Calculations on the effect of gas evolution on the current-overpotential relation and current distribution in electrolytic cells

Gas evolution during electrode reactions has several effects on the electrode behaviour. One of these effects is the nonuniform increase of the resistivity of the electrolyte with the resultant increase of IR drop through the solution and the distortion of current distribution. Calculations of these effects are presented for an electrode built of vertical blades. This geometry has the peculiarity that it allows the inclusion of linear polarization and gas effects in the treatment, without the necessity to use numerical or approximate solutions of the differential equations. It is shown that the system parameters can be combined into a single dimensionless parameter to describe those aspects of the electrode behaviour which depend on the gas evolution. The parameters examined include the geometry of the electrode, the polarization resistance, gas bubble rise velocity, and solution resistivity. Expressions are given for optimization of the electrode geometry to achieve minimum overpotential.Nomenclature b Polarization resistance ( cm²) - C Constant, =RT( + t)/lPtFs (A^–1cm) - E(x) Potential of the solution at pointx (V) - f _av Average volume fraction of gas (dimensionless) - (fy) Volume fraction of gas at heighty (dimensionless) - f(Y) Volume fraction of gas at reduced heightY (dimensionless) - F Faraday number (coulomb mol^–1) - h Height of the electrode (cm) - i Nominal current density of the electrode =I _T/hw (A cm^–2) - i(y) Local electrode current density at heighty (A cm^–2) - i(Y) Local electrode current density at reduced heightY (A cm^–2) - i _f(x) Faradaic current density at pointx (A cm^–2) - i _f(X) Faradaic current density at reduced lengthX (A cm^–2) - i _f,av Average faradaic current density in the slot=I _s/2hl(Acm^–2) - I _s Total current entering one slot (A) - I _T Total current flowing to the electrode (A) - I(x) Current flowing in the solution phase of one slot at pointx (A) - k Constant, = (2/b)^1/2 (cm^–1) - K Dimensionless parameter =hRT(2/b)^1/2/4lPzFs, or = 1–(1–iCh)^1/4 - l Horizontal length of the slot (cm) - n Number of slots on the electrode (dimensionless) - p Pressure of gas liberated on the electrode (assumed to be independent of height) (atm) - R Universal gas constant (cm³ atm K^–1 mol^–1) - s Bubble rise velocity (cm s^–1) - t Thickness of the blades (cm) - T Temperature of the gas (K) - dV(y) Volume of gas present in a volume element of the slot (cm³) - w Width of the electrode (cm) - x Horizontal distance from the back plate (cm) - X Reduced horizontal distance =x/l (dimensionless) - y Vertical distance from the bottom of the electrode (cm) - Y Reduced vertical distance =y/h (dimensionless) - z Number of Faradays needed to produce one mole of gas (mol^–1) - Width of a slot (blade spacing) (cm) - Measured overpotential of the electrode =(l)(V) - (x) Overpotential at pointx (V) - Resistivity of gas free electrolyte ( cm) - (y) Resistivity of gas filled electrolyte at, heighty ( cm).