A model for correlating mass transfer data at gas evolving electrodes

With reference to models for heat transfer phenomena in nucleate boiling, a model is presented to correlate mass transfer data at gas evolving electrodes. Mathematical treatment of the model results in an equation appropriate for practical use. Comparison with experimental data by several authors shows satisfactory agreement.     

Mass transfer at gas evolving electrodes with superposition of hydrodynamic flow

Mass transfer at gas evolving electrodes with additional major hydrodynamic liquid flow is influenced by two phenomena: effects directly resulting from the generated bubbles and effects by high liquid velocity parallel to the electrode surface. For the case superposition of both mechanisms, being of great industrial importance, a method is presented to quantitatively describe mass transfer.     

Heat transfer at gas evolving electrodes

The outlines of an available concept for heat transfer at gas evolving electrodes (Zuber—Magrini) are discussed. A new method for prediction of heat transfer on the basis of the analogy between heat and mass transfer is derived from known theoretical equations and tested in comparison to experimental data of various workers.     

Mass transfer at gas evolving electrodes

To elucidate the mechanism of the mass transfer at a gas evolving electrode, the thickness of the diffusion layer δ has been determined as a function of the volume rate of the gas evolution ν, for both hydrogen and oxygen evolving electrodes in alkaline solution. The effect of electrode material, alkaline concentrations, roughness, position and disk diameter of the electrode, gas pressure and of temperature upon the δ/gn relation is given. A low absolute value of the slope of the log δ/log ν, of about 0.3 is found experimentally when no coalescence of gas bubbles occurs and a high one, that is about 0.9 when coalescence occurs frequently. It has been concluded from the experimental results that the mass transfer can be explained on the basis of the hydrodynamic model when no coalescence of gas bubbles occurs and on that of the penetration model when coalescence occurs frequently.     

Mass transfer at gas evolving electrodes

A new convection—penetration model for mass transfer of indicator ions to a gas-evolving electrode with forced convection of solution is described theoretically. It has been found that the mass transfer of indicator ions to a gas-evolving electrode can be described well by the new model. The contribution of an oxygen bubble departing from the electrode surface to the mass transfer is much greater than the contribution of a departing hydrogen bubble.     

Mass transfer at cylindrical gas evolving electrodes

Mass transfer coefficients at cylindrical, H₂ evolving electrodes, were measured by determining the reduction rate of K₃Fe(CN)₆. The variables studied were: gas discharge rate V, diameter of the cylinder D, height and position of the cylinder. The diameters ranged from 0·2–2·5 cm, the cd from 25-380 mA/cm². For horizontal cylinders, the following correlation was found: log K = a + 2·17 log(V^0·11/D^0·08). The application of gas evolving cylindrical electrodes in industrial electrolysis is discussed in comparison with rotating electrodes.     

Mass transfer at gas evolving screen electrodes

Mass transfer coefficients at horizontal gas evolving screen electrodes were measured by determining the reduction rate of K₃Fe(CN)₆. The variables studied were: gas discharge rate, number of screens per electrode and distance between screens. The relation between the mass transfer coefficient and H₂ discharge rate was found to be:

The mass transfer coefficient was found to go through a minimum when increasing the number of screens per electrode. Screen spacing has a slight effect on the mass transfer coefficient.Mass transfer coefficients were also measured for the deposition of copper from a copper sulphate solution at a horizontal screen cathode stirred by oxygen evolved at a horizontal anode placed below the cathode. The relation between the mass transfer coefficient and the gas discharge rate was found to be.

Useful application for purposes of cell design is pointed out.     

A hydrodynamic model for the ohmic interelectrode resistance of cells with vertical gas evolving electrodes

A hydrodynamic model of a cell with gas evolving vertical electrodes is developed. The leading assumption is a separation of the ohmic resistance of the dispersion of gas bubbles in electrolyte between the electrodes into two parts: a stagnant boundary layer at the electrode(s) being enriched in gas and a flowing bulk in the centre region. The mathematical treatment of the model leads to equation (18) which allows to predict the mean ohmic resistance of the dispersion in the cell. Results are compared with experimental data.     

Note on mass transfer at gas sparged electrodes

Mass transfer at vertical plates with gas sparging obeys formally the same correlation as mass transfer in turbulent natural convenction due to concentration or temperature differences. A model is presented which allows a theoretical interpretation of this result.     

The role of mass transfer in the electrolytic reduction of hexavalent chromium at gas evolving rotating cylinder electrodes

The rate of electrolytic reduction of hexavalent chromium from acidic solution at a hydrogen-evolving rotating cylinder lead cathode was studied under conditions of different current densities, Cr⁶⁺ concentrations and rotation speeds. The rate of the reaction was found to follow a first order rate equation. The specific reaction rate constant was found to increase with increasing rotation speed until a limiting value was reached with further increase in rotation speed. Mechanistic study of the reaction has shown that at relatively low rotation speeds the reduction of Cr⁶⁺ is partially diffusion controlled, at higher speeds the reaction becomes chemically controlled. The limiting specific reaction rate constant was related to the operating current density by the equationK=0.044i ^1.385. The current efficiency of Cr⁶⁺-reduction was measured as a function of current density, initial Cr⁶⁺ concentration and rotation speed. Possible practical applications are discussed.Nomenclature A electrode area (cm²) - a, b constants in Equations 5 and 13, respectively - C bulk concentration of Cr⁶⁺ at timet(M) - C _o initial concentration of Cr⁶⁺ (M) - C _i interfacial concentration of Cr⁶⁺ (M) - d cylinder diameter (cm) - D diffusivity of Cr⁶⁺ (cm² s^–1) - e _o standard electrode potential (V) - F Faraday's constant (96 487 C) - current consumed in hydrogen discharge (A) - i current density (A cm^–2) - I cell current (A) - K _l mass transfer coefficient (cm s^–1) - K _r mass transfer coefficient due to cylinder rotation (cm s^–1) - K _o natural convection mass transfer coefficient (cm s^–1) - K _g mass transfer coefficient due to hydrogen stirring (cm s^–1) - K ₂ specific reaction rate constant (cm s^–1) - K overall rate constant (cm s^–1) - m theoretical amount of Cr⁶⁺ reduced during electrolysis (g) - P gas pressure (atm) - R gas constant (atm cm³ mol^–1 K^–1) - T temperature (K) - t time (s) - V linear speed of the rotating cylinder (cm s^–1) - hydrogen discharge rate (cm³ cm^–2 s^–1) - V _s solution volume (cm³) - z electrochemical equivalent (g C^–1) - Z number of electrons involved in the reaction - Re Reynolds number (Vd/v) - Sh Sherwood number (K _r d/D) - Sc Schmidt number (v/D) - rotation speed (r.p.m.) - kinematic viscosity (cm² s^–1)     

An approximate model for mass transfer with reaction inporous gas diffusion electrodes

An approximate model for reactant mass transfer in fuel cell electrodes has been formulated which considers gaseous diffusion in the hydrophobic Teflon phase, diffusion across a thin electrolyte film at the surface of the catalyst phase, and internal diffusion with first order reaction in the electrolyte-filled catalyst phase. An analytical solution is presented which indicates the fraction of the “activation only” current density that is obtained from the electrode. Application of this model for low reactant concentrations should allow a more quantitative evaluation of important mass transfer processes in fuel cell electrodes.     

Mass transfer characteristics of electrochemical reactors employing gas evolving mesh electrodes

Mass transfer rates were measured at a single screen and a fixed bed of closely packed screens for the simultaneous cathodic reduction of K₃Fe(CN)₆ and anodic oxidation of K₄Fe(CN)₆ in alkaline solution with H₂ and O₂ evolution, respectively. Variables studied were gas discharge rate, number of screens per bed and position of the electrode (vertical and horizontal). For single screen electrodes, the mass transfer coefficient was related to the gas discharge rate by the equations: $$\begin{gathered} K = aV^{0.190} , for H_2 evolving electrodes, \hfill \\ K = aV^{0.469} , for O_2 evolving electrodes \hfill \\ \end{gathered} $$ . Electrode position was found to have no effect on the rate of mass transfer for single and multiscreen electrodes in the case of H₂ and O₂ evolution. Mass transfer coefficients were found to increase with an increasing number of screens per bed in the case of H₂ evolution, while in the case of O₂ evolution the mass transfer coefficient decreased with an increasing number of screens per bed. A mathematical model was formulated to account for the behaviour of the H₂ evolving electrode which, unlike the O₂ evolving electrode, did not obey the penetration model. Power consumption calculations have shown that the beneficial effect of mass transfer enhancement is outweighed by the increase in the voltage drop due to gas evolution in the bed electrode.     

Free convection mass transfer at horizontal electrodes

The free convection mass-transfer behaviour of upward-facing horizontal surfaces has been investigated experimentally using an electrochemical technique involving the measurement of limiting currents for the deposition of copper on copper electrodes from acidified cupric sulphate solutions. The data are well correlated by the equations

Sh = 0·64(Sc . Gr)^0·25 for 3 × 10⁴ < ScGr < 2·5 × 10⁷ and

Sh = 0·16(Sc . Gr)^0·33 for 2·5 × 10⁷ < ScGr < 10¹². Electrode diameters varied between 0·1 and 12 cm and cupric sulphate concentrations between 0·01 and 0·3 M.

The data compare favourably with previous experimental results for the corresponding heat-transfer case.     

Mass transfer at gas sparged spherical electrodes

Rates of mass transfer were measured for the cathodic reduction of K₃ Fe(CN)₆ in a large excess of sodium hydroxide at a single sphere cathode stirred by oxygen evolved at a horizontal disc anode placed below. The effect of the oxygen discharge rate and sphere diameter were studied at different ferricyanide concentrations. The rate of mass transfer was found to increase by an amount ranging from 66% to 450% over the natural convection value depending on the operating conditions. The data were correlated using hydrodynamic boundary layer theory and Kolmogoroff's theory of isotropic turbulence. The data were found to fit the equation: Sh = 2 + 0.21 Sc ^0.33 (ed _s ⁴/v ³)^0.268 where e is the rate of energy dissipation/unit mass of the liquid. Previous data on mass transfer at fixed beds of spheres stirred by counterelectrode oxygen bubbles were also correlated.     

Potential distribution along gas evolving electrodes

This paper reports an experimental study of gas-evolving electrodes made of expanded metal. The variations of the cell voltage with the electrolyte velocity and the intensity of the current are studied for different orientations of the mesh with respect to the electrolyte flow direction. Using probes, the solution potential distributions along the electrodes are obtained.Paper presented at the International Meeting on Electrolytic Bubbles organized by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.     

Comparative analysis of mass transfer at vibrating electrodes

The application of oscillatory flows to electrochemical processes was found to increase the rate of mass transfer and improve the quality of deposit. Various mechanisms to which this phenomenon is attributable are discussed and expressions for the average rate of mass transfer, resulting thereof, are derived. Comparison with experimental data indicates that the stretched-film concept, although an oversimplification of the physical situation, is most successful in correlating the data.Nomenclature A Amplitude of oscillatory motion (cm) - c Concentration of the diffusing species (g mol cm^–3) - D Diffusivity (cm² s^–1) - F Frequency of oscillation (Hz) - k Instantaneous mass transfer coefficient (cm s^–1) - ¯k _vib Time-average vibratory mass transfer coefficient (cm s^–1) - L Length of active area (cm) - S Velocity gradient at solid-liquid interface (cm s^–1 cm^–1) - u Oscillatory velocity of fluid layers adjacent to the electrode (cm s^–1) - _u Rel Relative velocity between the electrode and the bulk of the fluid (cm s^–1) - v Relative velocity between the electrode and the fluid layers adjacent to it (cm s^–1) - W Width of active area (cm) - x Distance along the surface of the electrode (cm) - z Distance perpendicular to the surface of the electrode (cm) - Dimensionless distance=z(S/9Dx)^1/3 - Dimensionless distance=z ²/2 - Kinematic viscosity of the electroyte (cm² s^–1) - Angular frequency=2F     

Gas diffusion electrodes improve hydrogen gas mass transfer for a hydrogen oxidizing bioanode

Background

Bioelectrochemical systems (BESs) are capable of recovery of metals at a cathode through oxidation of organic substrate at an anode. Recently, also hydrogen gas was used as an electron donor for recovery of copper in BESs. Oxidation of hydrogen gas produced a current density of 0.8 A m^‐2 and combined with Cu²⁺ reduction at the cathode, produced 0.25 W m^‐2. The main factor limiting current production was the mass transfer of hydrogen to the biofilm due to the low solubility of hydrogen in the anolyte. Here, the mass transfer of hydrogen gas to the bioanode was improved by use of a gas diffusion electrode (GDE).

Results

With the GDE, hydrogen was oxidized to produce a current density of 2.9 A m^‐2 at an anode potential of –0.2 V. Addition of bicarbonate to the influent led to production of acetate, in addition to current. At a bicarbonate concentration of 50 mmol L^‐1, current density increased to 10.7 A m^‐2 at an anode potential of –0.2 V. This increase in current density could be due to oxidation of formed acetate in addition to oxidation of hydrogen, or enhanced growth of hydrogen oxidizing bacteria due to the availability of acetate as carbon source. The effect of mass transfer was further assessed through enhanced mixing and in combination with the addition of bicarbonate (50 mmol L^‐1) current density increased further to 17.1 A m^‐2.

Conclusion

Hydrogen gas may offer opportunities as electron donor for bioanodes, with acetate as potential intermediate, at locations where excess hydrogen and no organics are available. © 2017 The Authors. Journal of Chemical Technology & Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.     

A model for mass transfer in packed towers: mass transfer with controlling resistance in the gas phase

A model for mass transfer in the liquid phase in packed towers, proposed in a previous work[5], is employed in the case of mass transfer with controlling resistance in the gas phase. On taking into account the semistagnant liquid pockets by the liquid residence time distribution function, relationships are established between the volumetric mass transfer coefficients in different operations: evaporation, physical absorption, chemical absorption. The calculated values of the mass transfer coefficients agree well with experimental data.