Supporting Information of
Nathan T. Hancock and Tzahi Y. Cath*
Environmental Science and Engineering Division,
Colorado School of Mines, Golden, Colorado 80401, USA.
*Corresponding author. tcath@mines.edu
, phone 303-273-3402, fax 303-273-3413
Submission: April 14, 2009
Revision: June 11, 2009
Submitted to Environmental Science and Technology
Contents:
S1. Solvent Transport in FO (pages S1 & S2)
S2. FO Membrane Structure and Performance Comparison (pages S2 & S3)
S3. Description of FO Bench-Scale Apparatus Used in the Current Study (pages S3 & S5)
S4. Solution Chemistries and Properties (pages S5 to S6)
S5. Calculation of Mass Transport (pages S6 to S7)
S6. Supplemental Description of Experimental Procedures (pages S7 to S10)
S7. Bi-directional Hydrogen and Hydroxide Diffusion (pages S10 to S11)
Figures:
S1. Solute concentration profile across an asymmetric membrane in FO.
S2. SEM micrographs of a cross section of CTA-1 CTA-2 FO membranes.
S3. Schematic drawing of the FO bench scale system used in the current study.
S4. Physicochemical properties of three draw solution solutes.
S5. Influence of background NaCl concentration on measurement accuracy during ICP-
AES analysis of metal ions of interest.
S6. Ammonia concentration measured as function of ammonium dose for various background concentrations of NaCl.
S7. Apparent average flux of hydrogen ions.
Page | S1

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S1. Solvent Transport in FO
Water (solvent) flux in FO is driven by the chemical potential difference between two solutions, which is manifested in the osmotic pressure differential ( Δ π ) across a thin, semipermeable membrane between a hypertonic draw solution and a feed solution. The osmotic pressure of a solution is defined as:
π =
RT ln ( )
V
A
(S1-1) where R is the ideal gas constant, T is the absolute temperature, V
A is the molar volume of the solution, and a
A is the activity of the solution ( 1 ). Water flux ( J w
) in FO, RO, and pressureretarded osmosis (PRO) is commonly expressed as:
J w
= A ( Δ P − σ Δ π ) (S1-2) where A is the water permeability coefficient of the membrane, σ is the reflection coefficient, and
Δ P is the trans-membrane hydraulic pressure. Δ P in FO is negligible, and it must be greater than
σΔπ in RO in order to produce purified water.
Yet, water flux in osmotically driven membrane processes is not a linear function of the osmotic pressure difference between the bulk solutions. The non-linearity of osmotic flow in FO, and the relatively low water flux obtained with high driving forces, has been the focus of intensive research ( 2-6 ). These studies represent the current understanding of solvent mass transport in osmotically driven membrane processes, and their main conclusion is that the diminishing permeate flow with increasing osmotic driving force is the result of concentration polarization (CP) effects; both concentrative external CP, but primarily dilutive internal CP. The concentration profile across an asymmetric FO membrane is illustrated in Figure S1. C1 and C5 are the concentrations of the bulk feed and draw solutions, respectively; C2 and C4 are the concentrations at the feed-membrane and draw solution-membrane interfaces (resulting from external CP), respectively; and C3 is the concentration at the active layer-support layer interface
( 7 ). Few studies have also considered the influence of osmotic deswelling on the non-linearity of osmotic flow ( 5, 8 ); however, CP effects are generally considered to be the dominant process that reduces water flux at higher driving forces ( 9 ).
Page | S2

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J s
C
4
C
5
Feed
J w
Δπ m
Δπ bulk
C
1
Δπ eff
C
3
C
2
Draw
Solution support layer active layer
Figure S1. Solute concentration profile across an asymmetric membrane in FO ( 7 ).
Past studies ( 5, 10, 11 ) provided important insight into the influence of both dilutive internal and concentrative external CP on water flux. Eq. S1-3 correlates water flux with hydrodynamic and diffusive mass transfer coefficients to account for dilutive internal and concentrative external CP.
J w
= A


π
D , b exp ( − J w
K ) − π
F , b exp



J w k





(S1-3) where π
D,b is the osmotic pressure of the bulk draw solution, π
F,b is the osmotic pressure of the bulk feed, and both K and k are mass transfer coefficients associated with the diffusive and the hydrodynamic conditions within the membrane support and at the membrane active layer, respectively. Solute diffusion is explicitly considered negligible in the development of Eq. S1-3; furthermore, the connection between reverse solute diffusion and the effects of external concentrative and dilutive CP were not discussed in previous studies.
S2. FO Membrane Structure and Performance Comparison
SEM micrographs of the CTA-1 and CTA-2 membranes are shown in Figure S2. These images illustrate that CTA-1 has a typical thin film composite structure while CTA-2 has a unique structure with cellulose triacetate polymer cast directly onto a woven polymeric support mesh ( 9 ). A recent study by Achilli et al. ( 12 ) reported baseline water flux and reverse NaCl diffusion for CTA-1 and CTA-2 membranes (denoted as Membrane C and Membrane B, respectively) with a deionized water feed solution and NaCl draw solution under slightly
Page | S3

elevated temperature (23˚C). The lower selectivity observed for the CTA-2 membrane may be attributed to its thinner cross section and its ability to moderate internal boundary layer effects, thereby maximizing permeability and mitigating dilutive internal CP. Pure water permeability
(deionized water feed) through the CTA-2 membrane as a function of hydraulic pressure was reported in two previous studies ( 6, 9 ). In another study, salt rejection by the CTA-2 membrane was tested under hydraulic pressure and NaCl rejection of 95% was achieved ( 13 ).
Surface charge (zeta potential) of the FO membranes was measured with an electrokinetic analyzer (SurPass, Anton Paar, Graz, Austria). The surface of both membranes is negatively charged in solution pHs greater than 4.
(a) (b)
Figure S2. SEM micrographs of a cross section of (a) CTA-1 ( 6 ) and (b) CTA-2 ( 9 ) FO membranes.
S3. Description of FO Bench-Scale Apparatus Used in the Current Study
Two FO flow cells were constructed with symmetric flow chambers on both sides of the membrane that facilitated parallel, co-current or countercurrent flow along the membrane. The membrane surface area in cell #1 and cell #2 were 509 and 632 cm 2 , respectively. Each FO cell contains four narrow channels to minimize fluctuations in hydraulic pressure that could adversely affect the operation and performance of the process. Turbulence-enhancement spacers were not installed in the flow channels in order to simplifying hydrodynamic conditions and facilitate model validation with the experimental results. Cell #1 was utilized in most experiments conducted with the CTA-2 membrane, while both cells were operated in series during experiments that employed the CTA-1 membrane.
Page | S4

A flow schematic of the bench scale system is illustrated in Figure S3. A 3 L acrylic plastic feed tank was constructed and the volume of the feed solution was maintained constant during the experiments in order to operate continuously at constant feed concentration. Using a level switch installed in the tank, a peristaltic pump dosed deionized water into the feed tank whenever the water level declined, thus compensating for water that permeated through the FO membrane into the draw solution. The change of mass in the deionized water tank was recorded and utilized to calculate the water flux through the membrane. pH was measured using a probe submerged in the feed tank. Feed conductivity was constantly measured with a K=1 cm -1 cell constant probe (Cole-Parmer, Vernon Hills, Illinois). Feed solution was continuously circulated between the feed tank and membrane cell at 1.6 L/min using a gear pump (Micropump®, Cole-
Parmer, Vernon Hills, Illinois). Feed samples were drawn for analysis from a sampling port installed after the recirculation pump.
The draw solution side of the system was similarly designed; a 3 L draw solution tank was used and the solution was continuously circulated between the tank and the membrane cell at 1.6 L/min using a gear pump. A supervisory control and data acquisition (SCADA) system was developed to maintain constant experimental conditions and to collect data during the experiments. A coiled stainless steal tube heat exchanger was submerged in the draw solution tank and chilled water was recirculated through the tube. System temperature was maintained constant using an automated proportional valve (Hass Manufacturing, Inc., Averill Park, NY) that controlled the flow rate of processed chilled water through the coil. Draw solution conductivity was continuously measured using a K=10 cm -1 conductivity probe (Cole-Parmer,
Vernon Hills, Illinois). To maintain constant draw solution concentration, a peristaltic pump intermittently dosed a small volume of a concentrated draw solution (300 g/L) into the draw solution tank. Dosing was controlled by the SCADA system that maintained conductivity (and thus draw solution concentration) constant.
Page | S5

Figure S3. Schematic drawing of the FO bench scale system used in the current study.
S4. Solution Chemistries and Properties
Salts were primarily acquired from Mallinckrodt Baker (Phillipsburg, NJ). These include
HCl, H
3
BO
3
, NH
4
OH, MgSO
4
⋅ 7H
2
O, MgCl
2
⋅ 6H
2
O, CaCl
2
⋅ 2H
2
O, and CaSO
4
⋅ ½ H
2
O. K
2
SO
4 and
Na
2
SiO
3
were acquired from J.T. Baker, Inc. (Phillipsburg, NJ); Ba(NO
3
)
2
and Na
2
SO
4
was acquired from Fisher Scientific (El Monte, CA); and NH
4
HCO
3
was acquired from Sigma-
Aldrich (St. Louis, MO). NaCl was used in most experiments as solute for the draw solution. It was acquired from Sigma-Aldrich/Fluka (Buchs, Switzerland) and was chosen because of its exceptional chemical purity.
NaCl, MgCl
2
, or NH
4
HCO
3
were used in preparation of draw solutions. These chemicals were chosen for their relatively low molecular weight, low viscosity, high solubility, and previous interest or utilization in FO research ( 7 ). OLI Stream Analyzer 2.0 (OLI Systems, Inc.,
Morris Plains, NJ) was employed to calculate osmotic pressures, relative viscosities, and selfdiffusivities as a function of molar concentration for these three compounds. The results of these calculations are summarized in Figure S4a and b. MgCl
2
has the highest osmotic pressure on a molar basis but also the highest relative viscosity.
Page | S6

5
4
3
2
7
6
8
Osmotic Pressures
MgCl
2
NaCl
NH
4
HCO
3
1
0
0
(a)
1.8
1.6
1.4
1.2
1
0.8
0.6
Relative Viscosities
MgCl
2
NaCl
NH
4
HCO
3
0.5
1 1.5
Molar Concentration, M
2
0.4
0.2
2 10
-9
1.5 10
-9
1 10
-9
(b)
5 10
-10
NH
4
Cl
-
+
(in NaCl)
Cl
-
(in MgCl
2
)
Na
+
HCO
3
Mg
2+
-
0 0.5
1 1.5
2
Molar Concentration of Parent Salt, M
Figure S4. Physicochemical properties of three draw solution solutes, (a) osmotic pressure and relative viscosity and (b) ion diffusivity as a function of solution concentration at 20˚C and atmospheric pressure.
S5. Calculation of Mass Transport
Determination of Water Flux . Water permeation rate was determined by measuring the change in mass of the deionized water on the analytical balance (Mettler Toledo, Columbus, OH) as a function of time for the duration of each experiment. The mass of deionized water decreased linearly with time because water that permeated through the membrane from the feed solution into the draw solution was replaced by dosing deionized water (to maintain constant volume of the feed loop). The slope of mass versus time is the mass transfer rate through the membrane for an individual experiment. Water flux was determined by dividing the mass transfer rate by the water density and membrane surface area.
Determination of Salt/Solute Flux. Salt flux values reported in Figure 1a and 1b and
Figure 5b were calculated by measuring the steady-state increase of feed solution conductivity over a selected time period. A K=1 cm -1 cell constant conductivity probe was specifically calibrated for dilute NaCl or MgCl
2 solutions. Feed solution conductivity increased linearly as a function of time as draw solution solutes diffused into the feed solution. Salt flux was determined by converting the slope of the feed solution conductivity increase per unit time to concentration per unit time based on a calibration curve generated for each salt type; this value was then multiplied by the feed solution volume and divided by membrane surface area.
Page | S7

Solute flux values reported in Figure 1c and Figures 2 through 4 were calculated from direct analytical measurements of solute concentration in the feed and draw solutions. Solute concentrations recorded from samples drawn at the beginning and end of each experiment were converted to mass of solute by correcting for system volume and compensating for mass removed during the sampling process. Mass flux was determined by subtracting the solute’s initial mass from its final mass and dividing by the time interval between sampling and membrane surface area. Solute molar flux was determined by dividing the mass flux by the solute’s molecular weight.
S6. Supplemental Description of Experimental Procedures
NaCl, MgCl
2
, and NH
4
HCO
3
Specific Reverse Salt Flux Experiments. Due to the relatively low saturation concentration of NH
4
HCO
3
at standard temperature and pressure
(approximately 2.5 M), it was infeasible to maintain the draw solution at constant concentration through chemical dosing; therefore, the NH
4
HCO
3 draw solution was allowed to dilute over time.
To compensate for dilution, the initial NH
4
HCO
3 draw solution concentration was higher, and as a result, the arithmetic average osmotic pressure of the bulk draw solution during the experiment was equivalent to NaCl and MgCl
2
experiments.
All experiments started with 1 L draw solutions and were terminated after 2 L of water diffused through the membrane into the draw solution. Samples of both feed and draw solution were drawn for chemical analysis at the beginning, middle (after 1 L of water permeated through the membrane), and at the end of each experiment.
Coupled, Multi-component Diffusion Experiments. All feed solutions were prepared in 4 L volumetric flasks. Draw solutions were prepared in 1 L volumetric flasks for each experiment and concentrated dosing draw solutions of 300 g/L NaCl or MgCl
2
were prepared in
2 L volumetric flasks. All experiments were terminated after 2 L of water diffused through the membrane into the draw solution. Samples of both feed and draw solutions were collected with
133 mL plastic sampling bottles at the beginning, middle (after 1 L of water permeated through the membrane), and at the end of each experiment. pH was recorded at the time of sampling. pH was not adjusted at any time during experiments that tested MgSO
4
, CaSO
4
, K
2
SO
4
, Ba(NO
3
)
2
, and H
3
BO
3
salts nor during the deionized water or brackish water feed experiments. The pH of
Page | S8

feed solutions containing alkaline salts NH
4
HCO
3
and Na
2
SiO
3
was adjusted to 7.5 and 6.5, respectively, to protect the membrane’s integrity. Both feed and draw solution required constant pH adjustment during experiments with NH
4
HCO
3
feed solution to protect the membrane from elevated pH (above pH 8). Between experiments, the system was thoroughly rinsed with deionized water and subsequently drained of all fluids.
Analytical Procedures . Analyzing samples taken during FO experiments requires the measurement of trace concentrations of certain ions in the presence of overwhelmingly higher concentrations of other ions, such as sodium and chloride in the draw solution. In the case of draw solution samples, the primary ions of interest are the ions from the feed solution that diffused through the membrane. However, due to the intolerance of many analytical instruments to high concentrations of sodium or chloride, the draw solution samples must be diluted 20 to 30 times, thereby further limiting the detection of co-diffused feed solutes/ions in the diluted samples.
A test was conducted to determine the influence of high sodium concentration on the detection of other ions at trace concentrations during ICP-AES analysis. 20 mg/L of various ions of interest were dosed into separate solutions of increasingly concentrated NaCl solutions.
Results indicate that NaCl background concentration of up to 10 g/L does not lead to significant analytical error (Figure S5). The largest deviation was found in samples with 1 g/L NaCl, which is likely the result of over dilution of the stock solution. Based on these results, accurate values may be obtained for samples diluted to 10 g/L NaCl. While this dilution improves the detection of ions present in trace concentrations, a second series of dilutions is necessary to determine sodium concentration, because the maximum allowable limit for the ICP-AES is 500 ppm.
Page | S9

22
21
20
19
18
17
16
10
Si
4+
Ca
2+
Mg
2+
K
+
0 2 4 6 8
Background Concentration, g/L NaCl
12
Figure S5. Influence of background NaCl concentration on measurement accuracy during ICP-
AES analysis of metal ions of interest.
Feed solution samples were also diluted below their prescribed maximum concentration for accurate measurement of their dominant cation concentrations (typically below 500 ppm). All
ICP-AES samples were analyzed in duplicates.
Feed and draw solution samples were analyzed for anion concentrations (i.e., chloride, sulfate, and nitrate) using IC. Similar to ICP-AES, these samples required dilution to ensure that anion species were below their maximum allowable concentration (300 ppm for chloride and
SO
4
and 60 ppm for nitrate). All IC samples were analyzed in triplicates.
Samples containing ammonium were analyzed with a DR 5000 Spectrophotometer (Hach
Company, Loveland, CO) using the Hach Salicylate Method (Method #10031, Hach Company,
Loveland, CO). This method was chosen because the manufacturer reports low interference of relatively high chloride concentrations. A test was conducted to verify that NaCl did not interfere with ammonium measurements. Standard solutions of 3.4, 6.8, 10.3, 30, and 45 mg/L NH
4
HCO
3
-
NH
4
+ were mixed in four different water matrixes, including deionized water, 25 g/L NaCl, 50 g/L NaCl, and the synthetic brackish water solution. Results in Figure S6 reveal that the presence of sodium, chloride, sulfate, and other ions present in the synthetic brackish water did not
Page | S10

interfere with ammonium measurements when using this method. These results also indicate that at higher ammonium concentrations, the Hach method underestimates the true concentration; thus, a linear regression was utilized to correct for ammonium concentrations near the upper limit of the detection range.
40
Deionized Water
25 g/L NaCl
50 g/L NaCl
Brackish Water
30
20
10
0
0 10 20 30 40
Actual Concentration, mg/L NH
4
+
50
Figure S6. Ammonia concentration measured as function of ammonium dose for various background concentrations of NaCl. Hach method #10031 was use for sample analyses.
Contamination from borosilicate glassware was found to be significant for samples containing boron and silica and required polyethylene volumetric flasks for dilutions. When relevant, ammonium analysis was also performed in duplicate. Acid titrations for bicarbonate analysis required 100 mL of sample, which prohibited repeat measurements for all samples with low bicarbonate concentration. Samples of the deionized water used for dilution were also analyzed and their influence was subtracted from the measured concentration.
S7. Bi-directional Hydrogen and Hydroxide Diffusion
The concept of electroneutrality in aqueous solutions suggests that other charged ions must diffuse through the membrane to maintain charge balance. The only other ions available for transport during these experiments are hydrogen and/or hydroxide. pH in the feed solution was monitored during the experiments, and was observed to change at different rates during the
Page | S11

course of each experiment. pH variation, expressed through molar fluxes of hydrogen ion into or out of the feed solution is illustrated in Figure S7 for select experiments. It is important to note that there is ambiguity regarding either the enrichment of protons in the feed solution or depletion of hydroxide; thus, for the purpose of this discussion, molar fluxes were calculated based on hydrogen ion fluxes.
Results in Figure S7 suggest that hydrogen ions are likely diffusing faster through the membrane than hydroxide, or visa versa. In the case of the common anion salts (MgSO
4
, CaSO
4
, and K
2
SO
4
), the pH of the feed solution decreased during the experiment. This implies that hydrogen ions might have diffused from the DS into the feed solution to offset the greater loss of feed solution cations.
In contrast, feed solution pH increased during experiments with boric acid or sodium silicate feed solutions. In experiments conducted with barium nitrate feed solution, a unique phenomenon was observed whereby chloride ions appear to preferentially diffuse into the feed solution to correct for charge imbalance rather than the solution shifting its pH.
Na
2
SiO
3
H
3
BO
3
Ba(NO
3
)
2
K
2
SO
4
CaSO
4
H
+
Ions Leaving Feed
H
+
Ions Entering Feed
MgSO
4
-0.04
-0.02
0 0.02
Apparent H
+
Ion Flux, mmol/m
2
-hr
0.04
Figure S7. Apparent average flux of hydrogen ions either leaving the feed solution (  ) or entering the feed solution (  ) for selected sets of experiments. Error bars represent the range of apparent hydrogen ion flux through the four experiments in each set.
Page | S12

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