Polarisation in Electrodialysis Rotating-disc Studies BY ALEXANDER J. MAKAI-~ AND J. C. ROBIN TURNER* Department of Chemical Engineering, Pembroke Street, Cambridge CB2 3RA Received 15th February, 1978 Polarisation in an electrodialysis stack is difficult to examine because of the complex flow of the fluids through the stack. A rotating-disc apparatus has been built, for which the fluid mechanics are both well-known and convenient. Using anion-exchange membranes, the current against voltage plots at high voltages show considerable " water-splitting ", with large fluxes of H+ and OH- ions. The results correlate well with the treatments of Levich and of Cowan, and the enhancement of the anion fluxes by the water-splitting can be explained. Using cation-exchange membranes there is much less water-splitting, with anomalously high cation flux enhancement. Though these character- istics are desirable in practice, they are not explicable by the same approach as seems successful with anion membranes.In an earlier paper,' Brady and Turner have discussed the concentration and potential distributions close to an electrodialysis membrane. These depend upon the current density being passed through the membrane, the independent variable of the practical process of electrodialysis being the total voltage applied across a stack consisting of perhaps a hundred or more compartments separated by alternate anion and cation exchange membranes. In practice, the membranes are separated by inert spacers, which also define the compartments and the volume of liquid in them.Through these compartments the liquid is passed, and the fluid mechanics are not simple. As well as this, the composition of the fluid changes significantly as it passes through the compartnient (which is indeed the object of the process). Therefore, measurements of voltages, currents, and demineralization rates will be average over the membrane surfaces of a compartment. As the current density is raised (by raising the applied voltage) polarisation will set in, of variable severity depending on the position within the corn- part ment . We wished to examine whether the polarisation behaviour observed in practice could be described by our theoretical resu1ts.l To make a clear-cut comparison, it was necessary to we a system in which the fluid conditions were better defined than they are in an electrodialysis stack.The rotating-disc electrode, which is a well-known tool in electrochemical kinetics, see e.g., Albery,2 involves fluid-mechanics which are well-defined, and which have been solved theoretically by Levich. We have constructed a similar device using an ion-exchange membrane in place of the electrode, and have measured fluxes through such a membrane under conditions of increasingly severe polarisation. THEORETICAL When a horizontal disc electrode suspended from above is rotated, fluid spinning near the surface is flung out centrifugally, and is replaced by a stream flowing upwards t Present address : Union Carbide Corporation, Charleston, W. Virginia, U.S.A. 2850A . J . MAKAI AND J . C.R. TURNER 2851 towards the disc. Levich solved the problem of the convection combined with diffusion of a substance reacting at the surface of the electrode. He showed that provided that the Schmidt number (the ratio of the kinetic viscosity to the diffusion coefficient of the reacting solute) was high (and it is of order 1000 for liquid-phase solutions) then the gradient of the reactant's concentration was uniform over the whole surface of the disc. It is this property of" uniform availability " which makes the rotating-disc system a valuable tool. The value of this surface concentration gradient, when the surface concentration is reduced to zero by reaction, is given by (aCilaX)surface = WD; 3,- WC;. (1) Here D, is an appropriate diffusion coefficient, m2 s-l, and cp the concentration far from the electrode surface, kg mok3.v is the kinematic viscosity of the solution, m2 s-l, and O.I is the rotational speed of the electrode, rad s-l. W is a constant equal to 0.621. Gregory and Riddiford have shown that W in fact depends upon the Schmidt number, being 0.603 for the Schmidt number equal to 1000, and 0.582 when it is 100. The value 0.621 is that for infinitely large Schmidt number. It is common in boundary layer theory to describe a surface gradient in terms of that thickness, 6, across which the given surface gradient would produce the required change from surface to bulk-fluid conditions. In electrochemistry this is what we mean by the Nernst film thickness, used in the earlier paper.l For the rotating disc, this thickness, 6, is given by The current density i is given by S = W'1D$~*~-3.(2) and its maximum value, ilim, is hence, from eqn (l), where Z, is the valency of the reacting ion, and DR its diffusion coefficient, m2 s-l. These expressions as they stand apply to electrochemical measurements in the presence of " supporting electrolyte ", an excess of an electrolyte which is inert to the electrode reaction and which serves to maintain a very low potential gradient within the solution for any given i. In that case Ds is the same as DR. But in electrodialysis nothing is added ; the aim is to remove electrolyte. Again in electro- chemistry one may be able to consider an electrode reaction involving only one reagent ion, at least over a certain range of potential. In electrodialysis all the ions of a given sign, say cations, can pass into a cation membrane, thereby disappearing at the surface of the " electrode " as if by reaction, andithis will happen whatever the potential range involved.For a solution of a single salt, containing ions of valency Z, and z,, the absence of supporting electrolyte increases the limiting current density across a film of thick- ness 6, the appropriate expression being The question then arises as to which value of Ds to use in eqn (2) to determine 6, or in eqn (5). Eqn (2) was derived for the single reagent ion in supporting electrolyte, with a negligible potential gradient throughout 6. With a dilute solution of even a2852 FOLARISATION I N ELECTRODIALYSTS single electrolyte [the situation is more complicated with mixtures, see ref.(l)] it is not clear which value of Ds should be used in eqn (2) or (5). We have chosen to use the diffusion coefficient of the salt rather than of the ion constituent which passes into the membrane. If the ions have similar diffusion coefficients, the diffusion coefficient of the salt will also be the same. If the ions have different mobilities, that of the salt will be between them. Since Ds occurs only to the 1/3 power in eqn (2), the effect of an incorrect choice of Ds is smaller than might be feared, Albery6 has examined the problem, and has obtained results for the cases (a) where the supporting electrolyte is at an “ appreciably larger ” concentration than that of the reactant, or (b) where all the ions have the same D.The general case, of arbitrary concentrations and values of D, remains for further examination. We have used eqn (5) to estimate the “ Levich limiting current density ”. In practice, as this value is approached water splitting occurs, and fluxes of H+ and OH- ions cannot be ignored. If these fluxes are measured, we can then use the methods of ref. (1) to calculate the concentrations and potential profiles close to the membrane, but a value of 6 is still required. For this purpose we have used eqn (2) with D, equal again to the value for the salt. Cowan and Brown ’ suggested that a plot of A@/i against l / i could be used to locate the onset of severe polarisation. Here A@ is the potential drop across a membrane, or a cell pair if in a stack, in volts. When the current density, i, is raised, the apparent cell resistance, A@/i, stays approximately constant until a value of i is reached above which A@/i starts to increase sharply.In an electrodialysis stack, the sharpness of this change is blunted by the averaging of non-uniform effects across the membrane surface. With a rotating disc, a sharper transition was expected, and it was hoped to relate this to the “ limiting-current density ” given by eqn (4). As the current density is increased, the onset of water-splitting complicates the picture. Assuming the value of 6 given by eqn (2), the concentrations of the ions can be calculated, at any point within 6, from the measured fluxes, including those due to water-splitting. If there is only one type of ion, for example Cl-, (other than OH- ion from water splitting) which can enter the (anion) exchange membrane, it becomes possible to estimate the enhancement of its flux due to water splitting.It should be noted that both the total current density i, and the Cl- current density are increased by water splitting and the resultant fluxes of H+ and OH- ions. Then the calculation is done again, with the H+ and OH- ion fluxes set to zero, and with a trial reduced Cl- flux, until that C1- flux which produces the same concentration of C1- ion at the electrode surface is obtained. It was found that the choice of position within the boundary layer at which this matching was made had virtually no effect on the result. This is the “ unenhanced ” flux, and it can be compared with the ‘‘ en- hanced ”, or actual, flux.The potential distributions are not directly comparable. It will be seen that the “ unenhanced ” fluxes do show plateaux, even under severely polarising conditions leading to large water-splitting currents. To do this, the concentration of the C1- ion is calculated as just described. EXPERIMENTAL Fig. 1 shows the general layout. The membrane disc was formed by fixing a piece of ion-exchange membrane across the end of a flanged glass tube, g. The flat ground flange had an outside diameter of 30 mm and the open area in the centre had a diameter of 10 mm. The 10 mm annular flange minimises the fluid-mechanical edge effects, as required for Levich’s treatment. The glass tube, g, sealed at one end by the membrane disc, was fiiled with a solution, c, called the “ concentrate ” solution.The current-carrying electrode, p, was a flat spiral ofA . J . MAKAI AND J . C. R. TURNER 2853 platinum wire. The membrane/tube assembly could be rotated, at speeds from 150 to 1300 r.p.m., by the motor, m, while dipping into the “ diluate ” solution, d. This was con- tained in a plastic vessel in the wall of which was an ion-exchange membrane i. On the other side of this membrane was a further volume of “ diluate ” containing the other current- carrying electrode, a nickel plate, n, of area ~ 5 0 0 0 mm2. The purpose of the membrane was to prevent electrode products from n reaching the solution d, and it was of anion or cation-exchanger as appropriate for any experiment. Thus using the current-carrying electrodes n and p, connected to a d.c.power source, a controlled current could be passed through the membrane disc r. To measure the potential drop across r two Ag/AgCl potential electrodes, s, were used. One of these was located inside the rotating tube close to the membrane surface, and the other was placed in the diluate solution about 5 mm below the disc. This positioning could not be repeated very precisely in different runs, so the absolute values of the potential-drop measurements were rather arbitrary. However, we shall see that often we are mainly interested in the change in the potential-drop during a run, and provided the electrodes did not move duringlan experiment, such a change could be accurately measured. FIG. 1 .-Rotating-disc apparatus. Before a membrane was used, it was equilibrated with the solution employed in the experiment.During the experiment, readings of the potential drop and current were taken over a range of current densities extending to well above the “limiting” ion transport conditions, for several speeds of rotation. The concentration and temperature of the diluate bulk solution were also measured. The ionic transport rates were measured in separate experiments under similar conditions using constant currents for accurately timed periods with known solution volumes. The probe electrodes were not in place since it was found that these electrodes were damaged by the products of lengthy electrodialysis. Chemical analysis at the end of these runs gave the transport of each ion (as an average over the run).Solutions of single salts, and of mixtures, involving Na+, Ca2+, C1- and SO:- ions were used. The cations were analysed by atomic emission spectrophotometry, the anions by titration. The current carried by H+ (or OH-} ions through the cation (or anion) membrane was estimated by the difference between the total current and the current carried by the other cations (or anions). This could be done since the membranes were almost ideally perm-selective, i.e., there was negligible transport of cations through an anion membrane, and vice versa.2854 POLARISATION I N ELECTRODIALY SIS RESULTS Runs were performed using Neosepta AV-4T anion exchange membrane with solutions containing Cl-, SO%- and a mixture of the two. Another series of runs used Neosepta CL-2.5T cation exchange membrane with solutions containing Naf, Ca2+ and a mixture of the two.I00 200 (1/i)/cm2 A-l FIG. 2.-Cowan plots at different disc rotational speeds. 0.0174 rnol dm-3 NaCl solution. C1- transport through anion disc membrane. Disc speed : 0, 175 ; 0,250 ; x , 350 ; 8 , 740 ; +, 1200 Fig. 2 shows Cowan plots for the electrodialysis of C1- ions from a 0.0174 mol d r 3 NaCl solution at 19°C through the anion disc membrane. Five different disc rotation speeds were used. The results are in two groups, the potential electrodes having been changed between groups. It can be seen that a sharp break is observed r.p.m. 5 i0 15 AcpW FIG. 3.----Ion transport rates. 1290 rpm. 0.0174 rnol dm-3 Na C1 solution. Anion exchange in the curves, the position of which on the l/i axis can be closely estimated by extrapolatioii of the straight line sections of each plot.We shall call this break point the Cowan limiting current density. Timed electrodialysis runs were also carried out, from which the ion transport rates could be calculated. Using a rotation speed of 1290 r.p.m. the results in fig. 3 membrane. x , total ; 0, C1-; 8, OH-.A . J . MAKAI A N D J . C . R . TURNER 2855 were obtained. As A@ was increased above 5V the OH- ion transport, arising from water-splitting, rose from virtually zero to equal the C1- ion transport. The total current showed no plateau, and the C1- transport continued to increase up to the highest voltages employed, though not as markedly as the OH- transport. Using the procedure previously outlined, the " unenhanced " C1- transport can be calculated; the results are shown in fig.4. The unenhanced C1- transport does show a plateau at about 390 A m-2. This value is compared with the Cowan break- I I I / I I I 5 10 15 A(PP FIG. 4.-E!nhanced, or actual, C1- current density (0). Unenhanced, or corrected, C1- current density( 0). Conditions as for fig. 3. point value and with the Levich value, eqn (5), in table 1, which also shows the Cowan and Levich values obtained at a series of rotation speeds. Fig. 5 shows the Cowan values from table 1, together with a similar set for Na+ transport into a cation membrane, compared with the Levich plots, using eqn (5). It can be seen that these approaches correlate well, and that the Cowan breakpoints (which are comparatively easy to obtain) can be used to estimate boundary layer thicknesses, 6, in electro- dialysis stacks.TABLE l.-COMPARISON OF THE COWAN BREAKPOINT CURRENT DENSITY WITH THE LEVICH AND " UNENHANCED " LIMITING CURRENT DENSITIES 0.0174 mol dm-j NaCl SOLUTION AT 19°C ANION-EXCHANGER DISC disc rotation speed/r.p.m. 175 250 350 740 1200 1290 Cowan breakpoint current density/A m-' 145 175 200 270 350 370 Levich ilh/A m-' eqn (5) 134 161 191 277 353 366 - 390 " unenhanced " plateau - - - - Results of the other systems are given in detail by Makai.* The following conclusions can be stated : (i) for 0.0098 mol dm-3 Na,SO, at 1300 r.p.m., anion exchange membrane ; results very similar to fig. 3, giving an " unenhanced " SO;- plateau of 380Anr2, which can be compared with 350Am-2 from eqn (4), and 330 A m-2 from the Cowan breakpoint. (ii) For 0.0174 mol dm-3 NaCl at 1 300 r.p.m., cation exchange membrane. Results different in nature from those in fig.3.2356 POLARISATION IN ELECTRODIALYSIS The Hf ion transport from water-splitting is much smaller than OH- transport through the anion membrane. The Na+ transport continues to increase with increasing A@, but at a much greater rate than was the case with Cl- transport. The “ unenhanced ” Na+ transport does not show a plateau, but increases for the whole range of A@ covered. Cowan plots for a range of rotation speeds do show break- points, which correlate fairly well with eqn (5), see fig. 5. (iii) For 0.0092 mol dm-3 CaCl, at 1300 r.p.m., cation exchange membrane. Results very similar to (ii).Again low H+ transport and no “unenhanced” plateau. (iv) For mixed NaCl, Na,SO,, each at about 0.01 kg equivalents m-3 at 1300 r pm., anion exchange membrane. Results similar to the anion transport of C1- or SOi- individually. The 400 800 1200 10 ‘ 200 disc speed1r.p.m. FIG. 5-Dependence of Cowan limiting currents on disc rotation. 0 , Na+ transport through cation membrane ; 0, C1- transport through anion membrane. The lines are Levich plots, eqn (5). procedure for calculating ‘‘ unenhanced ” transports is not applicable for mixtures. (v) For mixed NaCl, CaCI,, each at about 0.01 kg equivalents m-3 at 1280r.p.m., cation exchange membrane. Results similar to the cation transport of Na+ or Ca2+ individually, including the anomalously high increasing transports with increasing voltage.DISCUSSION For transport through the anion exchange membrane a consistent picture can be drawn, in which the Levich treatment, the calculation procedure outlined here and the empirical Cowan plot approach are all in good agreement with each other. The high OH- transport produced at high A@ is undesirable in practice, but at least the theory and attendant calculations seem to be able to cope with the experimental data. For transport through the cation exchange membrane the situation is reversed. The Hf transport produced at high A@ is much lower (a desirable thing in practice), but the theory cannot explain the experimental data. The small H+ transport which did arise in our experiments came almost entirely from the bulk-phase H+ ion concentra- tion resulting from water-splitting at the anion-exchange membrane between the compartments, and not from water-splitting at the rotating cation-exchange membrane disc.Tests with alkaline bulk solutions showed this to be the case, the H+ transport through the disc being almost undetectable in that case. The real problem is how the anomalously high Naf, or Ca2+, transports can be explained. These high transports also occur in practical electrodialysis stacks, see Makai, * and Spiegler et al. There was the possibility that the fluid mechanics in theA . J . MAKAI AND J . C. R. TURNER 2857 cell compartments could be affected by the transport. But if so, why not at the anion membrane also ? The well-defined forced-convection flow field in a rotating-disc apparatus would seem to be able to dominate over free convection effects, which was a reason for these experiments.Nevertheless, the high cation transports remain and we can offer no explanation. From the results for mixed solutions it is possible to define a '' preference factor ", which is the ratio of the proportion of ions transferred to the proportion of ions in the bulk solution. As A@ is increased, the preferential removal of divalent ions (a desirable characteristic in the electrodialysis of brackish water) is reduced. It is easy to see that at high A@ the preference factor should fall towards unity, which is a subsidiary disadvantage of high-current-density electrodialysis. We would like to thank Dr. J. N. Agar for much helpful discussion, and J. M. Sturton for assistance with the atomic absorption analyses. A. J. M. is grateful to the Shell Co. of Australia for a Postgraduate Scholarship which supported this work. J. F. Brady and J. C. R. Turner, J.C.S. Farahy I, 1978,74,2839. W. J. Albery, Electrode Kinetics (Clarendon Press, Oxford, 1975). V. G. Levich, Physicochemical Hydrodynamics (Prentice-Mall, N.J., 1962), sect. 11, p. 60. D. Gregory and A. C. Riddiford, J. Chem. Soc., 1956,3756. V. G. Levich, Physicochemical Hydrodynamics (Prentice-Hall, N.J., 1962), sect. 52, p. 293. W. J. Albery, Trans. Faraday Soc., 1969, 61,2063. ' D. A. Cowan and J. H. Brown, Ind, and Eng. Chem., 1959,51,1455. * A. J. Makai, Ph.D. Thesis (Cambridge University, 1977). K. S. Spiegler, J. Sinkovic and 3. Leibovitz, Desalination Report No. 62, University of Cali- fornia, July 1975, p. 19. (PAPER 81265)