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Electrochemistry Volume 9

A Review of Recent Literature

The Royal Society of Chemistry

The Electrochemistry of Porous Electrodes: Flow-through and Three-phase Electrodes

BY N. A. HAMPSON AND A. J. S. McNEIL

1 Introduction

In the first of these reviews, we dealt with the recent literature of the flooded porous electrode and in doing this we specifically excluded flow-through electrodes and electrodes with a three-phase interface. We now consider these two important categories of porous electrodes.

Electrochemical technology is mainly concerned with arranging for electrochemical reactions to be carried out economically. This is frequently a very major problem, for although the electrochemical approach to a reaction generally offers a clean and effective method, often there is a limitation due to the heterogeneous electrode reaction. This limits the effective reaction rate. Even if the reaction is driven by the application of a considerable overpotential the rate of the desired reaction may be forced past the mass-transport-limited plateau so that the current goes into a side reaction and the process becomes both inefficient and non-selective. Flooded porous electrodes have limited use in electrochemical reactions where electrolyte flow is a prerequisite for successful processing and continuous operation. The development of reactors to fulfil these requirements has occurred during the last two decades. Fixed-bed reactors have been developed from the principles derived for catalytic reactors in which the catalyst is supported on a porous substrate upon which the reaction occurs. Chemical engineers have been concerned with the flow of fluids through such reactors and the hydrodynamics are well established. Indeed, the fluid-flow-through porous bed is not unnaturally the priority of the F electrochemical engineer who is concerned mainly with getting the maximum output from the reactor. The reactor is therefore arranged so that the mass-transport-limited plateau spreads across the whole length of the electrode bed. Other porous electrode arrangements are attempts to simplify or improve this basic flow-through principle, especially with provision for gas interaction to form the three-phase interface porous electrode. This latter arrangement is crucial for the operation of fuel cells and metal–air batteries. With changes in external (economic) conditions, these developments have slowed down after a burst of activity in the late 1970s. However, with the ultimate specificity offered by the electrochemical technique it is expected that an active interest in this area will be re-established. It is hoped that this review might mark the beginning of a new interest in these systems.

The layout of the review was suggested by the obvious connection of the three-dimensional electrodes with the porous flooded format. Flow-through porous systems are clearly linked as are trickle beds, fluidized beds, and three-phase interfacia1 systems. These latter have not been reviewed in any depth before and consequently a large amount of published work, especially from the Eastern Bloc countries, is included.

2 Flow-through Electrodes

Introduction. — While there is considerable literature concerning flow-through electrodes, there are relatively few reviews which guide the reader. A relatively recent review by Newman and Tiedemann referred to much of the literature up to 1977. Earlier reviews. dealt with the general extension of what might be termed conventional electrochemistry by its combination with chemical-engineering principles to produce new electrochemical technologies and to provide further insight into the 'classical' electrochemical industries, such as electrochemical energy conversion. Later reviews have provided evidence for the growth of a thriving electrochemical-engineering discipline, given additional impetus by industry's need to deal with low reactant concentrations at ever-increasing rates. This growth has stimulated further systematization in associated areas.

In an early review paper, Kalnoki and Brodal showed that flow-through porous electrodes engender improved reaction rates by comparison with either solid electrodes over which electrolyte flowed, or flooded porous electrodes in static electrolytes. Clearly the flowing solution enhances mass transport at the high-specific-area electrode. Conversely a dilute solution can be handled effectively by using low flow rates and extended porous electrodes. The fluidized-bed electrode developed by Fleischmann and his group is a close relative of the flow-through porous electrode.

Cell Dispositions. — There are clearly three possible dispositions of electrodes (see Figure 1): with the counter electrode beside the working electrode the solution may be flowing normally towards (a), away from (b) or parallel to (c), the counter electrode. If both anode and cathode are porous then it might be necessary to keep the anolyte and catholyte separate from a common feed. A downstream counter electrode tends to distribute the reaction in the porous matrix since the front of the electrode reacts under the least favourable mass-transport conditions; an upstream counter electrode produces a maximum reaction rate at the front of the electrode. The parallel flow format may have advantages for slow electrochemical reactions but it is said to be the most difficult to analyse.

Factors Affecting Reaction Rates. — Hydrodynamics. The processes which affect the reaction rate are the transport of mass to the electrode surface and the transport of charge across the interphase. The transport of mass to the surfaces of a porous matrix (packed bed) is determined by the solution velocity via the appropriate mass-transfer coefficient. The mass-transfer coefficient furthermore depends upon the other solution characteristics, most conveniently expressed using the dimensionless hydrodynamic constants. Examples of these relationships for characteristic solution ranges are available.

A further mass-transport factor arises from the transfer of material in the solution between different parts of the electrode. A concentration difference gives rise to simple diffusion. In addition, the non-uniform velocity in the matrix pores results in mixing of the fluid in the flow direction, which results in a dispersion of the concentration profiles (the axial dispersion). Dispersion coefficient relationships have been given for some simple cases by Sherwood et al. The axial dispersion must be taken into account in considering the mass-transfer coefficient and Newman and Tiedemann give an example of the effect. The mass-transfer coefficient is crucial to the behaviour of porous electrodes. Conventionally, the target is the correlation of the Nusselt number with the Péclet number, the Schmidt number, the porosity and the electrode depth. There has been some discussion of the definition of the mass-transfer coefficient; however, one can only measure [bar.k]m, the average value at limiting current conditions, where [bar.k]m = v/aL ln (C0/CL), where v is the superficial fluid velocity, a the specific interfacial area, L the electrode thickness, and C0 and CL the reactant concentrations at the entry and exit positions, respectively. It is thus more sensible to build up the theory from this operational standpoint. The Nusselt number ([bar.N]u = ε[bar.k]m/aD0, where ε is the porosity volume fraction and D0 the diffusion coefficient of reactant in the feed solution), has been correlated with the Péclet number (Pe) to give the well known curve due to Newman for a fixed Schmidt number, characteristic of a deep bed of spheres on a simple cubic lattice. The various theoretical implications of this model are related to the established mass-transport theory and experimental flow-through porous beds operating at the limiting current. The correspondence between theory and experiment was significant and this was recognised by Newman and Tiedemann. The magnitudes of the experimental unknowns, and indeed how the simple spherical model should be modified for any particular bed geometry, was not really clear. Transient methods rather than steady-state methods were not found to improve the situation. In fact, transient methods clearly involve difficulties with double-layer charging and the fact that it is only just possible under steady-state conditions to reduce the ohmic potential drop within the electrode to a sufficiently low value so that the concentration of the electroactive reactant at the wall is zero as required by the establishment of the limiting condition.

The above discussion of mass transport has been in terms of the solution velocity. Frequently the pressure across the porous electrode is a convenient measure of the solution dynamics. A relationship for fully developed flow in which the pressure drop ΔP (proportional to L, the bed length) taken into the dimensionless group ΔP/aLρv2 (where ρ is the fluid density) is shown as a function of the modified Reynolds number Re' = dvv/(1 - ε), where dP is the equivalent sphere diameter and v is the kinematic viscosity, has been given by Bird et al. This relationship is rather simplistic as it does not take into account internal structures of equivalent spheres, which in itself is an abstraction.

Electrochemistry. The advantage of the porous electrode lies in the high rates of reaction, and consequently reaction is usually arranged to be under limiting conditions. The mass-transport-limited current plateau is bounded at the low-overpotential side by the charge-transfer-controlled region, and on the high-overpotential side by the transition to a new reaction, usually the hydrogen-evolution reaction (HER) or the oxygen-evolution reaction (OER). The most satisfactory method of arranging the potential is to design the process so that one end of the porous electrode is at the low-overpotential side of the limiting-current plateau and the other end coincides with the other limit of the plateau (so that the current going into intruding side reactions is limited). This condition imposes an ohmic limitation on the reactor and for this situation Newman and Tiedemann have generated equations which enable reactor characteristics to be estimated in an approximate sense, and applied these to the cases of copper recovery, lead removal from acid solutions of PbSO4, and desalination.

Theory of Porous Flow Electrodes. — The literature as far as 1976 has been well reviewed. Since 1976 no in-depth review on porous flow-through electrodes has been written, although there seems to be a tendency to take a more general approach and treat the electrode/electrolyte system as an electrochemical 'black box'. 1977 marked a peak in interest in porous flow-through electrodes; since then, however, the annual number of published papers has decreased.

Flow-by Porous Electrodes. — Alkire and Ng have carried out an engineering analysis of a packed-bed electrochemical cell, the electrolyte flowing in the axial direction and the current in the radial direction (the packed-bed electrode confined within a thin cylindrical porous separator surrounded by a concentric counter electrode). Experiments were made using a sectioned porous electrode (packed copper spheres) in order to measure the axial-current distribution at and below the limiting current. Copper sulphate (acid) was used as the electrolyte. Difficulties arose because the presence of flow channelling caused the mass-transfer coefficient to differ from its reported value. Empirical calculations were established in order to estimate the mass-transfer coefficient. The exchange current density was estimated to be ca. 0.07 mA cm-2 in 1mmol dm-3 CuSO4. Comparisons of theory and experiment have been made in the cases of collection efficiency, axial-current distribution, electrode polarization, and reactor current. Agreement was obtained for a range of situations of various geometrical dimensions, porosities, flow rates and reactant concentrations. Various criteria were generated for the volumetric reaction rate. The approximate method of solution of the simplified model provided an accurate representation of the reactor assuming that axial dispersion and channelling effects were absent. When the latter were present, modification of the mass-transfer coefficient was found to give an accurate procedure. However, this treatment by Alkire and Ng of the two-dimensional potential and current distributions is clearly limited in generality. The same is true of the Tentorio and Ginelli investigation which considered the mass-transfer and current relationships at reticulate three-dimensional copper electrodes (metallization of polyurethane foams forms the cathode in a filter press cell) at which copper electrodeposition is occurring. They assumed that the only current component is in the direction normal to the electrolyte flow. Storck et al. have developed a mathematical model to describe the behaviour of three-dimensional electrodes operating under limiting-current conditions. An analytical solution for the three-dimensional potential distribution is based on several assumptions. A number of these are conventionally made (highly conductive metal phase, supporting electrolyte, and uniform porosity), although it is also assumed that axial dispersion is negligible and that the limiting current is given by ZF[bar.k]C, where C is the local concentration of electroactive species and [bar.k the mass-transfer coefficient. Integration of the resulting Poisson equation is done by Fourier-transform methods. Potential and overpotential variations are obtained and these are applied to the design of a three dimensional structure. In a further paper Enriquez-Granados et al. describe an experimental study of the efficiency of three-dimensional electrodes operating at limiting current conditions using the dispositional characteristics of the theoretical study. The packed bed was of spherical nickel particles with the ferri-/ferro-cyanide reduction as the single-electron process. The experimental potential distributions measured by means of a moving probe were found to be in excellent agreement with the theoretical predictions. This investigation rests on the assumptions of the theoretical part and in this respect most of the important reaction parameters are satisfactorily dealt with.

Flow-through Porous Electrodes. — Newman has summarized the more promising arrangements for flow-through electrodes in terms of their applications, with special reference to simultaneous reactions. The paper is based on another in which a one-dimensional model operates below and above the limiting current of a cathodic metal deposition. The calculations assume only one reactant species and that a simultaneous side reaction might occur; the model includes the effects of axial dispersion and diffusion. Ohmic, mass-transport, and kinetic limitations are shown to predict non-uniform reaction rates. Results are compared with the experiments of others for copper deposition from sulphate solutions with an intruding HER. Very satisfactory agreement between model predictions and experimental data has been obtained for overall reactor performance and deposit distributions. The calculations include a new set of dimensionless parameters.

Trainham and Newman have also used thermodynamics in order to estimate the minimum concentration attainable in a flow-through porous-electrode reactor. The physical technique employed treated the reactor as an electrochemical cell at equilibrium and hence found the minimum exit concentration for the ion in question. The calculated concentration reductions obtained by the flow of the solution through the reactor are compared with experimentally attained reductions in the cases of copper, silver, lead and mercury and for the oxidation of ferrous ions. The calculations are recognised as only leading to a lower limit, for it is obvious that kinetics and mass transport will reduce the bed efficiency.

A further paper by Trainham and Newman considers the effect of electrode placement and finite matrix conductivity using a one-dimensional model for a flow-through porous electrode. The effluent concentration is predicted as a function of matrix conductivity and electrode length for upstream and downstream placement of the counter electrode and current collector relative to the fluid inlet of the working electrode. The dimensionless numbers developed in the previous paper were used to compare the performance as a function of counter-electrode placement. It is emphasized repeatedly that for the most efficient (low exit concentration) operation the porous-electrode potential range must straddle the limiting-current plateau. However, the intrusion of side reactions causes the simple picture to be inadequate and the distributions of current and potential in the presence of the side reactions are all required if the particular system is to be optimised, for example, for metal-ion removal. The paper includes boundary conditions for the four regimes treated and the appropriate parameters for the electrodeposition of Cu and Ag, from which the dependence of the effluent concentration on the parameters of interest was calculated.

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Excerpted from Electrochemistry Volume 9 by D. Pletcher. Copyright © 1984 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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