Appendix S1. Effect of operating parameters on chromium (VI) removal
S1.1 pH
The effect of pH on the removal of chromium (VI) from wastewater using cross flow
nanofiltration was studied in the pH range of 5 – 12 at cross flow rate 700 L/h,
transmembrane pressure 10 bars and temperature 30 oC. The NF1 membrane selected for
carrying out the present investigation is stable up to pH 2, in accordance with the
specifications provided by the manufacturer. However, in the present case, the NF membrane
exhibited poor Cr (VI) rejection efficiency, mainly owing to the fact that the point of zero
surface charge for NF1 membrane (isoelectric point) was found to be less than 3. As such, an
increase in the electrostatic charge repulsion between the target anions and the negatively
charged membrane surface was observed in response to the increase in solution pH. This
behaviour can be attributed to the progressive increase in the negative surface charge of the
membranes and the dominance of chromate anions bearing higher charge valency in the
alkaline media, which had resulted in increased charged solute rejection due to Donnan
exclusion [33]. The objective of the present study was to determine the optimal process
conditions corresponding to maximum hexavalent chromium rejection. Hence, pH range of 512 was selected for examination owing to the fact that the region was considered as the ideal
or more concentrated region within the entire independent variable space, which enabled
easier evaluation of the near-optimal process factor levels by RSM, by eliminating
experimental trials under conditions which are considerably far from the corresponding near
optimal levels, and at the same time indicated the variation in response following the
transition from acidic to alkaline media.
The relation between the pH of the solution and the percentage removal of chromium (VI) is
shown in Fig. S1(b). The effect on rejection with respect to pH alteration exhibited a
consistent augmentation with increasing pH values.
Fig. S1
The rejection of chromium (VI) increased from 0.75 to 0.884 using NF1 membrane by
increasing the pH from 5 to 12. Similar inclination towards removal of chromium (VI) using
nanofiltration due to solution pH has been reported in the literature [38]. This behaviour may
be explained on the basis of change in chromium (VI) species with the pH of the medium and
change in membrane surface charge density [34]. Chromium (VI) exists in the aqueous
solution in different ionic forms (HCrO4-, CrO42-, Cr2O72-) depending on the chromium (VI)
concentration and solution pH. Monovalent species HCrO4- is dominant at pH below 6.5 and
as the pH is increased beyond 7 it gets converted into divalent species CrO42 – and Cr2O72-.
Further, with high pH membrane surface potential changes which cause charge repulsion due
to electrostatic interaction and hence the separation of ionic species based on Donnan effect
becomes dominant in nanofiltration. The charged NF membrane normally allows the
monovalent ions to pass through and reject more di and multivalent ions and thus enhances
retention of chromium ion. This amplifying rejection of chromium (VI) from wastewater with
regard to pH may also be attributed to the contraction or expansion of polyamide NF1
membrane pores due to existent or nonexistent repulsion between the dissociated functional
groups of membrane polymer at different pH values of the feed [32].
S1.2 Cross flow rate
Cross flow rate is an important parameter in removal of heavy metals from wastewater since
it has a significant contribution towards reduction of concentration polarization through
sweeping action on the membrane surface and thus tumbles the fouling [33]. However, there
is no study available showing the effect of cross flow rate on the removal of chromium (VI)
from wastewater using cross flow nanofiltration. This effect has been illustrated in the present
work by varying the cross flow rate in the range of 300 – 700 L/h at pH 7.5, transmembrane
pressure 10 bar and temperature 30 oC. The relation between the cross flow rate of the
solution and the percentage removal of chromium (VI) is shown in Fig. S1(c). The effect on
chromium (VI) retention with respect to cross flow rate variation demonstrated a regular
escalation with increasing cross flow rate. The chromium (VI) rejection from wastewater feed
using NF1 membrane increased by about 0.936 – 0.974 as the cross flow rate increased from
300 – 700 L/h. This tendency may be accredited to the decrease in concentration polarization
with the increase of the cross flow rate. In cross flow membrane module, the feed solution
flows parallel to/and over the membrane surface, and permeate is collected in a direction
perpendicular to the membrane surface. The problem of fouling is overcome to a great extent
because the retentate accumulated over the membrane is carried away by the continuously
flowing feed solution. This problem can further be minimized by increasing the cross flow.
Increase in cross flow rate leads to greater convective force which in turn enhances solvent
flux and the uncoupling effect between solute and solvent flux results in a corresponding
increase in retention of solute [33].
S1.3 Transmembrane pressure
The effect of transmembrane pressure for the removal of chromium (VI) from wastewater
using cross flow nanofiltration was studied in the range of 2 – 13 bar at a cross flow rate 700
L/h, pH 7.5 and temperature 30 oC. The pH range originally selected for study was 5-12. An
intermediate pH 7.5 was maintained in the present case, owing to the fact that the pH 7.5 was
the unbuffered pH of the prepared aqueous samples. The objective was to study the effects of
cross flow rate and transmembrane pressure on Cr (VI) separation without varying or
modifying the pH. The relation between the transmembrane pressure of the solution and the
percentage removal of chromium (VI) is shown in Fig. S1(d). The effect on rejection with
respect to transmembrane pressure adjustment revealed a steady intensification with
increasing applied pressure values. The rejection of chromium (VI) increased from 0.905 to
0.954 using NF1 membrane with decreasing the transmembrane pressure from 12.5 to 2.5.
Same nature of chromium (VI) rejection with transmembrane pressure was observed by
Babaee et al [18]. This behavior may be explicated on the basis of solution diffusion
mechanism prevalent in nanofiltration where solute and solvent fluxes are uncoupled due to
which increase of solvent flux with an increase of transmembrane pressure does not result in
a proportionate increase of solute flux and a relative increase of solvent flux impedes the
transport of solute though the membrane leading to greater solute retention [32-33]. The
presence of chromium (VI) as several monovalent or divalent anionic forms in water results
in an electrostatic repulsion when it interacts with negatively charged nanofiltration
membrane surface and this results in retention or removal of chromium from wastewater
feed. However, this trend was somewhat different from that for removal of chromium (VI)
using nanofiltration [20]. They observed that the retention of chromium (VI) ions first
increased with increase in pressure and then decreases as the pressure goes beyond 10 bar.
This difference in observation may be ascribed to the salt addition effect studied by them
where they added varying amount of different salts to the K2Cr2O7 solution. The plots in Fig.
S1, thus, mostly exhibit the main or linear effects of the process factors on the response,
wherein the linear and quadratic effects of the process variables are excluded. The plots by no
means attempt to establish the fact that the quadratic and the interaction terms of the model
are not significant, but rather graphically highlight the singular effects of the factors on
response, thereby providing an overview of the correlation between the response and the
process variables and that of the degree of variation witnessed in the response profile
following a variation in a process factor level, while keeping the other parameters constant.
Figure
Figure S1. (a) Pure water flux as a function of transmembrane pressure for NF1 membrane at
temperature 30 oC; (b) Influence of wastewater pH on chromium (VI) rejection; (c) Influence
of cross flow rate on chromium (VI) rejection; (d) Influence of transmembrane pressure on
chromium (VI) rejection.
Table
Table S1. Experimental design and response matrix.
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Coded values
X1
X2
X3
-1
-1
-1
0
0
0
0
1.682
0
-1
1
-1
0
0
0
0
0
0
0
-1.682
0
-1
1
1
1
1
1
1
1
-1
-1
-1
1
-1.682
0
0
0
0
1.682
0
0
0
1
-1
1
0
0
0
1
-1
-1
0
0
0
0
0
-1.682
1.682
0
0
Un-coded values
X1
X2
X3
5
400
5
8
550
10
8
802.27
10
5
700
5
8
550
10
8
550
10
8
297.73
10
5
700
15
11
700
15
11
700
5
5
400
15
2.95
550
10
8
550
18.41
8
550
10
11
400
15
8
550
10
11
400
5
8
550
10
8
550
1.59
13.05
550
10
Response
(Rejection)
0.9278
0.9722
0.9795
0.9567
0.9729
0.9700
0.9489
0.9623
0.9957
0.9778
0.9487
0.9429
0.9803
0.9752
0.9921
0.9789
0.9513
0.9762
0.9556
0.9889