Journal of Flow Chemistry

, Volume 9, Issue 1, pp 59–71 | Cite as

Mathematical modeling of the electrochemical degradation of 2-chlorophenol using an electrochemical flow reactor equipped with BDD electrodes

  • Alejandro Regalado-MéndezEmail author
  • Abril Cruz-López
  • Juan Mentado-Morales
  • Mario E. Cordero
  • Luis G. Zárate
  • Martín R. Cruz-Díaz
  • Gianpaolo Fontana
  • Ever Peralta-ReyesEmail author
Full Paper


The objective of this work was to develop a mathematical model of an electrochemical flow reactor for the degradation of 2-chlorophenol. The reactor operates in batch recirculation and undivided mode under mass transport control and under galvanostatic conditions. The mathematical model proposed here was simulated on COMSOL Multiphysic® 5.3 software (involving the continuity and Navier-Stokes equation in a laminar regime, and the diffusion-convection equation with reaction term) interacting with the MATLAB® version R 2017a software (continuous stirred tank). The electrolysis process was carried out at a current density of 0.14 A m−2, a liquid flow rate of 1 L min−1 and pH = 7.3. The main results show that the mathematical model proposed here is in a very good agreement with the experimental study (correlation coefficient of 0.9917 and a reduced root-mean-square error of 0.4041). The final concentration of 2-chlorophenol estimated by the mathematical model was 0.0013 mol m−3, while the experimental concentration reached was 0.0001 mol m−3, confirming the predictive capacity of the mathematical model, as well as the efficiency of the electrochemical process implemented.

Graphical abstract


BDD electrodes Electrochemical flow reactor 2-chlorophenol degradation Mathematical modeling 



Liquid flow velocity, m s−1

\( {D}_H=\frac{4{A}_{Cross}}{P_{Wet}} \)

Equivalent hydraulic diameter of the rectangular flow channel, m

ACross = Wch × (Sch − Se)

Area of cross section, m2

PWet = 2Wch + 2(Sch − Se)

Wet perimeter, m


Channel width, m


Channel thickness, m


Electrode thickness, m


Tank volume, L


Liquid flow rate, L min−1


Current density, A cm2

C2 −  CPh

Concentration of 2-chlorophenol, mol m−3

C2 −  CPh, 0

Initial concentration of 2-chlorophenol, mol m−3

\( {C}_{2- CPh}^{\mathrm{exp}} \)

2-CPh concentrations of experiment, mol m−3

\( {C}_{2- CPh}^{theor} \)

2-CPh concentrations of theoretical model, mol m−3


Logarithmic scale of acidity or basicity, dimensionless


Hydroxyl radical


Negative base-10 logarithm of the acid dissociation constant

\( {K}_{ow}^a \)

Octanol–water partition coefficient, dimensionless


Apparent first-order reaction rate constant, h−1


Reaction rate model, mol m−3 h−1


Outlet concentration of the 2-CPh from tank that feeds the reactor, mol m−3


Time, h


Diffusion coefficient, m2 s−1


Pressure, Pa


Initial pressure, Pa


Hydrodynamic pressure, Pa


Unit momentum vector, dimensionless


Volume force, N m−3

\( \tilde{n} \)

Unit normal vector, dimensionless


Gravity acceleration constant, m s−2


Number of data points


Molar flux, mol h−1 m−2


Correlation coefficient



Kinematic viscosity of the fluid, m2 s−1


Density of the fluid, kg L−1


Dynamic viscosity of the fluid, kg m−1 s−1


Dimensionless groups

\( \operatorname{Re}=\frac{u{D}_H}{\nu } \)

Reynolds number, dimensionless



Ultrahigh-performance liquid chromatography


Boron-doped diamond




Dimensionally stable anode


Residence time distribution


Continuous stirred tank


Reduced root-mean-square error


Computational fluid dynamics



The authors are thankful for the support of the Programa para el Desarrollo Profesional Docente (PRODEP), [Project DSA/103.5/16/10242 with CUP: 2II1605, 2016]. We also wish to thank Ph.D. Aitor Aizpuru for checking the text.

Supplementary material

41981_2018_27_Fig10_ESM.png (17 kb)

(PNG 16 kb)

41981_2018_27_MOESM1_ESM.tif (40 kb)
High Resolution (TIF 40 kb)


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Copyright information

© Akadémiai Kiadó 2019

Authors and Affiliations

  1. 1.Campus Puerto ÁngelUniversidad del MarOaxacaMexico
  2. 2.Escuela de Ingeniería QuímicaUniversidad Popular Autónoma del Estado de PueblaPueblaMexico
  3. 3.Departamento de Ingeniería y Tecnología, Facultad de Estudios Superiores CuautitlánUniversidad Nacional Autónoma de MéxicoCuautitlán IzcalliMexico

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