Fluid Dynamics and Mass Transfer Study of Electrochemical Oxidation

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Thermodynamics, Transport, and Fluid Mechanics

Fluid dynamics and mass transfer study of electrochemical oxidation by CFD prediction and experimental validation Li Liu, Wangfeng Cai, Yiqing Chen, and Yan Wang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04226 • Publication Date (Web): 17 Apr 2018 Downloaded from http://pubs.acs.org on April 17, 2018

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Industrial & Engineering Chemistry Research

Fluid dynamics and mass transfer study of electrochemical oxidation by CFD prediction and experimental validation Li Liua WangFeng Caia

a

YiQing Chenb Yan Wanga*

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300350,

P. R. China b

College of Architecture and Environmental Engineering, Shenzhen Polytechnic,

Shenzhen 518000, P. R. China

ABSTRACT: Flow hydrodynamics and mass transfer have been investigated using numerical simulation and validated using experimental measurements. UV-Vis measurements have been obtained to determine the apparent heterogeneous rate constant, kapp, and adsorption-desorption equilibrium constant, K, of the electrochemical oxidation of p-Methoxyphenol (PMP). Generation of gas bubbles was visualized using a high-speed camera, and MATLAB was used to obtain the average void fraction. The experimental results show good agreement with simulation results. Two-phase bubbly flow has been described by a mathematical model based on the Euler-Euler approach. To accurately predict the two-phase bubbly flow in an electrolyser, a developed model of interfacial area concentration has been adopted for bubble size effects. This study shows that different operating conditions affect the void fraction and gas bubble layer. Additionally, the mass transfer efficiency and mass

*

Corresponding author. E-mail address: [email protected]

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

transfer correlations have been investigated in order to design the optimal experiments for electrochemical oxidation.

KEYWORDS: Electrochemical oxidation, Computational fluid dynamics, Experimental measurement, Void fraction, Mass transfer

INTRODUCTION With the rapid development of industrial and agricultural technologies over the last decades, one of the most important emerging issues is that of refractory and toxic organics present in the effluents produced by various industrial and agricultural activities

1-3

. Electrochemical oxidation is considered a promising alternative to

traditional water treatment technology owing to its efficiency, versatility, and safety. This treatment approach has become a popular method used in waste water remediation and has attracted worldwide attention from academia and industry 4, 5. Among the different anode electrode materials, non-active electrodes have been receiving increased attention for the complete mineralization of organic compounds. PbO2 is the most widely investigated of these non-active electrode materials for electrochemical oxidation because it is relatively cheap and effective 6. Meanwhile, phenols are one of the most representative active and universal organic pollutants. Thus, phenols have been considered to be model pollutants in this study 7, 8. In recent years, numerous studies have been conducted to gain improved insight into the mechanism of electrochemical incineration

9-12

. Although different

electrochemical oxidation mechanisms have been proposed, they are all characterized by the same reaction steps including transport of the organic compound to the


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electrode surface, adsorption, and attack of the organic molecules on the electrode surface by hydroxyl radical, leading to mineralization of the organic compound. Additionally, free radicals oxidize the organic compound, leading to carbon dioxide and oxygen evolution through an unwanted side reaction, creating two main sources of gas release and induced fluid flow over the electrode vicinity during electrochemical oxidation. It is well accepted that bubble evolution has multiple effects on the electrolysis field, and there are two main “bubble effects”

13, 14

: (i) gas

bubbles stick to the nucleation sites and cover the electrode surface, decreasing the active surface of the electrode and increasing the resistivity of the electrolyte; and (ii) momentum exchange occurs in the electrode vicinity as a result of micro-convection, in which gas bubbles grow and depart. Because of these adverse effects on the electrolysis processes, researchers have proposed several methods to minimize “bubble effects”, such as the use of perforated electrodes and recirculation of the electrolyte. Therefore, further investigation into understanding bubble behavior is crucial for designing electrochemical reactors and improving the efficiency of electrolysis. Currently, experiment methods mainly aim to investigate the bubble population in the macro-electrode vicinity, and while the experimental research is reliable and intuitive, this technical method makes it difficult to obtain more locally detailed behavior on the bubble-scale

15,16

. In order to successfully gain more

microscopic information, numerical simulations have been widely employed for two-phase bubbly flow. Several researchers have applied different two-phase flow models to investigate the electrolysis process. For example, El-Askary et al.


17


simulated the hydrodynamic characteristics of the hydrogen evolution process during electrolysis using an Euler-Euler model, and have performed multiple studies predicting the hydrogen-generation process under various operating conditions. Hreiz et al.

18

presented an Euler-Lagrange simulation reproducing the widening of the

bubble curtain along the vertical electrode during water electrolysis. They studied two-phase flow hydrodynamics and presented a comparison of the Euler-Euler approach and the Euler-Lagrange approach in terms of their superiority and inferiority for an electrochemical cell with gas electro-generation. At present, locally homogeneous flow analysis and separated flow analysis are two methods used to model two-phase flow during electrolysis, and these two main approaches are further divided into many sub-models. Numerous studies have addressed the bubbly flow using the two-fluid model, which has been shown to be the more effective and accurate approach for electrolysis modeling. According to the two-fluid model theory, each phase is formulated via two sets of conservation equations, and these conservation equations contain terms for the balance of mass, momentum, and energy, which governs the interfacial mass, momentum, and energy exchange. The two fluids are considered to co-existing in the computational cell volume, and the volume fraction is used to distinguish each phase, so the two-fluid approach is also called the interpenetrating continuous method. In this study, an electrochemical cell of an oxidizing organic compound is investigated both experimentally and numerically. Utilizing a PMMA manufactured electrochemical reactor, the electrochemical oxidation of organic compounds in


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sodium hydroxide at ambient temperature was monitored with in situ UV-vis reflectance study, allowing the kinetic parameters to be obtained for providing the reaction information needed later in numerical simulation. Additionally, the bubble volume fraction is estimated by high speed camera method and compared with the simulation results to verify the numerical model. ANSYS Fluent software is used with the developed models in a three-dimensional computational domain to reproduce the spreading of the bubble curtain and predict the gas bubble velocity. At the same time, the gas bubble layer distribution as well as the influence of the operating conditions such as: current density, electrolyte velocity and electrode gap was investigated. The mass transfer had been investigated by simulating the Sherwood distribution in electrolysis cell, and the impact of the gas bubble layer on the mass transfer of phenols was quantitatively analyzed. The modeling strategy adopted in this study could serve as a reference for other electro-generated bubble flow phenomena.

(a)

(b)



Figure 1. Present reactor: (a) the schematic of the electrolysis cell; (b) the refined mesh in the boundary layer.

PHYSICAL MODEL A schematic of the electrochemical reactor is shown in Fig 1(a). The electrolysis cell is placed vertically and consists of a test section including two planer electrodes. The size of electrode is 4 mm thick, 30 mm width, 80 mm high. The electrodes are fixed on the wall by glued and the electric wire through rubber stopper connect to electrodes by soldering tin. And the gap distance between the electrodes is filled with a dilute solution of Na2SO4, the electrolyte flows into the electrochemical cell from bottom to top though the pump. The electrochemical cell is 30 mm thick, 12 mm width and 248 mm high. In order to limit local turbulence, we have designed 36.8 cm3 buffer area and 22.4 cm3 convergent area in the inlet and outlet of electrolysis cell. The PbO2/Ti and Pt material are considered as anode and cathode respectively. It should be noted that the mechanism of electrochemical oxidation of phenols to CO2 is very complex, and this study has adopted p-Methoxyphenol (PMP) electro-oxidation following Langmuir-Hinshelwood kinetics in accordance with many previous studies 19-21

. Gas formation and release at the electrodes in the adiabatic atmosphere occurs

according to the electrochemical oxidation reactions: At the anode: C7H8O2 + 12H2O → 7CO2 + 32H+ + 32e2H2O → 4H+ + O2 + 4e- (side reaction) At the cathode:


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O2 + 4H+ + 4e- → 2H2O The water decomposition with oxygen evolution invariably exist in all case of oxidation of organic species through oxygen transfer, and oxygen evolution account for a small proportion in the gas bubble layer. We reduced the effects of oxygen evolution by consuming oxygen through cathode reaction. In this case, carbon dioxide is generated at the anode in the electrochemical oxidation system and the gas and liquid are considered a two-phase mixture. For better understanding and analysis of the hydrodynamic behavior during the electro-oxidation process, the developed cell design and operating conditions should be adopted to reduce error.

NUMERICAL MODEL The choice of multiphase flow models can be broadly classified as either Euler-Euler multiphase models or Euler-Lagrange multiphase models, and these two distinct multiphase models have been applied to different types of bubbly flow. Therefore, the first major step is to understand the difference between the two multiphase models. The Euler-Lagrange algorithms are further divided into deterministic and stochastic sub-models, which are considered a good choice for low volume fractions or a wide size range of dispersed phase flow. However, bubble-bubble interactions are generally inaccurate and the “numerical void fraction” of the large number of bubbles is not represented in the Euler-Lagrange method, therefore the DPM cannot be used for the present study. The two-fluid flow model separately solves two sets of conservation



equations for each phase, and can describe the physics of the system accurately. And it is suitable and accurate for modeling the discrete particle with a short hydrodynamic relaxation time. Although the Euler-Euler approach generally assumes that bubbles have homogeneous properties in each control volume, the refining grid was used to avoid the problematic assumption

22

. Thus the Euler-Euler multiphase model is

generally considered to be a suitable model for simulating the hydrodynamic electrochemical cell in this study. To successfully simulate flow behavior in the electrochemical cell, several assumptions are made to simplify the hydrodynamic and electrochemical problems: 1-The fluids in both phases are Newtonian and incompressible; 2-The physical properties remain constant; 3-the oxygen evolution effects are neglected; 4-Surface tension effects are neglected; 5-The flow is assumed to be adiabatic and heat exchange is neglected, so the energy equation is not needed; 6-Bubble-bubble interaction is incorporated in the drag force. The bubbly flow process has been numerically and experimentally studied by a number of researchers. Despite the low Reynolds number ranges, deviations in the laminar flow computations have been observed by computational simulation and experimental measurements 23. Thus, all problems are considered to be turbulent flow


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in the recommended model. Therefore, a simple turbulence model is used to describe the turbulence behavior of the continuous phase in this study. The ionic species mass flux can be obtained with the Planck-Nernst law, and ionic species have a distinct mass flux due to the different ion diffusivities in the supporting solution. The local electric moment occurs in the electrolytic cell, resulting in electro-convection effects. Such effects are also neglected in the computational simulation.

Continuity and momentum equation. To represent the flow hydrodynamics and mass transfer in the electrolysis system, and the numerical volume of each phase is proportional to their number. The governing equations of mass conservation and momentum transport can be expressed for the Euler-Euler model as follows 24: ∂α k + ∇ ⋅ (α kU k ) = 0 ∂t

(1)

Where αk is the void faction of phase k, and Uk is the mean (ensemble averaged) velocity. The momentum equation is below: ∂(ρkαkUk ) +∇⋅ (ρkαkUkUk ) = −αk ∇P k +∇⋅ (αk (Tk + TkRe )) + Mk − ρkαk g ∂t

(2)

Where αk is the void faction of phase k, and Uk is the mean ρk is the fluid density, Pk is the pressure of phase k, and Tk, TRek, and Mk are the viscous stress, Reynolds turbulent stress, and interfacial force density, respectively. In the bubbly flow, the drag force, lift force, wall lubrication force and turbulent dispersion force are relatively the most important force. Zhan et al.


25

and El-Askary


et al.

17

studied the force effect for modeling the bubbly flow in electrolysis cell, the

results indicated that the drag force and turbulent dispersion force are significant in electrolysis. Each of the individual terms contain particular physical mechanisms of the interfacial momentum transfer. Assuming no phase change and neglecting surface tension, the interfacial forces acing on each phase differ in sign only according to Newton’s law 26: M c = −M d

(3)

M c = Fcdrag + Fctd

The Reynolds turbulent stress and phasic interaction as supporting information is described in APPENDIX A.

Turbulence modeling. Multiple researchers have proposed different turbulence models to describe the bubbly flow system including the two-equation k-ε, extended k-ε, and shear-stress transport k-ω turbulence models, all of which contain additional source terms that have been interpreted for the induced-turbulence effect of gas bubbles on electrolyte turbulence. However, Zhan et al.

25

made a recent comparison

of experiments and simulation in electrolysis cell. The research indicates that standard k-ε model gives the best prediction with the experimental data and this model requires less computation than other models. Thus the standard k-ε model was considered as turbulent model in this study. The governing equations of the k-ε model are 17:

ρc

Dk µt = ∇ ⋅ ∇k + (G − ρcε ) + S k σk Dt

µt ε Dε ρc = ∇ ⋅ ∇ε + (C1G − C2 ρ cε ) + Sε σε Dt k


(4)

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In the k-ε model, the generation term of the turbulent kinetic energy is represented as G, which includes Gk and Gb generated by the buoyancy and the averaged velocity gradient, respectively. C1and C2 are empirical constants. In addition, the user-defined sources are written as:

Sk = 2kαcCD (Ct − 1) + CD

ν t ∇αc U σ α αc r

(5)

Sε = 0 Where σα is 0.75 of the Prandtl number for the turbulent kinetic energy. Ct is the turbulent response coefficient, which is an important parameter in the k-ε turbulent model.

The interfacial area concentration model. In the two-phase system, the phasic interactions are considered the transfer source for the averaged governing equations. These source terms represent transfer phenomena through the interface between the phases. The interfacial transfer terms are generally expressed as a product of the driving force and interfacial area concentration. And a close relationship for interfacial area concentration is essential for modeling the two-phase system. The transport equation for the interfacial area concentration model can be written as 28: r ∂（ρg χ p） 1 Dρg 2 m& g χp + χ p + ρg (SRC + SWE + STI ) +∇⋅（ρg u g χ p ) = ∂t 3 Dt 3 αg

(6)

Where the interaction term, χp, represents the net rate of change of the particle number density distribution function resulting from particle breakup or coalescence. SRC, SWE and STI are the coalescence sink terms and breakage source term.

BOUNDARY CONDITIONS



To solve the governing equations for the computational cells, certain boundary conditions have been defined. The mean flow velocity was given a fixed value at the flow inlet and all relevant scalar fields are supplied. Turbulent intensity is defined as the characteristics of inflow turbulence: I = U ′ U avg = 0.16 Re−1 8

(7)

The value of the specified static pressure was used at the outlet boundary, and all variable fields were given a zero gradient. Mass friction and pressure fields were specified as having zero gradient. A no-slip boundary condition was applied to the liquid phase, and the axial velocity of the gas phase was expressed as 29,34: ud =

n ∗ r * Vm A

(8)

Where n, r, Vm and A are the stoichiometric number, reaction rate, molar volume of gas, and electrode area, respectively.

MESH GENERATION ICEM CFD was used to generate the computational mesh in this study. The computational domain contains over 1,000,000 non-uniform hexahedral cells, and is decomposed into 48 sub-domains for parallel processing. For more accurate simulation of steep gradients in near-wall regions, a boundary layer mesh was used, as shown in Fig 1(b). Meanwhile, the mesh for gas evolution surfaces have also been refined. The cell thickness was increased by the Bi-Geometric bunching law. The sub-grid viscosity has been neglected as a result of the grid scale refinement, and the first-node wall distance of y+ was less than 5 for the whole wall region.


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SOLUTION METHOD In the present work, an ANSYS Fluent software package was used to solve the governing equations. As a result of the need for information about the transient flow behavior, a transient solver using the Phase Coupled SIMPLE algorithm was adopted for fluid dynamics and mass-transfer studies. A set of discretized equations was generated on the staggered grid system. The void fraction was discretized with the QUICK scheme, and the second-order upwind scheme was adopted for discretization of the other governing equations. Absolute tolerances were set at 10-3 for the gas velocity, interfacial area concentration, and continuity equation, and 10-6 for the remaining equations. Under-relaxation was used with values of 0.05 for the pressure and volume fraction, and 0.1 for the mass fraction and turbulent quantities.

EXPERIMENTAL APPARATUS A schematic of the experimental apparatus is shown in Fig 2. The experimental test section includes the following components: a container and receiving vessel, a pump, a flow meter, an electrochemical cell, a DC power supply, and an imaging system. The container and receiving vessel have been machined out of glass to store and receive the electrolytic solution (0.1 M Na2SO4). The two vessels each have a capacity of 4.5 L. The electrolyte is pumped from the container through the electrochemical cell to the receiving vessel, via a flow pipe make of peroxide silicon. The flow rate of the experimental setup is 0.3 m/s according to the calibration curve of the flow flux and the rotating speed. And the oxygen aeration treatment was performed during the experiment. The two electrodes are fixed to opposite sides of the electrochemical cell



with a gap width of 12 mm. A DC power supply generates static direct current to the electrodes through a 3 mm diameter wire, which through rubber stopper connected to electrodes by soldering tin and glued. In order to measure the void fraction and bubble diameter, a visualization system is used in the region of the electrodes. This system consists of a CCD camera, an LED strobe light, and other accessories. Visual images of the two-phase flow pattern between the electrodes are taken by a FASTCAM Mini UX100 camera. A set of experimental test have been designed for the investigation of the kinetics parameters of electrochemical oxidation and measurement of the gas volume fraction. To avoid any leakage, the junctions of between the pipe and electrochemical cell are glued, and all components are placed in fixed positions.

Figure 2. Schematic representation of the experimental apparatus: A, container; B, pump; C, flow meter; D, electrochemical cell; E, imaging system; F, receiving vessel.

Electro-oxidation kinetics of p-Methoxyphenol. PMP degradation could be considered as a heterogeneous Langmuir-Hinshelwood mechanism, with the assumption of surface reaction as the controlling step and surface reaction with two adsorbed molecules. The hydroxyl radicals and PMP are adsorbed on an anode


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surface, react on the surface, and the product is desorbed

19

. In order to obtain the

kinetics parameters for the overall reaction rate during the electro-oxidation process, PMP oxidation experiments were performed in an electrochemical cell with an electrolyte volume of 87 cm3 at room temperature (23±1°C), using a working electrode of PbO2/Ti and Pt with a surface area of 22.4 cm2. A magnetic stirrer was used to keep the electrolytic solution well-mixed. A DC power supply provided three different current intensities (0.1 A, 0.15 A and 0.2 A) under galvanostatic operating conditions. During PMP degradation, the mass concentration of the PMP is 0.1253 g/L, samples of the electrolytic solution were taken with a dropper at periodically and the organic compound concentration was determined instantly using UV-Vis spectroscopy. The absorbance changes of the solution at different current densities during the electrochemical oxidation in the batch electrochemical cell at varying degradation times are shown in Fig 3. The absorption peak of PMP was observed at 287 nm, and slowly decreased during the prolonged electrolysis. The UV spectra indicate that the electrolytic efficiency is low, only about 7.72 % of the initial PMP has degraded after 20 min due to the low current density in the electrolysis process.



Figure 3. UV spectra of PMP in 0.1 M Na2SO4 solution during electrochemical oxidation: (a) 89 A/m2 current density; (b) 67 A/m2 current density; (c) 45 A/m2 current density. Some researchers

30

systematically studied the kinetics of the electrochemical

oxidation of PMP, the PMP are determined by their surface concentration according to the Langmuir-Hinshelwood mechanism and that the number of electrons transferred per mole of organic compound oxidized depends on the electrode potential. And the complete mineralization of organic species when the voltage is above 1.5 V for PMP oxidation, which agrees with the reported PMP degradation data.


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Figure 4. Relationship between the oxidation rate and concentration of PMP: (a) 89 A/m2; (b) 67 A/m2; (c) 45 A/m2. The concentration of the organic compound at different times was calculated using the standard concentration-absorbance curve, derived from the principle of the Lambert–Beer law. The relationship between concentration and time could be obtained for the electrolysis process. As shown in Fig 4, the PMP oxidation rate increased linearly with the PMP concentration in solution during the time of 0-20 min. However, there was a deviation in the case of high concentrations. This indicates that the PMP oxidation process follows the Langmuir-Hinshelwood mechanism. Because surface adsorption is a fast process, the rate of PMP oxidation can be represented as:

r =−

∂cpmp ∂t

= kappθ pmp

(9)



Where kapp is the apparent heterogeneous rate constant, and θpmp is the fraction of adsorption sites on the surface occupied by adsorbed PMP. According to previous studies, kapp and θpmp can be described as:

kapp = kθOH

θ pmp =

Kc pmp

(10)

1 + Kc pmp

Where k and K are the oxidation rate constant and the adsorption-desorption equilibrium constant, respectively. Hence the overall rate equation can be expressed as: r=−

∂c pmp ∂t

=

k app Kc pmp 1 + Kc pmp

(11)

The nonlinear least squares fitting method was used to processing the data for PMP concentration against the degradation time, while the robust LAR and Trust-Region algorithms were also considered in the fit method. The oxidation rate constant and adsorption-desorption equilibrium constant values obtained using nonlinear fitting for the PMP electrochemical oxidation at different current densities are listed in Table 1. The sum of squares due to error (SSE), R-square (R2) are used to evaluate the fitting effect of common indicators. Under different operating conditions, the results of fitting SSE and R2 are shown in Table 1. It can be seen that there is a certain error in the fitting results but the SSE is close to 0 and R2 is also close to 1, indicating that the L-H response model is relatively good for data fitting. The oxidation rate increases and the adsorption rate decreases with increasing current densities. Meanwhile, the PMP oxidation rate is much lower than the adsorption rate.


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Table1. Langmuir-Hinshelwood constants obtained for the electrochemical oxidation of PMP at a PbO2/Ti electrode. Current density(A·m-2)

Method

89 67

Nonlinear fit

45

kapp(mol·dm−3·s−1)

K(mol−1·dm3)

SSE

R2

1.827×10-4

0.4814

2.036×10-17

1.431×10-4

0.5444

1.425×10-17 0.8933

1.265×10-4

0.5783

9.295×10-18 0.9264

0.8738

The measurement of the gas fraction. Several measurement technologies have been used for the gas fraction: measuring the pressure difference or resistivity, measuring the volume expansion of the reaction system, or using high-speed photography. A comparison of existing methods suggests that using a high-speed camera gives effective accuracy. In this study, for the measurement of the gas fraction, the mass concentration of the PMP is 0.6355 g/L, images of the cell have been taken with a high-speed camera with a resolution of 1280×1024 pixels. An LED light is placed behind the cell as a backlight for the shadow image of the flow in the test section. The photos were taken continuously with an inter-framing time of 0.5 s. To acquire statistically reliable data for the steady state of bubble evolution and eliminate the Joule effect, a high-speed camera with a low frame rate stated working 5 minutes after connecting the current. Three different values for the current, namely 0.1 A, 0.15 A and 0.2 A, were available in experimental system, giving superficial current densities of 45 A/m2, 67 A/m2 and 89 A/m2, respectively. Plane images of bubble evolution are shown in Fig 5.



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Figure 5. Images of gas evolution on the anode with a current density of 89 A/m2: (a) original photo; (b) photo after pre-processing; (c) anti-phase photo from Photoshop; (d) transferred to the binary image by MATLAB.

RESULTS Model validation. For model validation, the experimental results for the gas volume fraction could be obtained and compared with the numerical data. In this study, the original photo has been processed via Photoshop, and a MATLAB code has been written to transform the real image into a binary image. Thus, the gas surface fraction was directly yielded by calculating the proportion of bubbles in the total area of the measurement window. The thickness of the fluid vein has been considered to calculate the gas volume fraction from gas surface fraction. The thickness of the fluid vein was determined by the depth of field and the average bubble diameter. Photographic parameters could be obtained from the imaging

system,

and

the

depth

of

field

was

calculated

online

at

http://www.dofmaster.com/dofjs.html. Different models have been used to calculate the bubble size in bubbly flow systems 31

, but there remain minor deviations between the model predictions and experimental


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measurements. However, the image of bubble located closer or further away from the focal plane become blurred, so we select the relatively clear bubbles in the gas layer by Nano Measurer. A total of 240 bubbles were selected from different positions in the bubble layer, and the diameters were measured. The result is shown in Fig 6. The statistical results indicate that the average bubble diameter is approximately 0.125±0.035 mm.

Figure 6. The histogram of bubble sizes in the gas bubble layer. The distribution of the gas void fraction determined from the experimental results and the numerical data at the gap between the electrodes for three different current densities are shown in Fig 7. Several methods have been reported for measuring the gas void fraction, and use of a high-speed camera has generally had sufficient accuracy in comparisons between the different experimental approaches. We select the relatively clear image statistics to obtain bubble size information for providing the simulation parameters, and the accurate interfacial force model have been adopted for simulating the bubble size change and the bubble motion. The gas volume fraction and the thickness of gas bubble layer are accuracy in the electrolysis process. So comparison of these results reveals relatively good agreement with experimental data



near the anode surface. However, deviations between the computational results and the measurements occur for the gas bubble layer. Nevertheless, deviations inevitably appear in the experiments due to operating conditions and methodical error. In the CCD test, the dark background of the images could be attributed to the low brightness of the LED light, resulting in the gas bubble density being estimated improperly during the MATLAB post-processing. The calculations of the depth of field and average bubble diameter are also sources of discrepancy during the process of converting the surface gas fraction to the volume gas fraction. Additionally, compared with the simulation of subcooled boiling flow

32

, the wall function results deviate

significantly in gas bubble motion, but there are no systematic studies of wall function in electrochemical cells. Overall, the numerical results demonstrate a successful performance when compared with the experimental data.


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Figure 7. Comparison of the void fraction from the experimental data and simulation result at the electrode gap with a constant inlet velocity for (a) 89 A/m2 current density; (b) 67 A/m2 current density; (c) 45 A/m2 current density.

Grid independence study. Discrete errors and rounding errors were the two main sources of large uncertainties between the experimental results and the numerical data, so a study of the grid independence was conducted. Three different grid refinements with either 1,108,207, 1,996,737 or 4,062,327 cells have been used for the numerical simulation. As shown in Fig. 8, a comparison of the averaged Sherwood number on the anode surface was obtained for the three different meshes. The deviation is relatively small between mesh 2 and mesh 3. The area-averaged Sherwood number is also reported in Table 2, and the error for mesh 2 is below 1.91 %. Therefore, the results indicate that a mesh with 1,996,737 elements is sufficient to accurately simulate the flow structure. Table 2. Area-averaged Sherwood number calculated for three different meshes. Averaged Sherwood number

ℎ | |

Mesh1

Mesh2

Mesh3

3.3495

3.5002

3.5684

6.13%

1.91%

-----



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Figure 8. Averaged Sherwood number distribution obtained from three meshes with increasing numbers of cells on the anode surface.

Gas bubble flow visualization. The raw image from the CCD obtained at the zone between the two electrodes is show in Fig. 9. A number of bubbles form bubble curtains, which spread laterally in the upward direction. It is apparent that some bubbles stick to grooves on the electrode surface, and these bubbles grow to a large size and are called Very Large Bubbles (region A in Fig 9). VLBs can remain on the electrode surface for long periods, but will eventually separate from the surface along with growing to an important size. Similarly, a large number of small bubbles can develop bubble clusters or “waves” in the bubble curtains (region B in Fig 9). Similar phenomena have been previously demonstrated in the research of Byrne et al.

33

and

Aldas et al. 34, and these phenomena were described with a pseudo-turbulence theory.


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Figure 9. Gas bubble evolution on the anode surface imaged by a high-speed camera.

Velocity profile and PMP distribution patterns determined by CFD. The contours of the liquid velocity for different inlet conditions are shown in Fig. 10. It can be observed that the fluid flow patterns have similar structures. Fig 11 shows the detail of the velocity vectors obtained to further analyze the flow regimes. In the plane of y=15 mm, different fluid zones have distinct features when the fluid enters the cell domain. A higher velocity magnitude is observed in the inlet flow distribution segments. There is also a lower velocity region, which connects to the inlet section near the wall, and is an important feature of the observed stagnant fluid that is greatly affected by the inlet expansion effect. Past the inlet section, a zone is attached to the center of the domain with a fully developed flow, and the flow of this zone changes from inlet expansion to fully developed flow. In the outlet section, the fluid is again gathered to the center of the segment and comes from the outlet.



uin=0.07 m/s

uin=0.18 m/s

uin=0.3 m/s

Figure 10. Velocity contours for the liquid at different electrolyte flow rates in the plane y=15 mm.

Figure 11. Detail of the liquid flow pattern at uin=0.3 m/s, I=89 A/m2. The concentration distribution of PMP for different current densities are presented in Fig 12. As can be seen, it is apparent that the concentration profile is a


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homogeneous high concentration field at the entrance and in the developed flow region. In contrast, the region of the anode shows diversification from low to high, as a result of the PMP oxidation reaction on the anode surface. In the top part of the electrode region, the concentration profile is lower than in the adjacent zone near the left wall, indicating that the gas bubble layer has a negative effect on the concentration distribution.

I=89 A/m2

I= 67 A/m2

I=45 A/m2

Figure 12. Contours of the mass fraction of PMP for different current densities in the plane y=15 mm.

The influence of the gas bubble layer for different operating conditions. The void fraction contours with lateral magnification for different operating conditions are shown in Fig 13. Similar characteristics can be observed, as the thickness of the gas bubble layer increases with the height of the anode. The gas bubbles were produced on the anode surface, and the subsequent movement of the gas bubbles was strongly



affected by the upward flow of electrolyte. However, different operating conditions have distinct influences on the enhancement of the gas bubble layer in the streamside direction. It is should be pointed out that the accumulation of gas bubbles have adverse effects, and thus the factors affecting the thickness of the gas bubble layer have vital importance for selecting the optimal operating conditions.

I=89 A/m2

uin=0.3 m/s

I=67 A/m2

uin=0.18 m/s

I=45 A/m2

uin=0.07 m/s


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δ=16 mm

δ=12 mm

δ=8 mm

Figure 13. Contours of the gas volume fraction for different operating conditions in the electrode region. Fig. 14 shows the effects of operating conditions on the void fraction in detail. The void fraction distribution at the top part of the anode reaction is shown in Fig 14(a). Comparing the results for the three different current densities, it can be seen that the void fraction increases with increasing current density, while the thickness of the gas bubble layers are same. The trend indicates that current density has little influence on the gas bubble motion. In addition, the void fraction is similar for the current densities of 67 A/m2 and 45 A/m2, due to the PMP oxidation reaction mechanism. As shown in Fig 14(b), the void fraction and gas bubble layer are greatly influenced by electrolyte flow velocity. At a high flow rate, the gas production rate increases and the corresponding decrease in the residence time of gas bubbles that lowers the void fraction near the anode surface. The high gas release rate reflects the large lateral velocity of the gas bubble, thus the thickness of the gas bubble layer increases with high lateral velocity.



The gap effects on the gas bubble layer and gas void fraction near the anode are described in Fig 14(c). The hydraulic diameter increases with increasing the electrode gap in the flow channel, resulting in a decrease in flow velocity. In general, the gas generation rate increases when the distance of the electrode gap is reduced. As discussed in the previous section, combining the comprehensive analysis of the flow velocity and gas release rate indicates that the thickness of the gas bubble layer decreases and the void fraction increases as the distance of the electrode gap increases.

Figure 14. Gas fraction distribution at the top of electrodes for (a) different current densities; (a) different electrolyte flow velocities; (c) different electrode gap distances.

Dimensionless analysis of mass transfer coefficient. Due to the complicated structure of the gas bubble layer and the heterogeneous properties of the gas bubbles, no systematic CFD study concerning the mass transfer coefficient of an


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electrochemical cell has yet been published. For the mass transfer at the anode, Santos et al. 35 proposed a convective mass transfer between the electrolyte and anode surface using mono-phasic CFD simulations. The mass transfer rate of the component through the stationary flow layer is equal to the convection mass-transfer flux: N A = − DAB

dω A |x =0 = kc (ω Ab − ω As ) dx

(12)

Dimensionless analysis has been used for mass transfer coefficients, and equation (12) can be written as: Sh =

kc d dω = d ∗ A |x =0 (ω Ab − ω As ) dx DAB

(13)

Where ωAb, ωAs are the mass fraction of bulk solute and anode surface, the d is the characteristic dimension.

Figure 15. Sherwood distribution on the anode for (a) I=89 A/m2; (b) I=67 A/m2; (c) I=45 A/m2. The Sherwood (Sh) field at the anode surface is shown in Fig 15. The Sh patterns are similar for different current densities, and mass transfer efficiency is low in all regions of the anode surface. It can be seen that the Sh distributions are symmetrical.



The mass transfer region can be divided to two areas: in the upper part of the anode surface, the Sh distribution shows periodic intervals of specific radians; and in the top part of the anode surface, the Sh field distribution has pseudo lines representing different values.

Figure 16. The histogram of percentage area as a function of Sh/Shmax for I=89, 67, 45 A/m2. To reinforce these observations and analyze the gas bubble effects on mass transfer, histograms (Fig 16) were generated for mass transfer efficiency. It was found that the mass transfer of main regions are 28-50 percentage of Shmax for different current densities. Comparing the three histograms of the mass transfer efficiency, it can be seen that current density does not have a strong impact on the Sh distribution. However, it is interesting to find that mass transfer efficiency decreased with increasing current density. Mass transfer was improved by electrochemical oxidation,


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which in turn produced the gas bubble layer that affects mass transfer. This mass transfer distribution can be attributed to the combined interaction of the electrochemical oxidation and the gas bubbles.

CONCLUSIONS This study presents an improved understanding of flow hydrodynamics and mass transfer in a parallel plate electrolyser. CFD simulation results are useful for comparisons between electrochemical cells with different geometries. The employed numerical models mainly considered interfacial interaction between the gas phase and electrolyte phase, bubble induced turbulence, and bubble coalescence and breakage, which could provide more accurate simulation results and excellent prediction of the electrochemical cell. To validate the present numerical simulation, experimental measurements has been obtained for the electrochemical cell with different current densities. The void fraction was determined by post-processing of the image taken by a high-speed camera. The experimental data indicated that the employed models can predict the gas release process in an electrochemical cell in a suitable manner. It was found that flow features, gas generation, and the void fraction all showed distinct effects from different operating conditions. The flow rate and current density greatly affected the void fraction distribution and gas bubble thickness. Meanwhile, the qualitative and quantitative dimensionless analyses of the mass transfer coefficient indicated that the bubble curtains have a negative effect on mass transfer, and can be considered a valuable parameter for selecting optimal operating conditions. In fact, it should be noted that the flow pattern is not ideal for mass transfer, and designing the



Page 34 of 37

optimal inlet and outlet conditions or turbulence promoting devices may be useful ways to improve mass transfer in the electrochemical oxidation region. In addition, the mass transfer model is promising and has potential for understanding the mass transfer phenomena in an electrolyser.

Supporting information paragraph: In order to better understand the momentum equation of the electro-oxidation process, the detailed

derivation of

TRek, Fdragc, Ftdc and Ct

are described in

Appendix A, which are shown in supporting information.

ACKNOWLEDGENTS The authors are grateful for the financial support from the Shenzhen science and technology research and Development Fund (Nos. JCYJ20160331113033413).

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Table of Contents


Fluid Dynamics and Mass Transfer Study of Electrochemical Oxidation

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