DONALD A. COWAN and JERRY H. BROWN1 Texas Electric Service Co., Fort Worth, Tex.
Effect
of Turbulence
on
Limiting Current in
Ind. Eng. Chem. 1959.51:1445-1448. Downloaded from pubs.acs.org by UNIV OF KANSAS on 01/05/19. For personal use only.
Electrodialysis Cells Conversion of brackish and saline water is important if industry is to have sufficient process water in the future, aside from the need for potable water in residential areas existing and still undeveloped. The results reported here offer an explanation to some of the basic problems in an electrodialysis system, and it is from essentially basic studies such as this that a vastly improved method could develop
In
saline water demineralizing by electrodialysis, polarization limits the amount of current which can pass through the cells. Although polarization in the bulk of the stream is destroyed by turbulent flow through the cell, above a critical current density polarization is again noticeable. If a laminar boundary layer exists wherein turbulent mixing does not occur, the current is diffusion-limited and therefore should be a function of seven variables: viscosity, flow velocity, and temperature of the fluid; dimensions of the cell; and the diffusion coefficient, mobility, and concentration of the salt. Current density in an electrodialysis cell has three critical values: above one, a polarizing voltage opposes current flow adding a cost element; above another, pH changes rapidly causing membrane damage; above the third, a charge gathers on the membrane. “Limiting current” designates the first value in that current is diffusion limited. The second value is nearly identical with the first; but pH change is greatest at the membrane-fluid interface where damage is most likely to result. The pH measured in midstream does not indicate the magnitude and, because it responds to freed ions only, changes oppositely to the pH in the fluid at the membrane, which polarizes first. A paradox of electrodialysis is thus accounted for, and a complete theory of polarization, pH change, and charged surfaces emerges. Its immediate practical importance will be in fixing the flow velocity conditions needed in a practical electrodialysis demineralizer.
1 Present address, Science Division, University of Dallas, Dallas, Tex.
Experimental The electrodialysis cell consisted of several channels through which water
could flow, alternate streams being controlled separately for velocity and concentration. Electrodes were placed so that electric current was transverse to stream velocity. Cell channels were 2.54 cm. wide with 10 U-turns a centerline run of 429 cm.; reduced the total exposed area to 1036
Spacer thicknesses of 0.16, 0.32, and 0.64 cm. were used. No obstructions were in the channels. With two exceptions, the salt used was sodium sulfate in treated municipal water. Runs were made with cation-selective, anion-selective, and alternate membranes as in a demineralizing system. Membranes tests were available commercially (Ionics, Inc.), except for experimental, low-resistance membranes supplied by sq. cm.
another manufacturer.
i
Polarization of sodium sulfate with concurrent Two dipH change. luting channels 0.32 cm. thick with 718 jumho/cm. conductivity, flowing at 94 cm./second
Figure 1. Small decrease in current efficiency at the highest current density shown indicates that ionic current is still largely furnished by the electrolyte VOL. 51, NO. 12
·
DECEMBER 1959
1445
Electrical measurements of voltage ratios for the cell were made directly with a Wheatsone bridge arrangement of which the cell was one leg and a 30-amp., 50-mv. shunt in the main line to the cell was another; the other branch was made up of a 10-turn variable resistor and a set of fixed precision resistors. A potentiometer across the same shunt resistor effectively measured the current to the cell. The relative conductivity before and after dilution was measured with conductivity cells in the influent and effluent streams as part of an alternating current bridge employing 1000-c.p.s. signal, amplifier, and null detector. The pH was read on a standard calomel electrode pH meter. Electrical measurements were accurate to 2%, flow velocities to 5%, and temperature to 1%. Data were occasionally erratic, probably because of entrapped charges in the membranes.
intercept and the cell voltages plus their derivatives as the slope. Polarization voltage manifests itself as a rapid change of slope. The pH of
to current
RECIPROCAL
CURRENT
-
AMPS'1
Figure 2. Point of limiting current density, at which negative slope cuts positive slope, was chosen from polarization of potassium chloride in distilled water A. B.
0.64-cm. channels, 0.32-cm. channels,
Re Re
= =
4840 5400
a
changes.
The current
Figure 3. as
Limiting current density inflow velocity increases
Conductivity, 3000 .umho/cm.; 0.64-cm. channels; velocities, 29, 43, 58, and 87 cm./second
1446
Were Made in the Dialysis Cell with Anion-Permeable Membranes Cation-Permeable Membranes, and Combinations of Both w,
Cm.
c°,a /¿mho/ Cm.
Rfb
Ohms 1.48 1.50 1.59 1.50 0.76 0.79 0.75 0.72 0.74 0.38 0.38 0.39
Rif
Ohms
Fluid Temp., 0 C. 14.5
hf Re-5
Amp.
jwr /
5.6 79 3300 108 14 4900 7.6 136 10 6610 9.5 2.59 186 14 9920 13.0 2.32 72 9.1 1.38 13 3250 11.5 91 5 1.25 14.6 4990 6570 14.3 113 5 1.32 14.0 18.9 5 18 8080 150 1.20 22.2 176 5 9730 1.20 16.5 10.0 42 13 3300 5 0.905 13.3 3300 56 5 0.785 13.6 62 12 6550 14.7 5 1.015 16.0 67 12 7930 5 0.39 1.015 5.3 84 3300 5 1.43 1.68 19.4 7.5 67 3270 5 0.71 0.98 18.9 5.0 80 2 1.42 18.7 3300 3 1.78 7.5 67 17.2 3240 3 2 0.72 1.04 141 3.8 29 6160 3 3 1.14 1.94 93 4490 4.5 1.17 29.2 3 3 0.70 129 6.0 1.18 28.6 4860 3 3 0.71 187 8275 8.8 3 1.21 27.3 3 0.73 8.8 187 24.8 9850 3 3 0.76 1.42 213 10.0 25.2 11830 3 3 0.76 1.39 10.7 116 4840 4 4 1.63 2.02 26.7 15.6 96 4 26.3 5450 4 33105 0.82 1.62 15.1 108 4400 24.0 8 3310 0.85 1.76 10.7 87 24.5 4400 8 0.84 1.72 3310 3.8 81 4040 33 2.63 26.5 3 1250 2.47 5.6 79 4040 26.0 3i 1900 1.63 2.09 3 7.5 80 25.5 4040 1.24 1.63 3 3> 2500 10.4 86 4040 25.8 0.90 1.19 3 3J 3425 11.0 92 4040 1.27 24.7 3000 1.03 3 3' 0 Conductivity of streams in which boundary layer limits current. 6 Calculated total resistance of fluid in cell. ” Total resistance of cell, including membranes, as determined by 6 ! Limitintercepts of graphs. d Calculated as if temperature were 25° C. 1 Limiting current. Potassium chloride. 5 Low ing current number. 9 Anion permeable. h Cation permeable. resistance membranes. 5 5 5 5 5
creases
efficiency for the cell
Runs
No. of Membranes C1
a
at the highest current density shown, evidence that the fluid against the membrane was not exhausted of electrolyte; had the current above the pH change point been carried only by hydrogen and hydroxyl ions, current efficiency would be less than 50% at the high current density shown.
indicates that a plot of V/I against 7_I will have the resistance of the cell as an
A»
begins to change at
(some current was shunted through the electrode streams) in the run shown in Figure 1 was 82% at low values of current density and decreased only to 78%
=
I.
stream
value very near the value at which the resistance slope changes and continues to decrease as current density increases. At low current densities, to the right of this point in Figure 1, readings of V/I at various 7 values can be taken randomly with corresponding values repeated, but at higher current densities to the left of the slope-change point, values cannot be repeated upon a reduction of current density. That V/I remained above normal even after a current interruption of 20 minutes while the water continued to flow indicates a charge on or in the membrane opposite in sign to that which the membrane ex-
Results The voltage drop across an electrodialysis cell consists of electrode potentials Ve, concentration potentials Ve, polarization voltages Vp> and ohmic voltages IR. Accordingly, the relation (1) V/I R + (V, + Vc + Vp)/I
Table
diluting
current
INDUSTRIAL AND ENGINEERING CHEMISTRY
0.64 0.64 0.64 0.64 0.32 0.32 0.32 0.32 0.32 0.16 0.16 0.16 0.16 0.64 0.32 0.64 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.64 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32
3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 718 1300 1300 1300 1300 1300 3310*
2.32 2.19
ELECTRODIALYSIS Analysis
CELLS
0.0234 volt and + 0.47 so that ~ 0.0205 volt. The effect of Vp becomes =
=
The deduction of an empirical relation for limiting current density is complicated by the fact that this critical value is a function of seven variables. The conditions of continuity are: Div j 0 Div KE 4 Div (jtF~l + D grad N) dN/dt At an interface, these become;
(2)
=
=
(3)
=
4
{Km/Cm
=
C is related to
Kf/C,)j
-
(4)
noticeable at some value v, small but greater than ; polarizing limiting current can be designated by -In
S)
(l
ii
-
·
(12)
-
Change of pH. The charge per unit volume q in the boundary layer can be obtained from Equations 4 and 8 :
normality: C
aN
=
The mass condition becomes
The transfer number t now refers to the ion not being transferred through the interface; its value changes from near zero to t at the membrane, and the diffusion coefficient changes from 0 to D. For the steady state, dA'/dt 0, the density at the boundary is =
j
=
(FD/t) (bN/by) +
current
constant
(6)
The constant is zero if t is zero in the membrane. For a boundary layer of thickness 5, in which the diffusion coefficient D is constant, if t changes only at the interface the concentration gradient, bN/by, may be expressed as Figure 4. Thickness of the stream has small effect on limiting current density
bN/by
a
0.32-cm. channels; velocities, 51.4, 79, 104, 28, and 54 cm./second 1
1
(N0
=
(7)
where A'0 is the normality in midstream. Similarly, conductivity has the gradient bC/by (Co Cf)/b and in the boundary layer is =
The point at which the negative slope of Figure 1 cuts the positive slope when continued downward is designated as “limiting current density” because of its apparent relation to diffusion. The dependence of this point on fluid velocity, channel width, and concentration has been determined experimentally. This point was selected as the one corresponding to the point defined by such an intersection in a study made with a 3300jumho per cm. solution of potassium of about chloride in distilled water 12 amitos per cm. (Figure 2). The shape of the curves in Figures 1,3,4, and 5 is affected by the presence of other ionic species in the supply water. A series of runs was made at a fixed concentration of 2120 p.p.m. of sodium sulfate (0.0303 AT), as indicated by a 3000-^mho per cm. reading on a conductivity meter compensated to 25° C. With five anion-permeable membranes and no cation membranes, runs at various velocities were made with 0.64-cm. channel spacers (Figure 3), with 0.32-cm. spacers (Figure 4), and with 0.16-cm. spacers. For these graphs the intercepts have been moved to coincide, the actual intercepts appearing as R¡ in Table I.
,)/
-
C
C, + (Co
=
(8)
-
(9)
Cf)y/S
-
Figure 5. Transfer numbers can be determined from the ratio of limiting current at the two different membranes A. Cation membranes. 8. 3 anion-2 cation membranes. C. Anion membranes. Velocity, 29 cm./second; 0.64-cm. channels
The conductivity at the interface can be eliminated from the expression through the gradients in Equations 6 and 8
ac/ay where
a
term
C
a
ci^l=]lL=j,e
=
is
—
introduced:
Co
—
j
/(
—
y)
Polarization. The voltage drop boundary layer is
(10) across
For sodium sulfate at 25° C., with D 1.124 10~5 sq. cm. per second, a 99 mho sq. cm. per equiv, t 0.38 (4) at the anion-permeable membrane, ~ has the value 0.0285 volt, and at the cation permeable membrane + is 0.0175 volt. However, Figure 5 shows that the effective transference numbers are 0.53 and =
=
—
Figure 6.
Limiting current is inversely
proportional to the thickness of the unstirred boundary layer in a turbulently flowing cell Low values thick
are
VOL. 51, NO. 12
from
·
narrow
channels 0.1 ó
DECEMBER 1959
1
cm.
447
4?
Sti (1
=
At the polarizing q
=
^
~
7'5/Coe)-2
(13)
current
(Equation 12):
(e”/e
1)2
~
(14)
If
has a value of about 10-3 cm. and v of 0.05 volt, at polarizing current, q has a charge density at the interface corresponding to the hydrogen ion concentration for pH 7, and the charge increases without limit as the limiting
number approaches unity. The previous definition for limiting current will therefore serve as the limit defined by charge concentration. The immobilization of charge in the boundary layer frees charge of the opposite sign so that a divergence of current exists. In general, this will not be precisely offset by the corresponding source in the other boundary layer but must find its sink in the concentrate stream. Because cations usually have smaller transfer numbers than anions, the imbalance is such that a drop in pH of the diluting stream results. Charge on the Membrane. The charge on the membrane face is governed by Equations 4 and 10.
the value L 4.4; from Nikuradze the value 6.8; from experimental data on kinetics of dissolution at high viscosities, values between 2.5 and 4.6, and from heat transfer data, the value 4.0. The dimensionless boundary layer thickness in units of us' is: ad w'V 0.395 -1/8 =
vL
jw'
current
Membranes whose Km/Cm is about that of the water will collect only a small surface charge until the polarizing current is approached. Then a charge opposite in sign to that which the membrane conducts collects on the surface and apparently becomes entrapped so that it does not disappear when the exis halted but continues to cess current effect an added, erratic voltage in subMemsequent tests for some time. branes of high specific conductivity exhibit the effect at currents below the polarizing limit so testing is difficult. Organization of Data. The limiting current defined by polarization (Equation 12) is the value observed in these experiments. The boundary layer thickness is expected to be a function of Reynolds number Vw'/v and w' 4 (area/perimeter). Because C
