conditions and the mass transports at

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equilibrium state follow Henry’s law, a ratio between the water flux and solute flux can be

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defined based on the ratio between the two coefficients

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apparent parameters are lumped-sums of a number of parameters that can be altered depending

266

on the operating conditions as given in Eqs. S2 and S3.

29

as shown in Eq. S1. Nevertheless, the

267

In general, the water permeability coefficient can be considered a pure water

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permeability coefficient since the majority of species transporting through the membranes is

269

water 13, 16. For this reason, in Eq. S2, mole fraction (Cw) and partial molar volume (Vw) of water

270

in the active layer would be imperceptibly dependent on several operating factors, such as solute

271

concentration and hydraulic pressure. In contrast, the active layer thickness (∆x) can be primarily

272

altered by hydraulic pressure that results in the potential increase of active layer thickness due to

273

membrane compaction (i.e. compacted support layer structure arguably acting as additional

274

active layer). The dependence on water concentration can be ignored, yet the impact of

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membrane compaction has not been properly discussed ignoring this potential error. In Eq. S3,

276

the distribution coefficient at equilibrium state (ks) (Eq. S4) defined in


19

exhibits independence


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29, 33-35

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on solute concentration and, in numerous FO simulation studies

, it was presumed to be

278

constant when osmotic pressure is the only driving force. Notwithstanding, as proposed in the

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two modified S-D models after Lonsdale, hydraulic pressure can facilitate solute transport due to

280

bulk flow of water through defects which comes to an analogy that the use of solute

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permeability, not considering the effect of hydraulic pressure, cannot properly accommodate the

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true nature of the distribution coefficient in FO membranes. In addition it is likely that the

283

hydraulic pressure dependence of active layer thickness can also significantly affect the solute

284

permeability. The statements regarding the hydraulic pressure dependence of the two apparent

285

parameters are further elaborated in the later section.

286 287

Water Transport in Case-II. Here applied pressure was set at a value equivalent to the osmotic

288

pressure difference; for the ideal membrane there would be no water flux. By taking the accuracy

289

of the electronic balance into account, any recorded mass change that falls into the range (i.e. 0 ±

290

0.01 g/min) was considered to be null. The equivalent range of volumetric flux is 0 ± 0.32 L/m2h

291

for effective membrane area of 18.75 cm2. As depicted in Figure 3a, the CTA-ES membrane

292

showed a plausible correspondence over the tested range, though the data set projected a slowly

293

increasing trend of noticeable significance within the error range of the electronic balance.

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However in the case of PA-TFC membrane (Figure 3b), all values significantly deviated from

295

the error range implying the membrane is significantly more vulnerable to hydraulic pressure

296

than the CTA-ES membrane. In all, higher impact of hydraulic pressure as opposed to osmotic

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pressure was observed for both membranes. Such incremental impact with increasing hydraulic

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pressure directly suggests a relation with structural integrity of a membrane, which will be

299

further elaborated in the following sections.


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301 302

Figure 3. Volumetric fluxes under null-pressure condition for (a) CTA-ES membrane and (b)

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PA-TFC membrane with relevant standard deviations (SDs)

304 305

To achieve the null-flux condition, the hydraulic pressures were manually adjusted to the

306

specified values given in Figure 4a and within the range are the volumetric fluxes of modified

307

hydraulic pressures for the PA-TFC membrane given in Figure 4b. This leads to the important

308

question of how much flawlessness (i.e. ability to behave as non-porous membrane) do these

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membranes exhibit in regards to hydraulic and osmotic pressures. The two membranes

310

unanimously showed increasing volumetric flux trend with increasing null-pressure condition,

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yet to a negligible degree in CTA-ES. Since hydraulic pressure is a physical force directly

312

affecting the integrity of the membranes, mechanical stability can play a major role in

313

determining the response to hydraulic pressure. Such change is in correspondence with solute

314

transports since water and solute transports are coupled. Thus, to quantitatively assess the

315

flawlessness, it is necessary to assess the solute fluxes for a thorough analysis.

316



317 318

Figure 4. (a) Hydraulic pressures manually adjusted to achieve null-flux condition for PA-TFC

319

and (b) the corresponding volumetric fluxes within the error range along with corresponding SDs

320 321

Comparison of Solute Transport between Case-I and Case-II. If the membranes behave as

322

perfectly semi-permeable barriers, solute flux should increase due to the maximum effective

323

osmotic gradient according to the fourth assumption of the S-D model as given in Case-II. As

324

illustrated in Figure 5a, the CTA-ES membrane seemingly corresponds well to the initial

325

hypothesis. It is intriguing to note the solute flux increment (i.e. Js,Case-II / Js,Case-I) gradually

326

increased with increasing feed concentration yet in an asymptotically approaching manner to

327

approximately two fold (Figure 5b). Such trend can be interpreted by the following explanation.

328

In the perspective of the conventional S-D model, CP phenomenon associated with the water

329

transport in Case-I would become more significant as feed concentration increased. In Case-II,

330

the negligible water transport in Case-II induced infinitesimally low CP thereby maximizing the

331

concentration gradient across the active layer, consequently resulting in the observed trend.

332

However, this explanation is valid only when the membrane is perfectly non-porous, thus the

333

degree of flawlessness should be assessed. Properly accounting Eq. S4, if the solute fluxes

334

perfectly correspond to the diffusion theory in Case-II, a thick straight line in Figure 5c can be 18 ACS Paragon Plus Environment

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drawn based on the assumption that the membrane-specific distribution coefficient is constant.

336

Real membranes are far from ideal ones and a discrepancy (dotted curve) can be observed. The

337

reasons for such deviation can be originated from the presence of hydraulic pressure, which

338

causes 1) facilitated transport of solute species and 2) membrane compaction. Considering the

339

volumetric flux decline of the CTA-ES in time-function in Figure S2a, it can be stated the

340

hydraulic pressure compresses the membrane structure and potentially increase the effective

341

thickness of the active layer. Nevertheless, the effect of membrane compaction is not severe for

342

CTA-ES considering the relative consistency, thus deemed a minor reason. Hence, it can be

343

arguably said that the hydraulic pressure more significantly affects the facilitated solute transport

344

through the membrane and consequently alters the distribution coefficient. This is directly

345

indicative to the fact that, by definition, solute permeability coefficient (i.e. B value) is also

346

changing in the perspective of conventional solution-diffusion theory (i.e. Eq. S3).

347

In contrast, the drastic increase of volumetric flux through the PA-TFC when under the

348

null-pressure condition raised a necessity to reduce the hydraulic pressure to acquire the null-flux

349

(Figure 4), thereby depress the presence of CP in the vicinity of the active layer. The results

350

presented in Figure 5d at low concentration range do not follow the initial hypothesis (i.e. solute

351

flux increment < 1 in Figure 5e); this addresses an important finding that the theoretical concept

352

of the conventional S-D model regarding the enhanced effective osmotic pressure at which no CP

353

is present is invalid. The discrepancy in Figure 5f was more significant than that of CTA-ES

354

which supports the statement that the PA-TFC membrane is more vulnerable to hydraulic

355

pressure. More drastic volumetric flux decline of the PA-TFC in Figure S2b indicates the

356

membrane underwent severer deformation compared to the CTA-ES, leading to the active

357

participation of membrane deformation in causing the severer discrepancy along with the



358

facilitated solute transport for the PA-TFC. Hydraulic pressure was equivalent to osmotic

359

pressure in null-pressure condition whereas hydraulic pressure was lower than the osmotic

360

pressure in null-flux condition. As depicted in Figure S7, the difference of solute flux between

361

the two conditions became incrementally significant and this indirectly supports the statement

362

that hydraulic pressure alters distribution coefficient, thereby affecting the solute permeability

363

(i.e. Eq. S3). More importantly, solute permeability cannot be solely explained by the solution-

364

diffusion theory only. In sum, the discrepancies shown in Figures 5c and 5f for the two

365

membranes indicate that solute permeability coefficient (B) assumed in the conventional S-D

366

model is in fact dependent on hydraulic pressure when both hydraulic and osmotic driving forces

367

actively engage in determining the membrane performance. This statement is further elaborated

368

in the following section.

369


Page 20 of 39

Page 21 of 39


370 371

Figure 5. (a) Solute fluxes (Js), (b) solute flux increment ratio (Js/s = Js,Case-II / Js,Case-I) and (c)

372

non-linear regression of Js,Case-II under null-flux condition for CTA-ES and (d), (e), (f) for PA-

373

TFC

374 375

Irreversible Thermodynamic Assessment. Onsager reciprocal theorem is the stepping stone of

376

irreversible thermodynamic transport models such as K-K and S-K. Staverman interpreted the

377

theorem as the following: “this theory results in a relation between the influence of parameters

378

describing the deviation of a system from equilibrium upon each other’s rate of change” 15. For a

379

system composed of two solutions separated by a membrane, the volumetric and solute transport

380

rates determine the deviation from the equilibrium state (i.e no mass transport). This enables the

381

coupling of the two transport identities as had previously been discussed by K-K

382

fluxes interact with each other, thereby a set of phenomenological coefficients can be specified


13

; the two


Page 22 of 39

383

for hydraulic and osmotic driving forces and a coefficient represents the reciprocal relation

384

between them. Based on Eqs. S5 and S6, Eqs. S7 and S8 can be derived to assess the two fluxes

385

bound to the reciprocal relation given in Eq. S9

386

phenomenological relation can be drawn as shown in Eqs. S11. According to the reciprocity (Eq.

387

S9), the relative velocity of solute to solvent (JD) (Eq. 1) can be equated by introducing Eq. S10

388

and S11 to S8. For entropy production being always positive, Eq. S12 should be met according to

389

the irreversible thermodynamic assumption 13.

13

. For the null-flux condition, since Jv = 0, a

390 391

= −

,

∆ = − ∆

(1)

392 393

Normalizing the solute fluxes in Figures 5a and 5d with respective feed concentration yields the

394

relative velocity of solute through the membranes under the null-flux condition. By plotting the

395

relative solute velocities with respect to osmotic pressure, phenomenological 1st-order

396

polynomial relations can be drawn (Figure 6). The steeper slope of the PA-TFC compared with

397

the CTA-ES once again confirms the higher vulnerability of the PA-TFC to hydraulic pressure

398

as discussed in the earlier section. Here, we define the slopes as membrane-specific vulnerability

399

coefficients (λ); λ is a measure of susceptibility of a membrane against hydraulic pressure under

400

null-pressure or null-flux condition. This susceptibility is determined by the structural

401

characteristics of the whole membrane (not necessarily the support layer only) responsible for

402

solute transport. The CTA-ES membrane showed higher modulus of elasticity (i.e. Young’s

403

modulus) than PA-TFC membrane as reported in our previous work

404

TFC membrane is mechanically less stable thereby the structural integrity is more susceptible to

405

change upon employing hydraulic pressure. As such, mass transports can be altered due to the 22 ACS Paragon Plus Environment

21

. This indicates the PA-

Page 23 of 39


406

change of mechanical properties of membranes in association with hydraulic pressure. Prior to

407

explain the linear relation, assessment of the volumetric transport coefficient (LP) is required due

408

to its active participation on solute transport.

409

410 411

Figure 6. A phenomenological 1st-order relation of relative solute velocity (JD) with variations

412

of ∆π

413 414

The water permeability coefficient (A) has so far been measured employing hydraulic

415

pressure-driven apparatus to represent the water permeability of FO membranes in numerous

416

studies. Despite the arguable assumption stating that the hydraulic and osmotic pressures exhibit

417

identical nature in non-porous FO membranes, the measured values were widely adopted to

418

estimate the water transport when osmotic pressure is the only driving force. However, the

419

reported water permeability coefficients of the CTA-ES membrane were found to be in a wide 23 ACS Paragon Plus Environment


420

variation (Table S1) since the water permeability is primarily dependent on membrane

421

compaction duration and the range of applied hydraulic pressure. Here, we report the impact of

422

hydraulic pressure range on water permeability due to its paramount importance to mass

423

transport. As shown in Figure 7, asymptotically decaying trends of water permeability (i.e. A

424

value), derived from the results in Figures S3 and S4, were found for the two membranes, from

425

which the degree of membrane compaction (i.e. structural change resulting in the increase of

426

membrane density) caused increase of structural resistance to water transport. Being a less rigid

427

body, the PA-TFC membrane showed more severe non-linearity as opposed to the CTA-ES. Even

428

under the same hydraulic pressure, the degree of membrane compaction negatively affects the

429

water permeation (Figure S5). These results clearly disprove the plausibility of implementing the

430

water permeability coefficients obtained based on hydraulic pressure variations for estimating the

431

performances of FO membrane processes when osmotic pressure is the only driving force.

432

Hence, the membrane performance is primarily dependent on the structural resistance induced by

433

hydraulic pressure when osmotic and hydraulic pressures are participating as active driving

434

forces. At this point, considering the assumption that solvent and solute transports are coupled, a

435

proper phenomenological consideration is necessary to estimate the hydraulic pressure

436

dependence of solute transport (i.e. facilitated solute transport) under the null-flux condition (i.e.

437

adjusted hydraulic pressures), for which the above linear relations are in correspondence.

438


Page 24 of 39

Page 25 of 39


439 440

Figure 7. Decaying water permeability coefficients (A) due to membrane compaction caused by

441

hydraulic pressure

442 443

If the linear relations are valid, solute permeability coefficients measured using the

444

conventional method (i.e. hydraulic pressure-based) must correspond to the relations. The solute

445

permeability coefficients of the two membranes reported in

446

to represent the concentration range below the testing range of this study (i.e. 0.06 – 0.357 M

447

NaCl)) are in fairly good agreement with the estimated values from the regression plot (i.e.

448

yellow dots). Slight deviations from the estimated values possibly originated from the compacted

449

membrane structure at 10 bar in the previous study. This suggests the solute permeability at 0 bar

450

of hydraulic pressure can be empirically estimated (i.e. the point of intersection between the

21


(e.g. 0.034 M (2,000 mg/L) NaCl


Page 26 of 39

451

regression plot and the y-axis in which no membrane deformation is guaranteed) testing under a

452

wide range of hydraulic and osmotic pressures. Let these two points represent the solute

453

permeability coefficients of the non-deformed CTA-ES and PA-TFC membranes (i.e. B values

454

for the conventional S-D model). To a good approximation, volumetric flux is considered to be

455

identical to water flux since the majority of the species preferentially transported through the

456

membrane is water as discussed in the earlier section for Case-I. This enables use of the

457

volumetric transport coefficient (LP) representing the measured water permeability coefficients in

458

Figure 7. Note the LP values were calculated using the equation for the regression plots in Figure

459

7 for the adjusted pressure conditions (i.e. specified in Figure 4a with blue bars) since the linear

460

relations shown in Figure 6 are only valid under the null-flux condition, not the null-pressure

461

condition. For ∆π > 0, the following relation (Eq. 2) can be established and rearranged with

462

respect to λ (Eq. 3) since the term on the left-hand side in Eq. 2 is derived based on the

463

irreversible thermodynamic theory to explain the overall transport phenomena.

464 465

− ∆ = + ∆

466

= − −

(2)

(3)

∆

467 468

Since LP varies depending on membrane structure deformation due to hydraulic pressure, with

469

constant λ, any coupled variation of hydraulic and osmotic pressures (i.e. LP, σ, ∆P and ∆π) for

470

the null-flux condition alters LD. From the regression plot in Figure 7, estimated LP values for the

471

hydraulic pressures that correspond to σ (i.e. adjusted hydraulic pressures) can be obtained.

472

Under the null-flux condition (i.e. Jv = 0), the Staverman reflection coefficients (σ) for respective

473

null-flux condition can be obtained (Figure S6) following the definition given in Eq. S10, which


Page 27 of 39


474

incorporates the adjusted hydraulic pressures in Figure 4a. Only the reflection coefficients for the

475

PA-TFC membrane were obtained, since the CTA-ES membrane showed volumetric fluxes

476

falling into the error range along with the fluctuation of the hydraulic pressure induced by the

477

rotation of the feed pump head given in the SI (i.e. ± 0.025 bar). Considering these limitations,

478

the CTA-ES membrane was considered to be effectively a non-porous membrane with non-

479

quantifiable flaws (i.e. σ ≒ 1 and < 1) in the following analyses.

480

481 482

Figure 8. Membrane specific characteristics of the CTA-ES membrane on inter-dependence: (a)

483

Variations of LD within the operating range of ∆π, (b) impact of inter-dependence represented by

484

σ2 on Js,Case-II and (c) variations of LPD with respect to σ and (d), (e), (f) for the PA-TFC

485

membrane. (f) Depicts the governing transport mechanism shift from diffusive transport to

486

convective transport 27 ACS Paragon Plus Environment


487 488

Figures 8a and 8d depict the variations of LD with respect to osmotic pressure of the two

489

membranes. LD represents the ability of a membrane to utilize osmotic pressure for solute

490

transport. For a perfectly non-porous membrane (i.e. σ = 1), hydraulic and osmotic pressures

491

equally engage in the solute transport, thus λ = 0. In addition, if no membrane deformation can

492

be guaranteed even with the presence of hydraulic pressure (i.e. strictly rigid body, where

493

Young’s modulus = ∞), LD can be determined by ∆π alone with a fixed LP of a non-deformed

494

membrane (i.e. the estimated true A values in Figure 7). Taking these characteristics into account,

495

the CTA-ES membrane is more likely to efficiently accommodate the diffusive driving force for

496

solute transport regardless of hydraulic and osmotic pressure variations. On the other hand, a

497

deviation from the ideal behavior was noticed for the PA-TFC in between 5 and 7.5 bar of

498

osmotic pressure, and a rapid transport mechanisms transition was suspected. To elucidate the

499

suspected transition, understanding the reciprocal coefficients (i.e. LPD or LDP) offers possible

500

clues. To see the impact of the reciprocal coefficients in association with LP on solute flux under

501

the null-flux condition, the solute fluxes were re-plotted with respect to σ2. For the CTA-ES

502

membrane (Figure 8b), only the presence of flaws could be identified considering the volumetric

503

flux variations in Figure 3a within the experimental limitations stated above, yet the results for

504

the PA-TFC membrane offered clearer clues on the suspected shift. Referring to the adjusted

505

hydraulic pressures in Figure 4a, an abrupt transition occurred between 4.95 and 7 bar for the

506

PA-TFC (Figure 8e). These results indicate that, with increasing hydraulic pressure, the structural

507

integrity of this membrane reached to a yield point at approximately 5 bar and completely lost its

508

ability to act as a quasi non-porous membrane. Here, we can define the yield point as yield

509

hydraulic pressure (∆Pyield) of the membrane. This means the change of inter-dependence


Page 28 of 39

Page 29 of 39


510

between Jv and JD significantly deviated from the fairly non-porous state at ∆Pyield. As

511

comprehensively given in

512

hydraulic and osmotic driving forces to affect the Jv and JD. To put it more precisely, within the

513

operating conditions of this study, osmotic pressure induces volumetric transport and hydraulic

514

pressure depresses the solute transport for an ideal membrane, hence the solute rejection

515

increases. For porous membranes, the two driving forces cannot actively generate the effects (i.e.

516

reduction of σ). Similarly, from Figure 3a, presumption of the non-quantifiable variations of σ at

517

one-thousandth interval (Figure 8c) implies what is genuinely occurring in the ideal membrane

518

under the co-presence of hydraulic and osmotic pressures. The trend of the solute flux increments

519

in Figure 5b is in clear correspondence with the anticipated results. It is intriguing to note, upon

520

employing hydraulic pressure, the inter-dependence can be slightly deteriorated, though it

521

converges into a relatively consistent value in association with the feed concentration, yet in an

522

asymptotically increasing manner. Higher negativity of LPD means higher inter-dependence

523

between Jv and JD. This suggests the initial behavior of FO membranes experiencing deformation

524

by hydraulic pressure associated with feed concentration variations. Note the results in Figure 8c

525

were derived only to help understand the response of ideally non-porous membranes, which still

526

needs validation by more accurate and sophisticated measurements.

13

, the inter-dependence, in the physical meaning, is the ability of

527

Meanwhile, the PA-TFC membrane can explain the overall response of real membranes

528

due to the severer vulnerability to hydraulic pressure. An analogous analysis on the PA-TFC

529

membrane was conducted in Figure 8f. Upon presumably reaching a condition at which the PA-

530

TFC no longer acts as an ideally non-porous membrane with increasing hydraulic and osmotic

531

pressures corresponding to null-flux (i.e. the point starting to show relative inconsistency in LPD

532

at σ ≒ 1 and < 1), active engagement of convection takes place along with diffusion and the



533

initiation of severe alteration of LPD can be observed. It is important to note, even with small

534

amounts of hydraulic pressure changes, the inter-dependence was significantly deteriorated until

535

it approaches to a critical level. Here, the yield reflection coefficient (σyield) can be defined. Upon

536

reaching σyield, any hydraulic pressure above ∆Pyield leads to an important statement that the

537

membranes starting to show noticeable independence between Jv and JD in association with

538

hydraulic and osmotic pressures, is likely to behave as a porous membrane. In scientific

539

perspective, diffusive transport governs when the membranes are non-deformed, yet, upon

540

introduction of hydraulic pressure, a rapid engagement of hydraulic pressure depresses solute

541

transport until the membrane-specific limits are reached; above the critical point, convective

542

transport becomes dominant. Similarly, it can be postulated that if pressures are continuously

543

increased, such a trend of abrupt governing transport mechanism shift would also be found in the

544

CTA-ES at a specific σ, although this was not observed within the operating range of this study.

545

Nevertheless, the responses of the two membranes under lower null-pressure conditions

546

than 2.5 bar still needs more sophisticated elucidation. In addition, the second and third

547

assumptions of the S-D model (i.e. the assumptions on uncoupled solvent and solute transports

548

stating no interactions among species and no solvent-solute-membrane interactions) could not be

549

investigated, since the membranes were considered as black boxes, assuming coupled solvent

550

and solute transport and embodied solvent-solute-membrane interactions in the results of this

551

study. Studying charge characteristics and hydrophilic/hydrophobic interactions would deepen

552

the understanding in future studies.

553

In retrospect, it is virtually impossible to measure the true water and solute permeability

554

coefficients of non-deformed FO membranes for them to be implemented in S-D models, since

555

these parameters require driving forces when defined. To be more clear, the Fick’s law, the


Page 30 of 39

Page 31 of 39


556

fundamental basis of the conventional S-D model, assumes the presence of a concentration

557

gradient of respective species across the membrane 36. When hydraulic and osmotic pressures co-

558

exist, chemical potential includes the two driving forces and the water transport is assumed to

559

follow Henry’s law coupled with the non-porous active layer assumption. These theoretical

560

backgrounds are only valid when the membranes are non-deformed. In this regard, hydraulic

561

pressure is the source of membrane deformation and causes deviation from the true values, thus

562

any permeability coefficients obtained by employing hydraulic pressure are apparent and

563

potentially not intrinsic. Hence, it can be concluded that previously reported parameters and the

564

relevant fluxes estimated by the S-D models are prone to errors. It could be claimed that use of

565

sufficiently low hydraulic pressure, such as 1.5 bar, as used in 37, would minimize errors but this

566

is a membrane-specific assumption.

567

The impact of hydraulic pressure on pore size of the active layer has not yet been fully

568

elucidated. There still is a possibility of membrane shrinkage or enlargement at low enough

569

hydraulic pressure, which can be suspected as membrane specific. However, based on the results

570

of this study, it can be hypothesized that the pores (or defects) can be enlarged resulting in the

571

increased solute flux under high enough hydraulic pressure as observed in this study.

572

Nevertheless, the true permeability coefficients of non-deformed membranes can be estimated by

573

thoroughly considering the deviations due to hydraulic pressure, thereby achieving improved

574

accuracy.

575

The true natures of hydraulic and osmotic pressures still remain unanswered, though a

576

certain degree of understanding was achieved in regards to FO membrane performance.

577

According to the results in Figures 3 - 6, the mass transports cannot be explained solely by

578

diffusion and this leads to a conclusion that the initial hypothesis of the SD model should be



579

denied. Thus, the results disprove the fundamental assumption of the identical nature of

580

hydraulic and osmotic pressures in regards to estimating the performance of FO membranes with

581

flaws. Upon experiencing deformation due to hydraulic pressure, a governing transport

582

mechanism shift from diffusive to convective can occur. The yield hydraulic pressure (∆Pyield)

583

and yield reflection coefficient (σyield) quantitatively restrict the operating hydraulic pressure

584

range that is membrane specific based on the vulnerability coefficient (λ). Accordingly, water and

585

solute permeability coefficients (i.e. A and B) can vary depending on the hydraulic pressure

586

imposed and the true values can be empirically estimated by testing them under a range of

587

operating hydraulic and osmotic pressures; though, this statement requires further validation.

588

Also, from the S-D model assumptions, hydraulic pressure gradient is assumed to be constant

589

across a semi-permeable membrane while solvent activity linearly changes with respect to

590

distance (i.e. active layer thickness); vice versa for the pore-flow model. One can draw pressure

591

profiles across the membrane by considering the two models to explain the responses of this

592

study. However, this does not have any scientific values since no evidence can support such

593

argument at this stage. It is primarily because the assumptions on pressure profiles across a semi-

594

permeable membrane in the conventional S-D theory have not yet been experimentally validated

595

and same for the pore flow theory, neither.

596

Conclusively, the membrane characterization method suggested in this work is able to

597

quantitatively measure the vulnerability of FO membranes to hydraulic pressure based on

598

irreversible thermodynamic assessment. This method can be employed to characterizing FO

599

membranes and, in practice provides information on the acceptable operating hydraulic pressure

600

range. Specifically, when spiral-wound FO membrane elements are serially connected, a more

601

severe pressure build-up at the feed inlet of the lead element can be expected. The membrane-


Page 32 of 39

Page 33 of 39


602

specific limits obtained by the method suggested in this study can be employed to determine the

603

maximum number of serially connected elements guaranteeing their ability to act as effective

604

solute rejecting barriers. In addition, any membranes categorized as non-porous but with

605

unknown flaws in a water-treatment scheme, RO membranes for instance, can be subject to test.

606 607

ASSOCIATED CONTENT

608

Supporting Information

609

Supporting details and methods; important aspects of the conventional S-D model for FO;

610

irreversible thermodynamic theory; osmotic pressure measurement; volumetric flux variation in

611

Case-I; water mass permeation rates during membrane compaction; water permeability

612

coefficients after membrane compaction; water permeability measurement protocol; summary of

613

previously reported water permeability of CTA-ES; Staverman reflection coefficient of PA-TFC;

614

experimental set-up and operating conditions

615 616

ACKNOWLEDGEMENTS. This research was supported by a grant (code 17IFIP-B087389-

617

04) from Industrial Facilities & Infrastructure Research Program funded by Ministry of Land,

618

Infrastructure and Transport of Korean government.

619 620



621

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