The bubble coverage of gas-evolving electrodes in a flowing electrolyte

Abstract

During operation of gas-evolving electrodes, a fraction of the electrode surface is covered with adhering gas bubbles, which are known to exert substantial effect on mass and heat transfer, on overpotential, on limiting current density and on ohmic resistance. For this reason, many investigations were conducted to obtain experimental data of the fractional bubble coverage (or fractional shielding) in stagnant liquids. However, very little attention has been paid to the behaviour in liquid flow, although the majority of industrial electrochemical reactors are operated with flowing electrolyte liquids. The paper presents a theoretical analysis and experimental results of the effect of liquid velocity on the bubble coverage.

Introduction

Operation of electrodes without gas evolution differs from that of gas-evolving electrodes in that the electrochemical processes of the latter ones are superimposed by physical processes induced by gas bubbles adhering to the electrode. These bubbles not only deactivate the parts of the electrode surface that they cover or shield, but their growth also causes microflow in the electrode boundary layer. Both effects strongly interfere with the operation of the electrode.

It is known that the fraction of the electrode surface covered with or shielded by adhering bubbles is an important operation parameter. A degree of coverage (Bedeckungsgrad) was introduced by Ibl and Venczel in 1961 and defined as the fraction of the electrode surface contacted by adhering bubbles [1], [2]. For non-wetting liquids or bubbles with contact angles ϑ≥90°, this definition is unproblematic. Such contact angles occur in molten salts under certain conditions. Operating electrodes in contact with aqueous electrolyte solutions commonly exhibit contact angles close to zero. A more general definition for arbitrary values of the contact angle was given in 1980 [3]: The bubble coverage Θ denotes the fraction of the electrode area shaded by normal projection on the electrode surface, Fig. 1. Even from today's view-point this definition appears reasonable since the area below an adhering bubble essentially does not participate in electrode reaction as shown by estimates of Tobias [4], [5] and Müller [6] and their coworkers.

The action of bubbles adhering to the electrode surface is manifold. As the covered fraction of the electrode surface is electrochemically completely inactive, the true current density j of gas-evolving electrodes is larger than the nominal current density, I/A. As the current density below bubbles in wetting liquids, ϑ<90°, is very small [5], [6] the true current density is approximately

$$\text{j=}\text{I}\text{A}\text{1}\text{1−}\text{Θ}$$

Therefore, the adhering bubbles, represented by the fractional bubble coverage Θ, affect the slope of I-U curves and necessitate corrections of measured ‘electrode overpotential’ data or particular means to eliminate the detrimental action of bubbles [7].

For the same reason, Θ controls the upper operational limit given by the limiting current density. As seen from Eq. (1) the true current density may be substantially larger than at electrodes without gas evolution as the bubble coverage approaches unity. The limiting current density is reached at moderate values of the nominal current density if smooth gas release is impeded, e.g. at gas-evolving electrodes facing downwards. This fact is of particular importance in industrial alumina electrolysis, since it explains the action of the bubble coverage on the so-called anode effect [8], [9].

Bubbles in the interelectrode gap are known to induce an increase in the ohmic interelectrode resistance. As the volumetric gas fraction is nowhere larger than in the bubble layer contacting the gas-evolving electrode [10] the bubble coverage Θ plays an important role and serves as a parameter to estimate ohmic voltage drop [11], [12].

Finally, bubbles in contact with the electrode surface affect heat transfer and, particularly, mass transfer of reactant to and of product from the electrode surface in a more complex way. Adhering bubbles not only reduce the active area of heat and mass transfer but induce additional effect by the microconvection in the vicinity of the growing gas bubbles pushing away liquid in radial directions with large velocity. Furthermore, detaching bubbles cause turbulences in the electrode boundary layer enhancing heat and mass transfer [13]. Mass transfer equations are commonly written in the form

$$\text{Iε}\text{(n/υ)F}\text{=kA}\text{Δ}\text{c}$$

not exhibiting the bubble coverage. This definition must not suggest that the bubble coverage is not involved. All available mass transfer equations [13] incorporate it in the mass transfer coefficient k. In case a mass transfer equation does not explicitly exhibit Θ [14] it is an approximation applicable in a limited range of the (nominal) current density where the shielding effect is fairly compensated by the action of microconvection.

In application to the gaseous product the situation is further complicated by the fact that the product is transported from the electrode by two possible paths [15], [16]. The product, primarily formed at the electrode as dissolved gas is not totally transferred to the bulk; a fraction of the total rate is transferred to the gas–liquid interface of the adhering bubbles (or more strictly, of the bubbles present in the concentration boundary layer of the electrode), crosses the interface and causes bubble growth. Only the complementary amount enters the bulk. As a result, the mass flow rate to the bulk varies within the concentration boundary layer. Mass transfer equations for dissolved gas take this feature into account [17]. It stands to reason that the bubble coverage is the controlling parameter in that it affects not only the active electrode area and the (nearly congruent) mass transfer area but also the gas–liquid interfacial area and thus the effective rate of mass transfer to the bulk.

The value of the fractional bubble coverage Θ is not only affected by the conditions of mass transfer to adhering bubbles. Bubbles at electrodes can only be formed at active nucleation sites, i.e. irregularities on the electrode surface. Therefore, Θ depends on state and material of the electrode surface. Moreover, nucleation requires a sufficient interfacial supersaturation with dissolved gas which, in turn is controlled by the current density and the mass transfer coefficient k. The latter is affected by the above mentioned (bubble-induced) microconvection and also by (liquid flow-induced) macroconvection. In this way, the velocity of liquid flow parallel to the electrode surface must exert effect on the bubble coverage.

Hitherto, little notice has been taken of this effect. Numerous experimental data are available for stagnant electrolytes, but only one old, but valuable investigation on flowing liquids is known to the authors. Sillen [18], [19] investigated the bubble coverage at anodes and cathodes in flowing KOH solution and presented some data showing the effect of current density and of flow velocity. Data of Θ decreased as the flow velocity was increased. Sillen concluded that the action on Θ is probably small at large values of the nominal current density and low velocity.

Usually, estimates of mass transfer or limiting current density are satisfied with bubble coverage data obtained in stagnant electrolyte, i.e. the common laboratory arrangement. However, this procedure would only be justified in case discrepancies to flowing liquids are not noticeable. As shown below, such simplification is not admissible if the velocity is not very small. Industrial electrochemical reactors are all (or at least in the vast majority of cases) operated with flowing electrolyte. Flow velocities in the order of 1 m s⁻¹ are not extraordinary. It is the object of the present paper to develop a theoretical basis of the action of flow velocity on the fractional bubble coverage and to verify the result by laboratory investigation.