CFD simulation of biphasic flow, mass transport and current distribution in a continuous rotating cylinder electrode reactor for electrocoagulation process

CFD simulation of biphasic flow, mass transport and current distribution in a continuous rotating cylinder electrode reactor for electrocoagulation process

Journal Pre-proof CFD simulation of biphasic flow, mass transport and current distribution in a continuous rotating cylinder electrode reactor for ele...

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Journal Pre-proof CFD simulation of biphasic flow, mass transport and current distribution in a continuous rotating cylinder electrode reactor for electrocoagulation process

A. Daniel Villalobos-Lara, Tzayam Pérez, Agustín R. Uribe, J. Arturo Alfaro-Ayala, José de Jesús Ramírez-Minguela, Jesús I. Minchaca-Mojica PII:

S1572-6657(19)31075-6

DOI:

https://doi.org/10.1016/j.jelechem.2019.113807

Reference:

JEAC 113807

To appear in:

Journal of Electroanalytical Chemistry

Received date:

5 November 2019

Revised date:

19 December 2019

Accepted date:

26 December 2019

Please cite this article as: A.D. Villalobos-Lara, T. Pérez, A.R. Uribe, et al., CFD simulation of biphasic flow, mass transport and current distribution in a continuous rotating cylinder electrode reactor for electrocoagulation process, Journal of Electroanalytical Chemistry(2019), https://doi.org/10.1016/j.jelechem.2019.113807

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© 2019 Published by Elsevier.

Journal Pre-proof

CFD simulation of biphasic flow, mass transport and current distribution in a continuous rotating cylinder electrode reactor for electrocoagulation process

A. Daniel Villalobos-Lara, Tzayam Pérez*, Agustín R. Uribe, J. Arturo Alfaro-Ayala, José

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de Jesús Ramírez-Minguela, Jesús I. Minchaca-Mojica

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Departamento de Ing. Química, División de Ciencias Naturales y Exactas, Universidad de

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Guanajuato. Noria Alta s/n, Gto., México. CP 36050

*Corresponding author email: [email protected] Telephone: +52 4737320006 Ext. 8132

Journal Pre-proof Abstract

The mass transport performance of Al3+ ion is responsible for the production of the coagulant inside the electrocoagulation reactor, and therefore, the contaminants removal depends on it. Similarly, the hydrogen gas generation in the counter electrode affects the performance of the reactor due to the resistivity generated in the solution and the biphasic

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fluid dynamics. The proposed model solves simultaneously the secondary current

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distribution, the mass transport of aluminum and hydrogen, and the momentum transfer of a

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turbulent biphasic system in a continuous rotating cylinder electrode reactor coupled with two sedimentation tanks. The theoretical analysis for this system revealed well-mixed

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conditions and a cuasi-uniform current distribution in the RCE reactor due to the

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geometrical design and the low quantities of hydrogen gas produced at the different current

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values studied in this work. Meanwhile, slow flow velocities and dead zones were observed inside the sedimentation tanks. Also, comparisons between experimental, and theoretical

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Al3+ concentrations under stationary regime are also presented, founding good correlation.

Keywords: electrocoagulation, continuous rotating cylinder electrode, multi-coupled modeling, biphasic fluid dynamics

Journal Pre-proof 1. Introduction In recent years electrocoagulation (EC) process has been receiving greater attention as this technique offers higher removal efficiency compared to the conventional methods [1]. The EC process is used for destabilizing suspended, emulsified, or dissolved contaminants in an aqueous medium by introducing an electrical current through the solution [2]. Despite there are several mechanism reported to remove pollutants by electrocoagulation process, in

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general terms, it involves four steps; anode dissolution, formation of OH- ions and H2 at the

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cathode, adsorption/absorption of colloidal pollutants on coagulants, and flocs removal by

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sedimentation or flotation [1,3,4].

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The electro-generated Al3+ of Eq. (1) and OH- from Eq. (2) will transfer into the bulk

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solution and undergo further spontaneous hydrolysis reactions to form various monomeric

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and polymeric species, part of which will finally transform into hydroxide flocs [5–7]. Therefore, an important aspect to consider in the cell design is the electrogenerated

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aluminum ion because, the efficiency of electrocoagulation processes strongly depends on

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the aluminum mass transfer.

Al(s) → Al3+ (aq) + 3e−

(1)

2H2O+2e−→ H2(g) + 2OH−(aq) .

(2)

Besides the aluminum generation, the gas phase produced by equation (2) should be considered in electrochemical engineering science, since the dispersed phase modifies the electrical properties of the electrolyte or the behavior of the electrode (as well as mass and heat transfers), and therefore it modifies the macroscopic cell performance. For example,

Journal Pre-proof electrochemical reactions can be enhanced by increasing the mass transfer at the electrode surface, which can be induced by the electrochemical bubble production [8]. Otherwise, the gas bubbles and nanobubbles electrogenerated [9] sticking to the nucleation sites block the electrode reducing the cross-sectional area of pure electrolyte available for current transport [10], because bubble-dispersed phase acts like an electrical shield. This shielding effect depends on the density of the bubbles, which is called the gas volume fraction of the

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dispersion [8,11–13]. Besides, since gas bubbles rise upwards along electrode, electrical

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non-uniformity is generated along the electrode and the gas volume fraction increase,

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affecting flow field, electric field, temperature, mass transfer, electron transfer and other

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complex phenomena [5,13], and thereby the system performance is impaired.

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An effective geometry and design can help to eradicate such performance issues, because a

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proper design of the electrochemical reactor can help the fluid to be treated in a uniform fashion leaving no dead zones, short circuiting, channeling and fouling of electrode [14].

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However, all these previous complex phenomena mentioned in EC are difficult to analyze

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accurately only by experimental methods. Different numerical and experimental works have been reported relating to the design and behavior for electrocoagulation reactors [7,15‒18]. However, the amount of works reported employing computational fluid dynamics (CFD) is limited, for example, Choudhary et al. [14] developed residence time distribution (RTD) experiments and CFD simulations. These authors studied the flow behavior with a mass tracer, using a rotating cylinder electrode (RCE), electrochemical single reactor and two/three tanks in series. Song et al. [19] evaluated the potential and current distribution, considering a fluid flow and mixing, and also, the mass transfer involved in the EC system for As and Sb removal. Recently, the results obtained by Lu et

Journal Pre-proof al. [20] in a continuous parallel plate arrangement show the experimental and numerical generation and mass transfer of coagulant (Al3+), H+ and OH-, solving the Nenst-Planck equation while considering laminar flow regimen.

These previous communications evidence that numerical simulation coupling with experimental verification of the EC process not only developed a new way for optimization

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and exploration of the EC process, but also deepened the understanding of EC performance

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and further improvement of the theoretical basis of new EC systems. Nevertheless, there

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are no works reported that consider simultaneously the effect of the gas phase and the mass

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transfer of the ionic aluminum generated from equation (1) in a continuous rotating environment for EC process. In this way, the novelty of this manuscript is a proposal of

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multi-coupled modeling based on secondary current distribution theory and mass transfer

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with the effect of the electrolyte conductivity variation through the disperse fraction of the hydrogen generated by the electrolysis of water in a novel design of RCE reactor with two

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sedimentation tanks. Through the numerical analysis it was possible to determine the grade

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of current distribution which affects the generation of disperse phase and metal ions, which are the basis of the coagulants for the removal of contaminants in the water. Also, the theoretical hydrodynamic and mass transfer analysis developed could help to evaluate the degree of homogenization of the generated metal ion. Finally, an evolution and comparison of the experimental and theoretical stationary concentration of the aluminum ion Al3+ is presented to validate the propose model.

Journal Pre-proof 2. Methods and materials 2.1 Electrocoagulation rector Figure 1 shows (a) the real electrocoagulation lab configuration reactor, (b) the electrodes arrangement inside the RCE reactor and (c) the 3D computational domain of the system. This design was based on the fluid dynamics study, developed by Rosales et al. [21] at different continuous RCE reactor configurations. The system consists of two sedimentation

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tanks, coupled to a RCE reactor with 6 aluminum plates as anodes, which are placed on the

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surface of the reactor equidistantly at an angle of 60° to one another; and these are attached

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to the wall of the reactor. The aluminum used in all electrodes was the commercial

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aluminum 1100 with a purity of 99 %. The rest of composition is Si, Fe, Cu, Mn and Mg. Different works reporting on RCE systems showed that the most suitable geometry for the

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computational domain has to consider the six-plate electrodes without the face in contact

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with the concentric reactor wall [21–24]. In this context, these faces were covered with

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simulation.

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silicone glue in the experimental setup, in order to approximate the reality with the

Figure 1. (a) Electrocoagulation lab configuration system, (b) electrodes arrangement inside the reactor and (c) 3D computational domain of the system.

Journal Pre-proof The inflow of the reactor is in the center of its base, then, the fluid spills out from the top of the reactor to the first sedimentation tank, and after that, the fluid spills out again from the top of the first sedimentation tank to the second sedimentation tank. Finally, the fluid leaves the system at the outlet. The physical phenomenon of “water spilling” was considered as a continuous domain with an elevation of 0.5 cm in the computational

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geometry. Table I shows geometrical parameters of the system described.

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2.2 Experimental details and ion aluminum (Al3+) quantification

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A set of experiments was undertaken, varying the applied current density from 8 to 32 A/m2, employing 20 L solutions of 0.075 M sodium sulfate (Na2SO4) and 0.01 M sodium

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chloride (NaCl) with pH=7 at a constant inflow of 0.4 L min-1 and 100 rpm (10.5 Rad s-1)

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RCE rotational speed. The electrical conductivity was measured with an electrical

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conductivity meter U-10 Horiba Ltd model. Current densities were applied independently using a power source PsP-2010 GW INSTEK. 10 ml samples were taken at the top of the

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reactor every 2 min for 10 min for each current density applied. Aluminum ion (Al3+)

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quantification was carried out using an atomic absorption spectrometer PerkinElmer AAnalyst-200 model. For this determination, the pH between 0 and 1 was used, applying concentrated nitric acid to decrease the pH of the samples. The calibration curves were performed for each current density using an aluminum standard of 1000 ppm Golden Bell ® atomic absorption compound. The standard has the pH of 0, so, no acid was used in it. The calibration curves obtained were performed in the range of 0-100 ppm, getting a correlation of 0.9983. The blank used was distilled water.

Journal Pre-proof 3. Formulation of numerical simulation 3.1 Secondary current distribution model The current density j at any point within the cell can be calculated from the local potential gradient, according to Ohm's law [23]:

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(3)

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where kef is the effective electrolytic conductivity and φ is the local potential. The effective

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electrolytic conductivity is the pure electrolytic conductivity k0, modified by the presence

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of the disperse fraction ϕg and given by Bruggerman relation [13]:

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(4)

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The local potential distribution in the solution was described by the Laplace equation [23]:

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(5)

Both aluminum ions and hydrogen generation of Eqs. (1) and (2) could be represented by a secondary current distribution model, because the electrochemical reaction depends exclusively on charge transfer, and concentration overpotential can be neglected [24]. Under these conditions, the local current density may be related to the local overpotential η at the electrode. This excess potential is the potential difference between the metal potential , the potential solution adjacent to the electrode

and the equilibrium potential

[24]:

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(6)

A charged controlled kinetics was employed in the six plates and the RCE, respectively

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[24]:

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(8)

is the exchange current density; ba and bc are the anodic and cathodic Tafel slopes,

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where

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,

(7)

respectively. Variables φ and ϕ were solved simultaneously by coupling the Ohm’s law

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with a biphasic model described below.

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3.2 Biphasic κ-ε turbulence model

The following assumptions were considered to simulate the biphasic flow: It is assumed that the bubbles only occupy a small volume fraction, and they always travel with their terminal velocity. Thereby it is possible to solve only one set of RANS equations for the liquid phase and to let the velocity of the bubbles be guided by a slip model. The pressure distribution is calculated from a mixture-averaged continuity equation. The volume fraction of bubbles is tracked by solving a transport equation for the effective gas density. Turbulence effects are modeled using the standard two-equation κ-ε model with realizability constraints and bubble-induced turbulence production. The flow close to walls

Journal Pre-proof was modeled using wall functions. Based on these assumptions, next below is a brief description of the model with their corresponding equations.

The momentum and continuity equations for the two phases can be combined, and a gas phase transport equation is kept in order to track the volume fraction of the bubbles. The

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momentum (9) and continuity equation (10) for the continuous phase are [25,26]:

]

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[

(10)

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0

(9)

where μl is the dynamic viscosity, ρ is the density, P is the pressure,

is the velocity vector of the continuous phase. The so-called Reynolds stresses can

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and

is the gravity

be stated in terms of a turbulent viscosity μT, in accordance with the standard κ–

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ε turbulence model [25,26]:

*(

)

+

(11)

*(

)

++

(12)

(13)

Journal Pre-proof *

+

(14) (15)

where

, κ, ε, Pκ and

are the relative velocity between the phases, the turbulent

kinetic energy, the turbulent energy dissipation rate, the energy production term and the accounts for the bubble-induced turbulence, respectively. Cμ (0.09), Cε (1.46) Cε1 (1.44),

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Cε2 (1.92), σk (1), σε (1.3) are specific dimensionless model constants, which are obtained

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by data fitting for a wide range of turbulent flows [25]. The notation ( )T denotes the

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transpose of ∇u, and it should not be mistaken with any turbulent suffix.

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)

(16)

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∇ (

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For the disperse phase, the gas transport equation is:

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where ρg, φg, ug are the density, the volume fraction and the velocity of the gas phase, respectively. The gas velocity ug is the sum of the following velocities:

(17) where udrift is a drift velocity, defined as:



(18)

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In the liquid-gas bubbles interactions, there could be five different forces involved: pressure, buoyancy, drag, added mass and lift forces [27]. From these forces, it has been recognized that only a balance between drag and pressure forces have an important effect on the behavior of two-phase systems, where they are under forced convection conditions

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[8].

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For continuous systems, the pressure field is given by buoyancy forces; hence, this

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relationship (19) can also be considered as a buoyancy-drag force balance, where Cd is the

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|

(19)

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|

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inter-phase drag coefficient and db is the bubble diameter.

Furthermore, from equation (19), the value of drag coefficient Cd could be considered as a

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variable in relation to the slip velocity between phases. In this work, the Hadamard-

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Rybczynski (Eq. 20) model is proposed instead of other correlations [28], since such correlation is adequate to describe drag force for diameter bubbles less than 2 mm [27]. Because the relationship between gas and liquid viscosity is close to 0, corresponding drag coefficient expression of this model is described as follows:

(20)

Journal Pre-proof Finally, the standard κ-ε turbulence model does not solve properly in the regions closed to the walls, so then universal logarithmic wall functions are commonly used as a boundary condition [25,26]. The wall functions are established on a universal velocity distribution, which in a turbulent layer is defined by:

𝑢+ = 2.5 𝑛𝑦+ + 5.5

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(21)

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where the normalized velocity component inside the logarithmic boundary layer is 𝑢+, and

1/4

√ and y is the thickness of the wall) [25,26].

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velocity 𝑢𝜏 =

𝑢𝜏𝑦/ , where 𝑢𝜏 is the friction

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the dimensionless distance from the wall is 𝑦+ (𝑦+ =

At the inlet,

with a normal inflow velocity of ul = -nU0. In this work, the

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approximation of the inlet values of κ0 and ɛ0 was obtained from the turbulent intensity IT and the turbulent length scale LT by means of the following simple

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The boundary conditions used to solve the equations (9)-(20) are as follows:

assumed forms: κ0= 3/2(U0 IT)2 and ɛ0=Cµ3/4 κ3/2/LT, where IT and LT were fixed at 0.05 and 0.0655, respectively [26]. The turbulent intensity of the fully turbulent flows has dimensionless values between 0.05 and 0.1. The turbulent length scale can be determined as function of the radius by means of LT=0.07r, where r in this work is the inlet radius of 0.635 cm.

Journal Pre-proof 

At the RCE, an angular velocity of 100 rpm with an inlet disperse phase flux , where F is the Faraday constant (96485 C mol−1), m is the molecular weight of hydrogen gas (2.02x10-3 kg/mol), j is the local current density on the RCE surface (A m-2) and z is the charge employed in reaction (2).

At the outlet, a normal stress equals to a pressure at the outlet: [ ]

P0, with

and

. This last equation

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expresses that the turbulent characteristic of whatever is outside the computational

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domain is guided by the flow inside the computational domain. Such an assumption

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is physically reasonable, as long as relatively small amounts of fluid enter into the

At the top of the system, an outlet mass flux

, where jave is the

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system [26].

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average cathode current density on the RCE surface, without viscous stress of the



]𝑛

.

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continuous phase on the free surface [

For all remaining boundaries, a velocity u+ given by equation (21) at a distance 𝑦+ from the solid surfaces, and no gas flux for the disperse phase.

3.3 Aluminum ion mass transport model The mass transport of any species within a system, in which it is considered that there is no chemical reaction and the electric field effects are negligible due to the supporting

Journal Pre-proof electrolyte in excess, it can be simulated using the convection-diffusion equation for diluted solutions:

(22)

where ul is the local continuous phase velocity vector from the solution of the biphasic κ-ε

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turbulence model, ci and Di are the concentration of ion aluminum and the aluminum

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diffusion coefficient, respectively.

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In this work, the turbulent diffusivity Di,T was calculated employing the Kays-Crawford

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equation [29]:

(23)



(

)(

(



)))

(24)

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(

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)

where ScT∞ = 0.85 [29].

Equations (22)-(24) were solved employing the following boundary conditions: 

at the six plates, an inlet aluminum flux

, where j is the local current density

on the electrode surface and z is the charge employed in the reaction (1); 

at the outlet: −n ∙ ( + 

T)∇ci

 = 0;

Journal Pre-proof 

for all remaining boundaries −n ∙ Ni = 0.

3.4 Simulation Governing equations with variables φ, ϕg, ul, ug and ci were solved simultaneously in 3D by the finite element method, employing the commercial code COMSOL Multiphysics® 4.3. Parameters, electrolyte and gas properties, employed in the simulations, are shown in Table

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II.

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The solution of the models was verified at different mesh sizes, until the typical solution

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around these mesh elements was unchanged. The computational domain for the simulations was developed with a mesh with 807547 elements. The simulation times took

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approximately 480 min. The solver employed was iterative PARDISO direct method, and a

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relative tolerance of precision of the CFD simulations considered a convergence criterion

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<10−5. For all cases, mass and charge balances were verified.

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4. Results and discussion

4.1 Current density distribution Figure 2 shows the normalized current density distribution on the RCE surface (Figure 2(a)), and on the surface of working electrode plates (Figure 2(b)) for jave= 16 A m-2. According to Figure 2(a), the current distribution on the RCE surface is practically uniform along the z-coordinate. However, at the bottom of the RCE, it presents significant current variations due to the location of the RCE above the inlet of the fluid, because the RCE length is not symmetrical with the working electrode length, which originates border effects, as it is discussed by Madore et al. [23] and Low et al. [24] in rotating Hull cells.

Journal Pre-proof Figure 2(b) shows the current distribution for the working electrode plates, and it is seen a practically uniform distribution, except at the regions close to the insulating walls and close to the top of the reactor. In such regions, the current significantly decreases due to the effect of the geometry of the reactor. Similar plots for jave=8 and 32 A m-2 were obtained (not

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shown in this work), and the behavior was the same.

Figure 2. Normalized current density distribution (a) on the RCE surface, and (b) on the surface of working electrode plates for jave= 16 A m-2.

Current distribution profiles on the center surface of the working electrodes and on the surface of the RCE were obtained from the bottom (z=0) to the top (z=L) of the reactor. Normalized current distribution vs normalized electrode length profiles are showed in Figure 3 for averaged current density values of 8, 16 and 32 A/m2. It is clearly observed

Journal Pre-proof that current distribution is more uniform at lower averaged current densities, and border effects are more evident at higher averaged current densities for both electrodes. Figure 3(a) shows border effects on the RCE surface at the bottom of the reactor, and this behavior agrees with Figure 2(a). Current distribution profiles (not shown in this work) as a function of the RCE perimeter were also obtained. However, along the angular coordinate, it was found a uniform current distribution, and the behavior was the same, as it was reported by

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Pérez and Nava [30].

Figure 3. Normalized current density distribution profiles as a function of the normalized length at jave =8 (solid line), 16 (dash line), and 32 (dot line) A m-2 (a) on the surface of the RCE, and (b) on the center surface of the working electrode from the bottom (z=0) to the top of the reactor (z=L).

Journal Pre-proof The normalized current distribution profile for one working electrode plate is shown in Figure 3(b). Higher averaged current densities develop non-uniform current distribution; however, current density deviations present a magnitude order of 1x10-3. Therefore, current density distribution is practically uniform at the center of the plates. The same behavior was observed for every working electrode plate. Normalized current distribution profiles are also presented by Song et al. [19] in a continuous rectangular parallel plates arrangement.

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However for this chase, border effects are more evident due to the geometrical arrangement

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between anodes and cathodes.

The Wagner number is used to characterize the relative importance of the charge transfer

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control on the current distribution. The current distribution is expected to become more

(25)

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uniform, as the Wagner number increases [23,24].

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Where l is a characteristic length, which in our case is equal to the anode and cathode gap, l = 1.8 cm. In this work, at jave= 8, 16 and 32 A/m2, the calculated Wagner numbers were 0.83, 0.42 and 0.21, respectively; so, effectively, the Wa number is directly proportional to uniform current distribution. In general terms, the current distribution on the surface of all electrodes is practically uniform in the most of their regions; and the current distribution variability is mainly originated by the geometrical configuration of the reactor. A uniform current distribution is very important to avoid parasitic reactions such as oxygen evolution reaction in some regions on the electrode surface, which has an impact in the current

Journal Pre-proof efficiency applied [30]. Besides, the current density also depends on the disperse phase, as it was mentioned in introduction section. Nevertheless, the effect of this variable does not

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have a significant contribution in the current density distribution, as it is discussed below.

Figure 4. Disperse phase volume fraction in the middle of the domain at z-y plane for jave= 32 A m-2

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at 100 rpm with an input flow of 0.4 L min-1.

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4.2 Effect of disperse phase in the current density distribution and momentum transfer The numerical solution of the proposed model allowed to obtain a disperse phase volume fraction distribution inside the system. Figure 4 shows the stationary disperse phase volume fraction in the middle of the system in a z-y plane for jave=32 A m-2 with a rotational speed of 100 rpm and 0.4 L min-1 inflow velocity. According to Eq. (4), the electrolyte conductivity k0 is very related with the disperse phase, and hence, with the current density (Eq. (3)). The electrochemical kinetic parameters used in this model, the averaged current densities employed, and the RCE reactor open boundary to the atmosphere developing small values (<3 %) of disperse phase fraction for the highest averaged current density

Journal Pre-proof studied in this work, as it is observed in Fig 4. Therefore, it is expected that the value of the electrolyte conductivity in the bulk solution does not decrease significantly due to the insignificant resistivity of the bubbles produced. Consequently, the effect of the disperse phase on the current density distribution is practically negligible for this study case.

Also, Fig. 4 shows that hydrogen gas concentration increases along the z-coordinate of the

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RCE following the flow direction. Similar results could be found in several references,

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[8,11,31] however the gas phase behavior differs from them due to the effect of cathode

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rotation. Moreover, the gas dispersion throughout the entire reactor is more evident in such

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references. Al-mashhadani et al. [32] developed a study in a non-electrochemical rotating biphasic flow system varying the bubble size. In this work such authors found that the

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grade of dispersion is proportional to the bubble size. This last could be related with the

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grade of dispersion inside the RCE reactor due to the size employed in this work. Nevertheless, the gas bubbles will not have a determinant effect on the flow pattern due to

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the low level of gas produced (<3 %), because the forces that are coming into the system do

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not contribute to a change in magnitude or direction of the continuous phase that flows into the system; hence, an analysis of the continuous phase is sufficient to describe the momentum transfer of the system studied.

Figure 5 shows (a) the velocity magnitude field of the continuous phase in the middle of the domain at z-y plane and (b) the streamlines patterns of the system for 100 rpm with an input flow of 0.4 L min-1. It is clearly observed that higher velocity zones and many spiral streamlines are found close to the rotating cylinder, as it was expected; meanwhile, inside the sedimentation tanks, slow velocity zones are observed. Such “dead zones” in the

Journal Pre-proof sedimentation tanks are originated by the flow patterns, which develop descendent movements along the z-axis, as it is shown in Fig. 5(b). In practice, these high velocity zones and spiral streamlines help to coagulation process because increase the mass transfer in the bulk solution between the aluminum ion and the suspended solid; whereas, the slow flow patterns and dead zones in the sedimentation tanks are desirable to develop the flocculation and sedimentation process, because it increase the residence time to favor the

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flocs growth and density increment [4,33]. However, an analysis of the complex three-

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phase solid-liquid-gas flow with the flocs is out of the scope of the present communication.

Figure 5. a) Velocity magnitude distribution of the continuous phase in the middle of the domain at z-y plane and b) flow lines patterns of the system for 100 rpm with an input flow of 0.4 L min-1.

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4.3 Aluminum mass transport and experimental validation In order to validate the biphasic flow simulation and current distribution analysis, the Al 3+ concentration was theoretically and experimentally determined. For the theoretical calculation, the convective term in Eq. (22) only considers the local velocity vectors from the continuous phase, obtained from the biphasic turbulence model. This last is because the

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motion field of the continuous phase has not been affected by the disperse phase produced,

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as it was previously discussed.

Figure 6 shows Al3+ concentration profiles in the middle of the domain at z-y plane for

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different times of (a) 5 s, (b) 50 s, (c) 200 s and (d) 500 s with jave= 32 A m-2, 100 rpm and

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0.4 L min-1 inflow rate. It is seen in the figure that the accumulation of the ion inside the

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system through time achieves the stationary state at 500 s in the RCE reactor. Although theoretical aluminum ion concentration moves through the first sedimentation tank as can

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be seen in the figure, in practice, this ion and ‒OH from Eq. (2), will transfer into the bulk

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solution and undergo further spontaneous hydrolysis reactions to form various monomeric and polymeric species, part of which will finally transform into hydroxide flocs [5–7]. This process occurs in a fraction of seconds; therefore, an analysis inside the RCE reactor is more relevant.

When aluminum concentration reaches stationary state inside the RCE reactor, it is observed in Fig. 6(d) a quasi-uniform distribution, suggesting well-mixed conditions to perform electrocoagulation process and therefore it increases the efficiency to remove the contaminants because the formed metal hydroxides are available in almost all regions of the

Journal Pre-proof reactor. Different simulated conditions were proven, obtaining the same behavior (not shown in this work). This last one puts in evidence the good performance of the RCE in the

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electrocoagulation process.

Figure 6. Aluminum ion concentrations in the middle of the domain at z-y plane at different times of a)5s, b) 50s, c) 200s and d) 500s for jave= 32 A m-2 at 100 rpm with an input flow of 0.4 L min-1.

Recently, Song et al. [19], and Lu et al. [20] analyzed the monophasic flow of two continuous parallel plates arrangements for EC, and the flow pattern presented in such works differs from the presented in Fig. 5(b) due to the geometrical design and the rotating electrode. However, the grade of homogenization of the species presented inside the system

Journal Pre-proof could be discussed. In the system presented by Song et al. [19] more slow velocity zones are generated which affects the mass transfer. Therefore, the dispersion grade of the electrogenerated ion is not favored. These slow velocity zones could minimize by increasing the flow rate. However, this affects the generation of flocs and the proper interaction between pollutants, reducing the removal efficiencies [19]. In this way, the combined effect of the RCE with both sedimentation tanks is better, because the propose

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system presents a high velocity zone (RCE) to promote coagulation process, and a slow

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velocity zone (sedimentation tanks) to promote flocculation process [4,33]. In the results

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reported by Lu et al. [20] it was found that at the direction of the streamline from inlet to the outlet, the concentration of electrogenerated aluminum does not increase along the

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whole channel. Instead, Al3+ only increase in the vicinity of the electrode surface near to

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the inlet area. After that, the concentration of Al3+ decreases gradually. In this way, the

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electrogenerated specie inside the RCE reactor achieves more uniform concentration distribution than traditional parallel plates systems, confirming the convenience to employ a

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rotating electrode to develop well-mixing conditions.

Finally, in order to validate the proposed model, the stationary aluminum concentration in a point at the top of the reactor was compared with experimental aluminum ion concentration after 500 s at the same sample point. Figure 7 (a) shows comparisons of aluminum ion concentration at different averaged current densities for the proposed numerical model (▲), the experiments (●) and calculated data by the classical first Faraday’s law equation of electrolysis (■). As it can be observed, there is a good approximation between the experimental and numerical results for all current densities with an error less than 10%. Similar behavior of Fig. 7(a) can also be observed in the results obtained by [20]. The

Journal Pre-proof difference between the data calculated by Faraday’s equation and the experimental results obtained, is a common result in real electrochemical systems because the classical first Faraday’s law equation is an averaged idealized expression which does not contemplates other phenomena such as the hydrodynamic inside the system or the chemical dissolution [33]. In this way, the data obtained by the numerical model presented a better correlation because it considers real effects that occurs simultaneously such as the rotating biphasic

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flow, the current distribution in the electrodes and the mass transfer. Several trial However, the

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simulations higher than 32 A/m2 were obtained (not shown herein).

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correlation between numerical and experimental data become worse as the current

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increased. It is common that at higher current density values for EC process, the parasitic oxygen evolution reaction became more evident [4], therefore it should be considered in the

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anode; however, such analysis is out of the scope of the present communication.

Experimentally, it is complex to quantify the generation of hydrogen gas. However, a

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comparison was made between the volume fraction of the dispersed phase obtained by the

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proposed model and calculated by Faraday's first law of electrolysis, and Figure 7(b) shows the values obtained for the range of currents studied.

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Figure 7. (a) Comparisons of stationary Al3+ concentration and (b) disperse phase volume fraction between experimental data (●), calculated data by the classical first Faraday's law equation (■) and

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the numerical model (▲) at different averaged current densities.

5. Conclusions

In the present work, a theoretical analysis of the generation of aluminum ions (Al 3+) and molecular hydrogen gas (H2) was carried out using a multi-coupled numerical model of secondary current distribution, turbulent biphasic hydrodynamic and mass transport by convection-diffusion in a new design of a RCE reactor with two sedimentation tanks. By quantifying the dispersed fraction, it was found a variation in the conductivity of the electrolyte due to the presence of bubbles product of the electrochemical kinetics employed. However, through the geometry design and the currents employed, it was

Journal Pre-proof possible to assume constant electrolyte conductivity in the system, so that the results of the current distribution would not be significantly affected. From the momentum analysis, it was determined that the dominant movement pattern corresponds to the continuous phase and the effect of the dispersed phase does not produce a variation of it. Moreover, the maximum and minimum velocity regions were determined; these results verify that the zone of a greater agitation corresponds to the RCE reactor, and the zones where a low

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speed is necessary to favor the flocculation and sedimentation processes, correspond to the

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sedimentation tanks. By analyzing the results of the concentration profiles, it was possible

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to obtain the stationary concentration of Al3+ inside the reactor for the different current densities employed, founding a well-mixing reaction environment. Comparisons between

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experimental, numerical, and by the first Faraday’s law concentration values strongly

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suggest that it is possible to predict, and perhaps, control the behavior of the concentration

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of Al3+and H2 at different current densities. However, the experimental concentration of the generated hydrogen and other species such as OH- must be considered in future theoretical

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complex model.

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works. Also, the parasitic oxygen evolution reaction should be included to develop a more

Acknowledges

A. Daniel Villalobos Lara is grateful to CONACYT for the Scholarship No.583917 granted. The authors are grateful to PRODEP for the economic support via the Project NPTC-UG615. The authors also acknowledge the University of Guanajuato.

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Journal Pre-proof Table I. Geometrical reactor parameters 8.5 cm

Inlet diameter

1.27 cm

RCE diameter

4 cm

RCE height (in contact with the solution)

30 cm

First sedimentation tank height

15 cm

First sedimentation tank diameter

34 cm

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RCE area, ARCE (in contact with electrolyte)

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Reactor internal diameter

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Height of the plates used as anodes (attached to the reactor walls)

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Anode and cathode gap, l/ m

386.8 cm² 30.5 cm 1.8 cm

Journal Pre-proof Table II. Parameters, electrolyte and gas properties 1.01x10-9

Dynamic electrolyte viscosity, μ/Pa s,

0.001

Hydrogen Density, ρg/kg m−3,

0.083

Bubble diameter, db /m [34]

8x10-6

Solution Density, ρl/kg m−3,

1000

Absolute temperature, T/°K

293.15

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Global diffusion coefficient of Al3+, Di/m2 s−1 [20]

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Volumetric inflow rate, Q/L min−1

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Angular velocity of RCE, wr/Rad s-1

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Mean linear inflow velocity, U0/m s−1

Anode open circuit potential,

/V vs SHE [35] /V vs SHE [35]

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Cathode open circuit potential,

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Electrolytic conductivity, k0/S m-1

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Cathodic Tafel slope, bc /V dec-1 [35]

0.4 10.5 0.04 1 -0.68 0.57 0.12 48.5

Anodic Tafel slope, ba /V dec-1 [35]

0.28

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Exchange current density j0/ A m-2 [35]

Journal Pre-proof Figure captions

Figure 1. Figure 1. (a) Electrocoagulation lab configuration system, (b) electrodes arrangement inside the reactor and (c) 3D computational domain of the system.

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surface of working electrode plates for jave= 16 A m-2.

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Figure 2. Normalized current density distribution (a) on the RCE surface, and (b) on the

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Figure 3. Normalized current density distribution profiles as a function of the

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normalized length at jave =8 (solid line), 16 (dash line), and 32 (dot line) A m-2 (a) on the surface of the RCE, and (b) on the center surface of the working electrode from the

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bottom (z=0) to the top of the reactor (z=L).

Figure 4. Disperse phase volume fraction in the middle of the domain at z-y plane for

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jave= 32 A m-2 at 100 rpm with an input flow of 0.4 L min-1.

Figure 5. a) Velocity magnitude distribution of the continuous phase in the middle of the domain at z-y plane and b) flow lines patterns of the system for 100 rpm with an input flow of 0.4 L min-1.

Figure 6. Aluminum ion concentrations in the middle of the domain at z-y plane at different times of a)5s, b) 50s, c) 200s and d) 500s for jave= 32 A m-2 at 100 rpm with an input flow of 0.4 L min-1.

Journal Pre-proof Figure 7. (a) Comparisons of stationary Al3+ concentration and (b) disperse phase volume fraction between experimental data (●), calculated data by the classical first Faraday's law equation (■) and the numerical model (▲) at different averaged current

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densities.

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Credit author statement

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A. Daniel Villalobos-Lara: Investigation, Writing - Original Draft, Formal analysis Tzayam Pérez: Writing - Original Draft, Validation, Supervision Agustín R. Uribe: Resources, Conceptualization J. Arturo Alfaro-Ayala: Conceptualization José de Jesús Ramírez-Minguela: Conceptualization Jesús I. Minchaca-Mojica: Conceptualization

Journal Pre-proof Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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Highlights Electrocoagulation RCE reactor was modeled by CFD simulation. Biphasic flow, current distribution and mass transport were coupled. Disperse phase effects were evaluated.

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Good correlation between numerical and experimental data.