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An efficient method for solving the model equations of a two dimensional packed bed electrode

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Abstract

A theoretical and experimental study of a flow-by packed bed electrochemical reactor consisting of graphite particles is given. The mathematical model describes the two dimensional distributions of electrode potential and reactant concentration in the reactor, and includes the influence of lateral dispersion between the feeder electrode and membrane. A new efficient numerical method, based on central finite difference and orthogonal collocation is used to solve the model. Results of the model simulations agree well with experimental measurement of the potential distribution for the ferrocyanide/ferricyanide system.

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Abbreviations

a :

specific surface area of packed bed electrode (cm−1)

c i :

concentration of speciesi(i = 2 for cathodic species) (mol dm−3)

c i0 :

inlet concentration of speciesi (mol dm−3)

C :

dimensionless concentration

c s :

concentration on the electrode surface (mol dm−3)

C s :

dimensionless concentration on the electrode surface

D s :

effective diffusion coefficient (cm2s−1)

Da :

Damköhler number

F :

Faraday's constant (96 487 C mol−1 of electrons)

i :

current density (A m−2)

i 0 :

exchange current density (A m−2)

I :

number of equation

j 2 :

electrochemical reaction rate per unit area (mol cm−2 s−1)

J :

number of node point

k a :

average local mass transfer coefficient (cm s−1)

n :

number of moles of electrons

N :

number of inner collocation points

N 2 :

flux of species 2 (mol cm−2 s−1)

Pe :

Peclet number

R :

gas constant (8.314 J mol−1 K−1)

Sh m :

modified Sherwood number

T :

temperature (K)

u a :

average axial velocity (cm s−1)

x :

lateral coordinate (cm)

x 0 :

electrode depth (cm)

X :

dimensionless depth of electrode

y :

axial coordinate (cm)

y 0 :

electrode length (cm)

Y :

dimensionless length of electrode

z 0 :

electrode width (cm)

α:

aspect ratio

αa :

anodic transfer coefficient

αc :

cathodic transfer coefficient

η:

overpotential (V)

ν:

stoichiometric coefficient

ζ:

dimensionless rate constant

δ2 :

effective conductivity of electrolyte (Ω−1 cm−1)

ϕ1 :

potential of electrode (V)

ϕ2 :

potential of electrolyte (V)

ϕeq :

equilibrium potential (V)

θ:

dimensionless potential

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Sun, Y.P., Xu, W.L. & Scott, .. An efficient method for solving the model equations of a two dimensional packed bed electrode. J Appl Electrochem 25, 755–763 (1995). https://doi.org/10.1007/BF00648630

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Keywords

  • Graphite
  • Model Equation
  • Finite Difference
  • Electrode Potential
  • Electrochemical Reactor