Abstract
Chemical engineering calculations are performed for a new type of monopolar electrolyser with power leads located on its sides, used for chlorate production. The calculation gives the value of the total cell voltage as well as of local current densities for given current load and given electrode dimensions, interelectrode gap etc. On this basis the optimization of the system is possible.
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Abbreviations
 a _{A} :

constanta for the calculation of anode potential, see Equation 2a (V)
 a _{K} :

constanta for the calculation of cathode potential, see Equation 2b (V)
 b _{A} :

constantb for the calculation of anode potential, see Equation 2a (V)
 b _{K} :

constantb for the calculation of cathode potential, see Equation 2b (V)
 a′ _{A},a′ _{K} :

constants in linearized Equations 3a and 3b (V)
 b′ _{A},b′ _{K} :

constants in linearized Equations 3a and 3b (Ω cm^{2})
 d :

electrode distance (cm)
 D _{G} :

average diameter of bubbles at pressureP _{0} (cm)
 F :

Faraday's constant; 964 96 C
 F _{G},F _{E} :

effective crosssection of interelectrode channel for the flow of gas and the electrolyte, respectively (cm^{2})
 F _{p} :

crosssection occupied by current leads placed in interelectrode channel for one cell (cm^{2})
 F _{T} :

total crosssection of interelectrode channel for one cell (cm^{2})
 F _{R} :

crosssection for one copper rod outside the cell (cm^{2})
 g :

acceleration due to gravity; 981 cm s^{−2}
 I _{o} :

total current (A)
 I _{T} :

current flowing through one cell=I _{o}/n _{c} (A)
 I _{ x } :

current flowing through an electrode strip at a heightx and a distancey from the origin (A)
 I _{T,x } :

current flowing through an electrode strip at a heightx andy=0 (A)
 I _{p,x } :

current consumed by electrochemical reaction at a heightx betweeny=0 andy=y (A)
 i _{ x,y } :

local current density (A cm^{−2})
 ī _{ x } :

average current density at a heightx (A cm^{−2})
 ¯i :

average current density=I _{T}/wL (A cm^{−2})
 K _{1} :

criterion cf. Equation 32
 K _{1,x } :

criterion cf. Equation 25
 K _{2} :

criterion cf. Equation 26
 K _{3} :

criterion cf. Equation 22
 K _{3,x } :

criterion cf. Equation 21
 K _{4} :

criterion cf. Equation 33
 K _{4,A} :

criterion cf. Equation 27
 K _{4,K} :

criterion cf. Equation 28
 K _{4,L} :

criterion cf. Equation 29
 K _{5} :

criterion cf. Equation 38
 L :

height of electrode (cm)
 L _{A},L _{K} :

length of copper rods outside the electrolyser (cm)
 n _{A} :

number of equivalents per mole for anodic process yielding a gaseous phase
 n _{C} :

number of cells in electrolyser
 n _{K} :

number of equivalents per mole for cathodic process yielding a gaseous phase
 n _{r} :

number of copper rods outside the electrolyser
 P :

local pressure (atm)
 P _{o} :

pressure on top of electrolyser (atm)
 P _{w} :

pressure of water vapour in equilibrium with electrolyte (atm)
 R :

gas constant (cm^{3} atm [mol° K]^{−1})
 (Re)_{G} :

Reynolds number for bubbles
 S _{A} :

anode thickness (cm)
 S _{K} :

cathode thickness (cm)
 s _{E} :

specific gravity of electrolyte (g cm^{−3})
 s _{G} :

specific gravity of gas (g cm^{−3})
 s _{M} :

specific gravity of gaselectrolyte mixture (g cm^{−3})
 T :

absolute temperature (° K)
 U _{A},U _{K} :

ohmic voltage drops in anode and cathode, respectively (V)
 U _{LA},U _{LK} :

ohmic voltage drop in anode and cathode leads, respectively (V)
 U _{M} :

ohmic voltage drop in the electrolyte in thez direction (V)
 U _{T} :

cell voltage (V)
 U _{AB},U _{CD} :

ohmic voltage drop between copper rods and electrodes, see Fig. 5 (V)
 ν _{E} :

rate of electrolyte flow in interelectrode channel (cm s^{−1})
 ν _{ET} :

rate of electrolyte flow in interelectrode channel at the top (cm s^{−1})
 ν _{G} :

rate of gas flow in interelectrode channel (cm s^{−1})
 ν _{GT} :

rate of gas flow in interelectrode channel at the top (cm s^{−1})
 ν _{R} :

velocity of bubbles corresponding to buoyance (cm s^{−1})
 V _{E} :

volume flow rate of electrolyte in interelectrode channel (for one cell) (cm^{3} s^{−1})
 V _{G} :

volume rate of gas flow in interelectrode channel (for one cell) (cm^{3} s^{−1})
 V _{GT} :

volume rate of gas flow in interelectrode channel at the top (cm^{3} s^{−1})
 w :

width of the active surface of an electrode (cm)
 w _{A} :

width of the inactive part of an anode (cm)
 w _{K} :

width of the inactive part of cathode (cm)
 w _{AE} :

width of the inactive part of an anode embedded in electrolyte (cm)
 w _{KE} :

width of the inactive part of a cathode embedded in electrolyte (cm)
 x, y, z :

length in the direction of coordinates
 α,α _{T} :

volume fraction of bubbles at a heightx and at the top
 ε _{A},ε _{K} :

anodic and cathodic potentials
 η _{A} :

anodic current efficiency for gas evolution
 η _{K} :

cathodic current efficiency for gas evolution
 v :

kinematic viscosity of electrolyte (cm^{2} s^{−1})
 ρ _{A} :

specific resistance of an anode (Ω cm) 5.76×10^{−5}
 ρ _{K} :

specific resistance of a cathode (Ω cm) 1.21×10^{−5}
 ρ _{E} :

specific resistance of electrolyte (Ω cm)
 ρ _{M} :

specific resistance of a gaselectrolyte mixture between electrodes (Ω cm)
 ξ _{A} :

ratio of active anode surface to the productwL
 ξ _{K} :

ratio of active cathode surface to the productwL
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Roušar, I., Cezner, V., Nejepsová, J. et al. Calculation of local current densities and terminal voltage for a monopolar sandwich electrolyser: application to chlorate cells. J Appl Electrochem 7, 427–435 (1977). https://doi.org/10.1007/BF00615947
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Keywords
 Physical Chemistry
 Total Cell
 Chlorate
 Chemical Engineering
 Engineering Calculation