Environ. Sci. Technol. 2009, 43, 6769–6775
Solute Coupled Diffusion in
Osmotically Driven Membrane
Processes
NATHAN T. HANCOCK AND
TZAHI Y. CATH*
Division of Environmental Science and Engineering, Colorado
School of Mines, Golden, Colorado 80401
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Publication Date (Web): July 29, 2009 | doi: 10.1021/es901132x
Received April 18, 2009. Revised manuscript received July
10, 2009. Accepted July 13, 2009.
Forward osmosis (FO) is an emerging water treatment
technology with potential applications in desalination and
wastewater reclamation. In FO, water is extracted from a feed
solution using the high osmotic pressure of a hypertonic
solution that flows on the opposite side of a semipermeable
membrane; however, solutes diffuse simultaneously through the
membrane in both directions and may jeopardize the process.
In this study, we have comprehensively explored the effects
of different operating conditions on the forward diffusion of solutes
commonly found in brackish water and seawater, and
reverse diffusion of common draw solution solutes. Results
show that reverse transport of solutes through commercially
available FO membranes range between 80 mg to nearly 3,000
mg per liter of water produced. Divalent feed solutes have
low permeation rates (less than 1 mmol/m2-hr) while monovalent
ions and uncharged solutes exhibit higher permeation.
Findings have significant implications on the performance and
sustainability of the FO process.
Introduction
Membrane processes such as reverse osmosis (RO) are
widely used in water treatment. RO membranes can reject
most constituents present in impaired water, but they can
achieve only moderate water recovery (1). RO has additional limitations, including high propensity to fouling
and scaling due to the presence of dissolved organic matter
and sparingly soluble salts in feed streams (2). Osmotically
driven membrane processes, such as forward osmosis (FO),
may address these deficiencies by taking advantage of
energy and transport characteristics unique to this process
(3-5); these include high solute rejection, low-pressure
operation, and low fouling propensity (5-7) that can assist
RO in achieving higher water recoveries. Studies have
identified FO as a potential process for purification of
industrial and domestic wastewater (3, 7-9). Novel FO
membrane bioreactors have been studied for wastewater
reclamation (10), and FO is being investigated for desalination of seawater (11) and brackish groundwater (4).
Osmosis is the spontaneous diffusion of water through a
semipermeable membrane from a feed solution of higher
water chemical potential (lower osmotic pressure) to a draw
solution (DS) of lower water chemical potential (higher
osmotic pressure) (12). During this process, the feed solution
is concentrated and the draw solution is diluted. To produce
* Corresponding author phone: 303-273-3402; fax: 303-273-3413;
e-mail: tcath@mines.edu.
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 2009 American Chemical Society
purified water and sustain driving force in the FO process,
continuous reconcentration of the DS by RO or distillation
is required. Although increasing entropy of the system by
dilution is thermodynamically unfavorable, specific applications may realize net benefits in terms of system performance
and operating cost (5, 13).
While the unique characteristics of FO make it an attractive
process for pretreatment of impaired water before treatment
with RO or distillation, FO is not without limitations, many
of which result from insufficient development and optimization of existing FO membranes and DSs. Low water fluxes
despite high driving force is one drawback of currently used
FO membranes (14); yet, solute diffusion from the DS into
the feed, and vice versa, may pose greater limitation on future
implementation of FO and other osmotic processes.
Solvent Transport. Intensive research has focused on the
effects of concentration polarization (CP) on the nonlinearity
of solvent (water) transport in FO (11, 14-16). CP is mostly
known in pressure-driven membrane processes where a
concentrationboundarylayerdevelopsonthemembrane-feed
interface because of the preferential diffusion of water
through the membrane (concentrative CP). In FO, both
dilutive internal CP in the membrane porous support layer
and external CP at the membrane-DS interface have the
strongest effect on diminishing water flux (more in Supporting Information S1) (5). Solute diffusion is considered to
have negligible effects on water flux; however, its ramifications on system optimization and environmental impact must
be considered.
Solute Transport: Bidirectional Diffusion in FO. The flux
of an individual solute (Js) through semipermeable membranes is governed by chemical potential gradients and is
commonly described using Fick’s Law (17):
Js ) B∆c
(1)
where B is the solute permeability coefficient and ∆c is the
trans-membrane concentration differential (18). In RO,
solutes diffuse from the feed into the permeate; however, in
FO, solutes diffuse in two directions: from the feed into the
DS (i.e., forward diffusion) and simultaneously from the DS
into the feed (i.e., reverse diffusion). Reverse diffusion is
different from back diffusion which is a the result of CP
phenomena in the feed-membrane boundary layer (17, 19).
Reverse and forward diffusion are the focus of the current
study.
During DS reconcentration cycles, solute diffusion through
the FO membrane may jeopardize a combined FO/RO or
FO/distillation system. Ions that codiffuse with water into
the DS may accumulate in the reconcentration process, and
those that have low solubility may precipitate and adversely
affect the performance of the hybrid process. Scale inhibitors
could be added to the DS, but will increase operating costs.
Solutes lost through reverse diffusion require replenishment
of the DS, and accumulation of DS solutes in the feed may
pose toxicological challenges for sensitive receiving environments or prove detrimental for adjacent treatment processes.
To optimize osmotic processes, a closer investigation of
solute transport phenomena is essential. To a first order
approximation, the literature asserts that salt transport across
the membrane is governed by the concentration differential
of each individual solute (17). This suggests that while the
cumulative concentrations of various solutes affect the
osmotic pressure, and therefore the water flux, only the concentration gradient of a particular solute will influence the
flux of that solute across the membrane as expected from
eq 1.
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Also, eq 1 may be acceptable for dilute solutions; however,
early theoretical studies (20, 21) used an irreversible thermodynamic framework to deduce that for RO, diffusion of
solutes occurs through both diffusion and convective transport originating from coupled effects associated with solvent
diffusion. This understanding provides a second level approximation for a binary system, in which solute flux (Js)
through a semipermeable membrane occurs in the same
direction as water flux, and can be represented by the
convective-diffusion equation:
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Js ) ω∆π + (1 - σ)Jvjc
(2)
where the first product represents diffusive mass transport
with ω being the membrane’s solute permeability coefficient,
and the second term represents convective mass transport,
where Jv is the water flux, jc is the average interfacial solute
concentration gradient between the feed and permeate sides,
and σ is the reflection coefficient defined as the ratio between
the negative solute-water phenomenological coefficient
divided by the pure water permeability (12). Although eq 2
is limited in its application for modeling of FO processes,
especially in mixed electrolyte solutions, it serves to emphasize the complex coupled nature of mass transport in
FO. Donnan equilibrium effects are one consequence of
coupled diffusion (22), and other unique characteristics of
solute diffusion in membrane processes are summarized
elsewhere (23).
The main objective of this study was to investigate
bidirectional mass transport of solutes in forward osmosis
of pure and mixed electrolyte solutions, with different draw
solutions, under various operating conditions, and with
currently available FO membranes. Specifically, the effects
of solution chemistry, membrane morphology, and hydrodynamic conditions on mass transport were investigated.
Solute coupled diffusion in osmotically driven membrane
processes requires further exploration before FO processes
can achieve broad acceptance and commercialization for
treatment of impaired water. The coupled nature of both
solvent-solute and solute-solute mass transport during FO
introduces a new level of intricacy that has not been explored
before.
Materials and Methods
FO Membranes. Cellulose acetate membranes are well suited
for use in osmotically driven membrane processes (5, 7, 24).
Two flat-sheet cellulose triacetate (CTA) membranes, specifically developed for FO by HTI (Albany, OR), were tested in
this study. The membranes are entitled CTA-1 and CTA-2;
CTA-1 is the less permeable and more selective of the two.
During all experiments, the membranes were oriented
with their active layer facing the feed. To maintain high quality
assurance and control, membrane integrity tests were
performed at the beginning and end of every set of experiments. Additional information is available in Supporting
Information S2.
FO Bench-Scale Apparatus. FO flow cells were constructed with symmetric flow chambers on both sides of the
membrane that facilitated parallel, cocurrent flow along the
membrane. A supervisory control and data acquisition
(SCADA) system was developed to maintain constant experimental conditions (i.e., feed volume, DS conductivity,
system temperature of 18 °C) and to collect data during
experiments. Feed and DS were continuously circulated
between their respective tanks and the membrane cell at 1.6
L/min using gear pumps (Cole-Parmer, Vernon Hills, IL) and
feed and DS samples were intermittently drawn for analysis.
A flow schematic and description of the system is provided
in Supporting Information S3.
Solution Chemistries. Salts and other chemicals used in
the experiments were all ACS grade and solutions were
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prepared in deionized water. Complete description is provided in Supporting Information S4.
Experimental Procedures
NaCl and MgCl2 Reverse Diffusion Characterization. The
effects of osmotic driving force on forward diffusion of water
and reverse diffusion of DS salts were investigated. Both
membranes were tested with deionized feedwater and DS
concentrations that ranged from 0.34 M NaCl to saturation.
The CTA-2 membrane was also tested with MgCl2 DS having
osmotic pressures similar to NaCl experiments (excluding
NaCl saturation). Each experiment was terminated after 1-2
h of steady reverse diffusion. See Supporting Information S5
for details on mass transfer calculations.
NaCl, MgCl2, and NH4HCO3 Specific Reverse Salt Flux.
Specific reverse salt flux (Jspecific) is defined here as the ratio
of salt flux (Js (mg/m2-hr)) in the reverse direction and water
flux (Jw (L/m2-hr)) in the forward direction, and is related to
the water-salt selectivity of the membrane. This quantity is
directly related to process efficiency and sustainability.
Specific reverse salt flux was quantified through experiments with three DSs at different concentrations, with
deionized water feed, and with the two FO membranes. The
concentrations of all DS were adjusted to have an osmotic
pressure of 4 MPa. NaCl and MgCl2 DSs were also tested at
an osmotic pressure of 1.9 MPa (constant concentrations of
0.43 and 0.86 M for NaCl, and 0.29 and 0.57 M for MgCl2).
NH4HCO3 DS was tested at one concentration (1.02 M). See
Supporting Information S5 for mass transfer calculations and
S6 for more details on experimental procedures.
Coupled, Multicomponent Diffusion Experiments. Feed
solutions composed of a single salt each were employed to
elucidate the influence of various chemical potential gradients on the forward and reverse diffusion of individual
chemical species. Feed solutions were prepared with concentrations of either 1 or 2 g/L as the feed solution salt (CaSO4,
K2SO4, MgSO4, Ba(NO3)2, or NH4HCO3) or as the target ion
(H3BO3-B or Na2SiO3-SiO2). Experiments with the CTA-1
membrane were conducted with select feed solution salts,
and included 1 or 2 g/L of CaSO4, NH4HCO3, or Na2SiO3-SiO2.
Each feed solution was tested with two different DS concentrations of 25 or 50 g/L NaCl.
Tests were also conducted with synthetic brackish water
feed solution (3.85 g/L MgCl2 · 6H2O, 5.13 g/L CaCl2 · 2H2O,
2.55 g/L Na2SiO3 · 9H2O, 2.7 g/L Na2SO4, and 18 mM HCl)
utilizing CTA-2. Experiments with NaCl and MgCl2 DSs were
conducted with two different concentrations leading to
osmotic pressures of 1.9 and 4 MPa, while an experiment
with NH4HCO3 DS was conducted with one concentration,
resulting in an average osmotic pressure of 4 MPa. More
details are available in Supporting Information S5 and S6.
Effect of Crossflow Velocity on the Reverse Diffusion of
NaCl. Reverse diffusion of NaCl was investigated under
different feed (deionized water) and DS (50 g/L) crossflow
velocities (37, 75, and 112 cm/s). Nine experiments were
conducted with all combinations of flow velocities on both
sides of the membrane. Reverse solute flux was calculated
with the same method used in the NaCl and MgCl2 reverse
diffusion experiments. Pressures and temperatures were
maintained constant.
Analytical Procedures. Samples were analyzed for cation
concentrations using inductively coupled plasma (Optima
3000, Perkin-Elmer, Fremont, CA) and for anion concentrations using ion chromatography (ICS-90, Dionex, Sunnyvale,
CA). Samples containing ammonium were analyzed using
Hach spectrophotometer method 10031. Samples containing
bicarbonate were analyzed using titration method 8203
(model 16900, Hach, Loveland, CO) with either 0.1 or 0.01
M H2SO4 solution. More details are available in Supporting
Information S6.
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Results and Discussion
NaCl and MgCl2 DSs: Water and Reverse Salt Fluxes. Water
flux and reverse salt flux as a function of DS osmotic pressure
are illustrated in Figure 1a for experiments conducted with
NaCl DS and with the CTA-1 and CTA-2 membranes. Results
indicate that water flux and NaCl reverse diffusion increase
with increasing DS concentration. The higher values observed
for the CTA-2 confirm that this membrane is less selective
and more permeable compared to the CTA-1; water flux was
37-48% higher and reverse salt flux was 62-72% higher
through the CTA-2 than through the CTA-1.
As observed in this and past studies (14, 19), a logarithmic
relationship exists in FO between water flux and driving force,
and because the current experiments were conducted with
deionized feedwater, this behavior is primarily the result of
internal CP. Data in Figure 1a also indicate that internal CP
affects reverse salt flux. When the diffusing water dilutes the
DS in the porous support layer, the salt concentration
differential is also reduced. Equations 1 and 2 predict that
a reduction in concentration differential will result in reduced
salt diffusion. Due to charge balance restrictions in the feed
solution, we assumed that both anions and cations reverse
diffused equally on a molar-equivalent basis. This assumption
was further explored and discussed below.
A second set of experiments was conducted with the CTA-2
membrane using MgCl2 DS and deionized water feed. MgCl2
concentrations were adjusted to have osmotic pressure
(theoretical driving force) similar to the DSs used in the NaCl
experiments. Water flux and reverse salt flux as a function
of the bulk DS osmotic pressure are shown in Figure 1b.
Despite the similar osmotic pressures of the two DS, it can
be seen that MgCl2 is a weaker DS; compared to results with
NaCl DS, water flux was 25-30% lower when using MgCl2.
However, in terms of salt flux, MgCl2 exhibited much slower
reverse salt flux: 59-67% lower than NaCl. The lower water
flux observed when using the MgCl2 DS is very likely the
combined effects of higher viscosity that increased the
severity of external CP, and the lower diffusion coefficient
of magnesium compared to sodium that increased the
severity of internal CP. The reduction in reverse salt flux
during MgCl2 experiments may also result from Donnan
equilibrium effects, whereby the relatively large magnesium
ion diffused slower through the membrane and subsequently
limited the diffusion of the counterion (chloride); yet,
intensified size exclusion caused by ion shielding and
nonspecific side reactions between magnesium ions may
also play a role.
Specific Reverse Salt Flux. To optimize FO processes it
is important to consider bidirectional diffusion; one method
to quantitatively evaluate this phenomenon is the ratio
between reverse salt flux and (forward) water flux. Larger
ratios reflect a decrease in the selectivity of the membrane
and lower efficiency of the process.
Specific reverse salt fluxes of three DSs through two
different FO membranes are illustrated in Figure 1c. For both
membranes, MgCl2 had the lowest specific reverse salt flux;
when tested with the CTA-2, water flux with the MgCl2 DS
was 33% lower compared to results with NaCl, but reverse
salt flux with MgCl2 was 57% lower compared to NaCl. Specific
reverse salt flux of NaCl was 55% higher for CTA-1 and 64%
higher for CTA-2 compared to MgCl2. For both membranes,
the smaller monovalent sodium ion has a higher diffusive
flux compared to magnesium, which also allows for more
chloride ions to diffuse into the feed solution. Chemical
analysis of samples drawn during each experiment confirms
that DS cations and anions diffuse through the membrane
at equal molar-equivalent ratios.
More interestingly, both the NaCl and MgCl2 DSs were
tested at two different concentrations (driving forces) and
they induced similar specific reverse salt flux through each
FIGURE 1. Effects of draw solution chemistry on water flux,
reverse salt flux, and specific reverse salt flux in (a) NaCl DS
experiments with the CTA-1 and CTA-2 FO membranes, (b) NaCl
and MgCl2 DSs experiments with the CTA-2 membrane only,
and (c) NaCl, MgCl2, and NH4HCO3 DS experiments with the
CTA-1 and CTA-2 membranes. In investigation of specific
reverse salt fluxes, the NaCl and MgCl2 DS were tested with
both the CTA-1 and CTA-2 FO membranes and at two different
driving forces (1.9 and 4 MPa), and the NH4HCO3 DS was tested
only with an average osmotic pressure driving force of 4 MPa.
Error bars indicate variation of results for different DS
concentrations. When present, a secondary x-axis correlates
osmotic pressure to molar DS concentration.
of the membranes (reflected in error bars shown in Figure
1c). The similarity in specific reverse salt flux despite
differences in the osmotic driving force indicates that this
ratio is related to the membrane’s selectivity.
Reverse salt flux of NH4HCO3 was far greater than that of
either MgCl2 or NaCl. NH4HCO3 has a higher diffusivity than
either NaCl or MgCl2 at the concentration tested (Figure S41b in Supporting Information), which reduces the severity
of internal CP. However, the substantial increase in reverse
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solute flux for ammonium and bicarbonate (observed with
both membranes) suggests that there may be additional
physicochemical effects that enhance the ability of these ions
to diffuse through these CTA membranes. The magnitude of
specific reverse salt flux of the three DSs provides a unique
observation on the sustainable use of these DSs. For example,
for each liter of water that permeates through the CTA-2
membrane, 140, 400, or 2,900 mg of MgCl2, NaCl, or NH4HCO3
are lost from the DS, respectively. This mass of DS salts will
transfer to the feed solution with possible implications for
downstream or adjacent processes, and will require replenishment to maintain operating conditions in the FO system.
Coupled, Multi-Component Diffusion. In addition to
examining the pure reverse diffusion of parent salts, experiments were conducted to elucidate the competitive nature
of simultaneous forward and reverse diffusion of solutes in
FO.
Single Salt Feed Solution Experiments with CTA-2. A set
of four experiments was conducted with each feed solution
to determine the mass transport characteristics of water and
individual ions. Experiments were conducted with individual
feed solutions and with NaCl DS. Solute fluxes in the forward
and reverse directions as a function of feed and DS
chemistries are summarized in Figure 2.
Results indicate that sodium and chloride reverse diffuse
at nearly equal-molar proportions for most feed solutions
tested (MgSO4, CaSO4, K2SO4, H3BO3, and NH4HCO3). The
only exception was experiments conducted with Ba(NO3)2
where chloride reverse diffused substantially faster than
sodium. One possible explanation is that the relatively small,
polar nitrate ion readily diffuses through the membrane while
the larger barium ion diffuses at a substantially lower rate
(17, 25, 26). This most likely led to a charge imbalance between
the two solutions that was corrected by a faster reverse
diffusion of chloride into the feed solution.
Data in Figure 2 correlate closely with the anticipated
diffusive behavior of solutes based on existing knowledge of
the membrane structure of CTA-2 (11). The membrane is
dense, nonporous, and negatively charged in the pH range
of interest. Diffusion behavior observed in Figure 2 indicates
that size exclusion and electrostatic effects have a substantial
role in controlling forward solute transport through the
membrane. For feed solutes, low molar fluxes for magnesium,
calcium, and barium indicate that divalent cations, with large
hydration radii, diffuse less readily through the membrane
than monovalent ions or polar molecules. Similarly, the large
negatively charged divalent sulfate ion had a very low molar
flux through the FO membrane. However, when present with
monovalent potassium ion, which exhibited a relatively high
forward flux, sulfate diffused faster through the membrane,
apparently to aid in maintaining solution electroneutrality.
Bicarbonate was also observed to diffuse at a relatively high
rate through the membrane, which may introduce process
limitations for FO desalination of brackish water. Diffusion
of salts composed of a common sulfate anion agrees with
previous studies (27) and follows the lyotropic series, whereby
the hydraulic radii and valence state of the cation is
responsible for limiting forward ion diffusion (17).
Coinciding with previous observations (28), boric acid
diffused significantly faster through the membrane than all
other solutes tested; this has important regulatory and
technical implications if FO is to be used as a seawater
desalination process. Results from these experiments revealed
that at an average pH of 6, boric acid rejection by the CTA-2
membrane was 12 and 33% for low and high water flux
conditions, respectively. In comparison, commercial RO
membranes may achieve 38-95% boron rejection at slightly
elevated pH of 8 (29). Silica is the only neutrally charged
molecule that was not shown to readily diffuse through the
membrane. The Na2SiO3 feed was the only solution that
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FIGURE 2. Summary of solute flux data from single salt
experiments with the CTA-2 membrane and NaCl DS. Forward
diffusing solutes are listed on left y-axis with values on the
lower x-axis, while reverse diffusing solutes are listed on the
right y-axis with values on the upper x-axis. (blue) Represents
experiments with 25 g/L NaCl DS and 1 g/L feed solution (FS),
(magenta) 25 g/L DS and 2 g/L FS, (yellow) 50 g/L DS and 1 g/L
FS, (green) 50 g/L DS and 2 g/L FS concentration. (*) Designates
solute flux divided by 10, (†) designates solute flux divided by
104, (X) data unavailable, and (diamonds) designates a net
solute flux because the same ion is present in both the feed
and DS.
became moderately opaque during the course of each
experimentsmost likely formation of silica colloids that were
well rejected by the FO membrane.
The pH of the feed solution shifted during specific
experiments. This raises an interesting question regarding
the bidirectional diffusion of hydrogen and hydroxide in FO.
Findings and discussions are available in Supporting Information S7. Yet, from results in Figure 2 it is difficult to decipher
if the reverse diffusion of DS solutes physically inhibits the
forward diffusion of feed solutes.
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FIGURE 3. Solute flux during single salt experiments with the
CTA-1 tighter FO membrane and NaCl DS. Symbols and color
codes are similar to those defined in Figure 2.
Single Salt Feed Solution Experiments with CTA-1.
Several single salt feed solution experiments were repeated
with the tighter CTA-1 membrane using NaCl DS. Molar fluxes
as a function of feed and DS chemistries are summarized in
Figure 3.
In all cases, the feed and DS solutes diffused slower
through the more selective, less permeable CTA-1 than in
parallel experiments with the CTA-2. Results indicate that
forward solute flux decreased by as high as 88% (in the case
of calcium) and by as low as 52% for bicarbonate. Reverse
diffusion of sodium and chloride through CTA-1 was observed
to decrease by equal rates of 82%, 73%, and 70% for the
experiments conducted with CaSO4, Na2SiO3, and NH4HCO3
feed solutions, respectively. It is likely that the higher rejection
of calcium ions in the CaSO4 experiment generated an
equivalent reduction in reverse diffusion of DS solutes
because of Donnan equilibrium effects.
Brackish Water Feed Experiments with CTA-2. Tests were
conducted with synthetic brackish water feed solution to
simulate operation of FO with more complex water chemistries. Forward and reverse solute fluxes as a function of
feed and DS constituents are illustrated in Figure 4. Results
reemphasize that MgCl2 has slower reverse diffusion for a set
driving force; however, there is minimal effect of DS on the
forward diffusion of brackish water constituents when
compared to results obtained with NaCl DS. When present
only in the feed solution, it was observed that sodium diffused
through the membrane more rapidly than the other constituents, likely because of its relatively small hydration radius
and lower valence charge. Calcium and silica diffused through
the membrane at nearly equal rates; yet, the lower rejection
of silica compared to calcium (results not shown) was not
expected based on prior results. One hypothesis is that silica
microcolloids are catalyzed in the presence of magnesium
and calcium ions (30), and the FO membrane better rejects
colloidal than dissolved silica. Lastly, similar to prior results,
FIGURE 4. Forward and reverse solute fluxes through the CTA-2
membrane during experiments with synthetic brackish water
feed solution and various DS. Forward diffusing solutes are
listed on left y-axis with values on the lower x-axis, while
reverse diffusing solutes are listed on the right y-axis with
values on the upper x-axis. (yellow) Represents experiments
with DS osmotic pressure of 1.9 MPa and (green) represents
experiments with DS osmotic pressure of 4 MPa. (*) represents
solute flux divided by 10 and (diamonds) designates a net
solute flux because ion is present in both the feed and DS.
the molar diffusion of sulfate was the lowest of all feed solution
species tested.
Similar forward diffusion trends were observed in experiments conducted with NaCl DSs. Comparable fluxes of both
calcium and sulfate were observed; yet, silica diffused even
slower than in the MgCl2 DS experiments. Based on the data,
it is possible that higher reverse diffusion of DS solutes may
have retarded the forward diffusion of silica. Further evidence
of this is provided in results from the NH4HCO3 DS
experiment.
Substantial reverse diffusion of ammonium and bicarbonate, beyond that of either NaCl or MgCl2, was observed.
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FIGURE 5. Effect of feed (deionized water) and DS (50 g/L)
crossflow velocity on (a) water flux, (b) reverse salt flux, and
(c) specific reverse salt flux. Blue colors represent lower flux
values and red colors represent higher flux values.
Remarkably, the faster reverse diffusion of these solutes
induced faster forward diffusion of sodium and chloride and
reduced forward diffusion of other solutes from the feed
solution; beyond levels observed during experiments with
the other DSs. In particular, the very slow diffusion of silica
may also be attributed to an increase in feed solution pH
that stems from reverse diffusion of ammonium and bicarbonate into the feed.
Effect of Crossflow Velocity on Reverse Diffusion. DS
and feed solution flow velocities affect external CP, and DS
flow velocity may indirectly affect internal CP; therefore, both
may impact water flux (more details on CP effects are available
in Supporting Information S1). Although the selective diffusion of water over solutes is purely related to the membrane’s active layer (not the porous support layer), altering
external CP may also affect solute flux in FO. Thus, in another
set of experiments with the CTA-2 membrane, both water
and reverse solute fluxes were measured under different feed
and DS flow velocities. Water flux as a function of feed and
DS flow velocities is illustrated in Figure 5a. Water flux reached
a maximum value at higher and equal flow velocities on both
sides of the membrane. Water flux decreased by ap6774
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proximately 20% from its maximum value when feed velocity
was low and DS velocity was high. In most membrane
processes, including FO, lower feed velocity results in higher
concentrative external CP effects (11, 19), and specifically in
FO, DS solutes that reverse diffuse through the membrane
may further concentrate the concentration boundary layer
on the feed side of the membrane. Similarly, increasing the
feed velocity enables a more rapid dilution of reverse diffusing
DS solutes; as the concentration in the feed boundary layer
decreases, the chemical potential gradient across the membrane increases and consequently water flux also increases.
Higher feed velocity and low DS velocity resulted in a
mild decrease in water flux (approximately 11%). At higher
feed velocities, DS solutes are being mixed faster into the
bulk feed solution; this reduces concentrative external CP
and initially promotes faster water diffusion. Simultaneously,
lower DS velocity combined with higher water flux creates
a more severe dilutive external CP at the interface between
the support layer of the membrane and the bulk DS. The
combination of changes in external and internal CP on both
sides of the membrane is most likely the cause for the ultimate
decline in water flux at higher feed velocity and low DS
velocity.
Reverse salt flux as a function of both feed and DS flow
velocities is illustrated in Figure 5b for the same experiments.
Higher reverse salt flux was observed during experiments
with mutually higher flow velocities, and the lower reverse
salt flux occurred during lower flow conditions. These results
may be explained through the same mechanistic arguments
used in describing the water flux data. At lower and equal
flow velocities, the reverse diffusing DS salts are concentrated
at the membrane surface on the feed side and the concentration boundary layer on the DS side of the membrane is
not well mixed and remains diluted. These two phenomena
resulted in diminishing chemical potential gradient between
the DS and feed solution and retardation in the net diffusion
of salts into the feed solution. Conversely, increased shear
flow on both sides of the membrane resulted in rapid
replenishment of DS solutes to reduce the effect of both
dilutive external and internal CP in the bulk DS and porous
support layer, respectively, and provided additional mixing
to alleviate concentrative external CP in the feed solution.
Optimizing process design may require compromising
between water production and reverse salt diffusion. The
influence of crossflow velocity on specific reverse salt flux
provides additional information that can aid in process design
and optimization. Specific reverse salt flux as a function of
feed and DS crossflow velocities was calculated from data in
Figures 5a and b, and is illustrated in Figure 5c. Based on
these results, FO processes should be operated with low feed
and DS flow velocities to minimize DS solute loss. Increasing
DS flow velocity while maintaining low feed flow velocity is
shown to produce the most significant adverse effect,
amplifying the specific reverse salt diffusion by close to 20%
above the minimum value under conditions tested in this
study.
On the other hand, mitigating reverse salt diffusion by
designing FO processes with low crossflow velocity operation
may reduce overall process performance. Feed solution
solutes will exhibit increased external CP behavior, which
will increase forward diffusion of these constituents, membrane fouling, and further reduce water permeation.
CP phenomena, both internal and external, affect water
flux in FO, but also have significant effects on reverse solute
flux. Results from this study also indicate that membrane
structure and DS chemistry play an important role in
bidirectional diffusion of solutes. In particular, the reverse
diffusion of DS solutes and the forward flux of sparingly
soluble salts, and boron, may introduce limitations on
seawater or brackish water desalination with FO. These
current limitations must be addressed through design of FO
membranes with increased water permeability and higher
selectivity. Solutes must have both high diffusivity in liquids
and low permeability through the membrane selective-layer
to be a good DS candidate. Process optimization requires
trade-off between driving forces for water flux and hydrodynamic and thermodynamic conditions for solute flux.
Acknowledgments
We acknowledge the support of California Department of
Water Resources (Grant 46-7446-R-08). Special thanks to Dr.
Dean Heil and Professor John Dorgan, and to HTI for
providing FO membranes.
Note Added after ASAP Publication
Downloaded by COLORADO SCHOOL OF MINES on August 29, 2009 | http://pubs.acs.org
Publication Date (Web): July 29, 2009 | doi: 10.1021/es901132x
Due to a production error, the wrong Supporting Information file was linked to the version of this paper published
ASAP on July 29, 2009; the correct version published ASAP
August 4, 2009.
Supporting Information Available
Details on solvent transport; membrane structure; bench
scale system configuration; experimental procedures; and
pH shift during specific experiments. This material is available
free of charge via the Internet at http://pubs.acs.org.
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