# Current distribution in a two-dimensional narrow gap cell composed of a gas evolving electrode with an open part

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## Abstract

On the basis of the observation of gas bubbles evolved by electrolysis, a two-dimensional vertical model cell composed of electrodes with open parts for releasing gas bubbles to the back side is proposed. The model cell consists of two layers. One layer forms a bubble curtain with a maximum volume fraction of gas bubbles in the vicinity of the working electrode with open parts. The other. being located out of the bubble layer, is a convection layer with a small volume fraction distributed in the vertical direction under forced convection conditions. The cell resistance and the current distribution were computed by the finite element method when resistivity in the back side varied in the vertical direction along the cell. The following three cases for overpotential were considered: no overpotential, overpotential of the linear type and overpotential of the Butler-Volmer type. It was found that the cell resistance was determined not only by the interelectrode gap but also by the percentage of open area and in some cases by the superficial surface area. The cell resistance varied only slightly with the distribution of the bubble layer in the back side.

### Keywords

Finite Element Method Cell Resistance Current Distribution Force Convection Back Side### Nomenclature

*b*linear overpotential coefficient given by

*b*=η/i*C*proportionality constant given by Equation 15

*d*_{1}distance between front side of working electrode and separator

*d*_{2}thickness of separator

*F*Faraday constant

*I*total current per half pitch

*i*current density at working electrode

*i*_{0}exchange current density

*L*length of a real electrolysis cell

*n*number of electrons transferred in electrode reaction

*O*_{p}percentage of open area given by Equation 1

*p*pitch, i.e. twice the length of the unit cell, defined by 2(BC) in Fig. 4

*q*thickness of bubble curtain, defined by (AM) in Fig. 4

*R*gas constant

*r*_{t}total cell resistance

*r*unit-cell resistance defined by (

*V − V*_{eq})/*I**r*_{rs}residue of

*r*from sum of*r*_{0}and*r*_{η}*r*_{0}ohmic resistance of solution when

*0*_{p}=0*r*_{η}resistance due to overpotential when

*0*_{p}=0*s*electrode surface ratio or superficial surface area given by Equation 2 for the present model

*T*absolute temperature

*t*thickness of working electrode defined by EF in Fig. 4

*V*cell voltage

*V*_{eq}open circuit potential difference between working and counter electrodes

- ν
solution velocity in cell

- ν
_{0} solution velocity at bottom of cell

*w*width of working electrode, defined by 2(DE) in Fig. 4

*x*abscissa located on cell model

*y*ordinate located on cell model

- α
anodic transfer coefficient

- β
linear overpotential kinetic parameter defined by

*b*/[ϱ_{bc}(p/2)]- dψ
infinitesimally small length on the boundary

- ε
volume fraction of gas bubbles in cell

- ζ
dimensionless cell voltage defined by

*nF(V − V*_{eq})/*RT*- η
overpotential at working electrode

- Λ
Butler-Volmer overpotential kinetic parameter defined by [

*nFi*_{0}ϱ_{bc}(p/2)]/*RT*- ν
coordinate perpendicular to boundary of model cell

- ϱ
_{1} resistivity of bubble-free solution

- ϱ
_{2} resistivity of separator

- ϱ
_{bc} resistivity of bubble curtain

- ϕ
potential in cell

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