Abstract
Using a continuous flow stirred tank electrochemical reactor model, the stability and transient response of electrolytic reactors is analysed in terms of a Liapunov function and digital simulation.
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Abbreviations
- a e :
-
electrode area
- A i :
-
reactor wall area; i=2, 3, 4, 5 denote the four vertical walls of a rectangular tank;A 1 is tank bottom area;A 6 is area of the electrolyte surface
- b :
-
slope of the polarization curve
- c :
-
electrolyte concentration;c i its inlet value;c * its steady state value
- C p :
-
specific heat of the electrolyte
- d 1 :
-
thickness of the reactor walls
- F :
-
Faraday's constant
- G :
-
electrolyte mass flow rate
- h 6 :
-
heat transfer coefficient associated with electrolyte surfaceA 6
- I :
-
electric current
- k :
-
geometric aspect ratio (electrode separation distance divided by electrode area)
- k 1 :
-
thermal conductivity of the reactor wall
- m e :
-
mass of the electrolyte in the reactor
- Q :
-
quantity defined by Equation 8a
- Q L :
-
rate of heat dissipation
- q :
-
electrolyte volumetric flow rate
- R :
-
quantity defined by Equation 8b
- R e :
-
electrolyte resistance
- S :
-
quantity defined by Equation 8c
- T :
-
electrolyte temperature;T i its inlet values,T * its steady state value
- t a :
-
ambient temperature
- t f :
-
floor temperature
- t :
-
time
- U :
-
voltage drop
- U i :
-
wall-to-ambient overall heat transfer coefficient associated with wallA i
- V(x):
-
Liapunov function
- V t :
-
active reactor volume (free electrolyte volume)
- X 1 :
-
dimensionless temperature
- x 2 :
-
dimensionless concentration
- z :
-
valency
- α, β :
-
lumped parameters defined by Equations 19a and b
- ΔHR :
-
heat of reaction
- ε, δ :
-
parameters of the Liapunov matrix
- γ :
-
quantity defined by Equation 8e
- Γ:
-
quantity defined by Equation 9a
- θ :
-
dimensionless time
- π :
-
electrolyte density
- σ :
-
electrolyte conductivity
- φ * :
-
quantity defined by Equation 9b
- ψ :
-
quantity defined by Equation 8d
- x1, x2 :
-
derivatives of x1 and x2 with respect to θ (Equation 12)
References
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Fahidy, T.Z. Stability and transient response of an electrolytic reactor. J Appl Electrochem 14, 231–240 (1984). https://doi.org/10.1007/BF00618741
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DOI: https://doi.org/10.1007/BF00618741