A Simple 1D Convection-Diffusion Model of Oxalic Acid Oxidation Using Reactive Electrochemical Membrane
Abstract
:1. Introduction
2. Mathematical Model
2.1. The Geometry of the System under Study
2.2. The Problem Formulation
- The transport number of organic compound is negligible compared to the transport number of the supporting electrolyte. Thus, only diffusion and convection fluxes are considered;
- The system under study is in a steady state, thus only the faradaic current is taken into account;
- Since the experiment proceeds under room conditions and the supporting electrolyte does not participate in the reactions, the gradients of temperature, activity coefficients, and density are ignored;
- The oxygen concentration in the solution exceeds the solubility limit only at the lowest TOC fluxes and is insufficient at given current density [31]; thus, the bubble-formation caused by oxygen evolution is not taken into account;
- The rate constant of oxalic acid oxidation by hydroxyl radicals is very small, thus, we assume that all the hydroxyl radicals are spent on the oxygen molecules formation;
- According to the conditions of the experiment [5], the bulk solution is considered perfectly mixed and renewable, so the oxalic acid concentration in it is assumed constant.
3. Results and Discussion
3.1. The Treatment of Experimental Data
3.2. Effect of Increasing Concentration at a Constant Transmembrane Pressure
3.3. Effect of Increasing Transmembrane Pressure at Constant Concentration
3.4. The Oxygen Evolution in Pores of the Reactive Electrochemical Membrane
3.5. The Current Density, Potential, and Overpotential Distributions
3.6. Effect of Current Density on Mineralization Current Efficiency
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Definition | Value | Reference |
---|---|---|---|
εs | fraction volume of solution in REM (porosity) | 0.41 | [5] |
εm | fraction volume of electrode material in REM | 1 − εs | [5] |
DOA | diffusion coefficient of OA | 1.0 × 10−9 m2/s | [41] |
DO2 | diffusion coefficient of O2 | 2.0 × 10−9 m2/s | [42] |
dispersion coefficient | v × 3 × 10−4 m | * | |
av | specific surface area of the electrode | 108 1/m | [5] |
electrolyte conductivity | 1.3 S/m | [5] | |
electrode conductivity | 1.3 S/m | ||
σ | permeability coefficient | 1.7 × 10−14 m2 | [5] |
μ | dynamic viscosity | 8.9 × 10−4 Pa×s | |
d | REM thickness | 2 mm | [5] |
exchange current density of OA | −10−6 A/m2 | * | |
exchange current density of O2 | −10−6 A/m2 | * | |
concentration of OA to which the exchange current density is referred | 0.75 mol/m3 | * | |
electron transferred coefficient in reaction (11) | 0.5 | * | |
electron transferred coefficient in reaction (10) | 0.125 | * | |
number of electrons transferred in reaction (11) | 2 | ||
number of electrons transferred in reaction (10) | 4 | ||
formal potential for oxidation of OA | 2.02 V | * | |
formal potential in reaction (11) | 1.8 V | * | |
stoichiometric coefficient of OA in reaction (11) | −1 | ||
stoichiometric coefficient of O2 in reaction (10) | 1 | ||
itot | total current density | −150 A/m2 | [5] |
temperature | 298.15 K | [5] | |
δ | diffusion layer thickness | 30 μm | [30] |
km | mass transfer coefficient | [35] | |
ψ | shape factor | 0.86 | |
ν | kinematic viscosity | 8.9 × 10−7 m2/s |
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Skolotneva, E.; Cretin, M.; Mareev, S. A Simple 1D Convection-Diffusion Model of Oxalic Acid Oxidation Using Reactive Electrochemical Membrane. Membranes 2021, 11, 431. https://doi.org/10.3390/membranes11060431
Skolotneva E, Cretin M, Mareev S. A Simple 1D Convection-Diffusion Model of Oxalic Acid Oxidation Using Reactive Electrochemical Membrane. Membranes. 2021; 11(6):431. https://doi.org/10.3390/membranes11060431
Chicago/Turabian StyleSkolotneva, Ekaterina, Marc Cretin, and Semyon Mareev. 2021. "A Simple 1D Convection-Diffusion Model of Oxalic Acid Oxidation Using Reactive Electrochemical Membrane" Membranes 11, no. 6: 431. https://doi.org/10.3390/membranes11060431