Keywords

Introduction

Industrial methods for producing aluminum require higher temperatures, which consume not only higher energy, but also are non-eco-friendly [1]. In recent years, room temperature ionic liquids (RTILs), which melt below 100 °C are showing a great promise to electrodeposit aluminum in a greenway at low temperatures. A mixture of imidazolium chloride-based ionic liquid such as 1-butyl-3-methylimidazolium chloride (BMIC) and aluminum chloride exhibit adherent, dendrite free deposition with high purity during aluminum electrorefining and electrowinning [2,3,4]. Several modelings have been developed to simulate the various type of cell conditions. Zhang and Reddy developed a mathematical 3-D model to forecast the current distribution, electric field distribution, fluid flow, and concentration for near room-temperature aluminum electrowinning cell using Ansys (paired with FLOTRAN and EMAG) and Ansys CFX programs [5, 6]. In this research, a model is developed to predict the current density distribution and secondary resistances for Al electrodeposition by using Ansys Fluent program. The electrolyte was an eutectic mixture of 1-butyl-3-methylimidazolium chloride (BMIC) and aluminum chloride (AlCl3) in 1:2 (BMIC: AlCl3) molar ratio where the anode is aluminum and the cathode is copper. Experimental data was used to calculate the contact resistance and investigate the electric potential distribution. This CFD software offers superior quality meshing, essential models for species transfer, electric potentials, fluid flow, heat transfer, solution accuracy, computational speed (allowing for parallel computations via domain decomposition), facilitating the implementation of complex boundary conditions and source terms via user-defined functions (UDF). This modeling study has five targets: 1. Analyzing the geometry and mesh of the model; 2. Analyzing the parameters on the boundary conditions; 3. Determining the properties of electrolyte and electrodes, such as density, viscosity, and electrical conductivity; 4. Calculating the contact resistance using experimental current density data; 5. Simulating the potential distribution on the electrodes and electrolyte.

Current density distribution plays an important role in the morphology of the deposition. Due to the geometry of the system, conductivity of cell component activation overpotential, diffusion overpotential and hydrodynamics of electrolyte, current density deviates in the different points of the electrode [7]. An accurate current density profile is possible to predict by using Ansys’s Fluent modeling, which can help to estimate the electrodeposition morphology. If we consider the electrochemical cell as a simple electric circuit, we may define the current and potential in this way,

$$ I = \frac{U}{{R_{{\text{s}}} + R_{{\text{e}}} + R_{{\text{c}}} + R_{{{\text{ct}}}} }} $$

where U is the electric potential, Rs is the resistance of solution, Re is the resistance of the electrode, Rc is contact resistance between electrode and electrolyte, and Rct is reaction resistance or charge-transfer resistance. Normally, solution resistance Rs and electrode resistance Re contribute much more total resistance. So here, we consider contact resistance Rc and charge-transfer resistance Rct as secondary resistances. Resistance at the interface between electrode and electrolytes plays an important role in the current density. Although the studies on this contact resistance have been done on energy storage systems, contact resistance studies on the electrodeposition method is rarely found [8,9,10]. When an electron transfers from the electrode to the electrolyte (or vice versa), it has to overcome the charge-transfer resistance. Conductivities of the solution were investigated in a previous study [11], and resistances of electrode materials were chosen from the modeling software. However, Rc and Rct are necessary to be defined in the present work. Also, Rc is attributed to contacting interface of electrode and electrolyte, and Rct is related to reaction, temperature, potential, as well as the concentration of reacted species. Therefore, the effect of temperature, potential, the concentration of Al species, type of ionic liquid, and surface morphology on secondary resistances are studied in the present work.

Process Modeling

The geometry of the electrochemical cell was developed by using the experimental cell dimensions. The diameter and height of the cylinder were 4 and 3 cm, respectively. The dimensions of the cathode electrode (Cu) were 1.5 × 1.5 × 0.1 cm, and the dimensions of the anode electrode (Al) were 1.5 × 1.5 × 0.15 cm. The distance between the two electrodes is 2.3 cm. One small cylinder with 0.5 cm height and 1 cm diameter was created at the bottom as a stirrer. All the above parameters are corresponding to the practical experiment. Then, a mesh with a good aspect ratio and skewness was established. The domain was filled with 1:2 mol ratio of BMIC-AlCl3 as an ionic liquid electrolyte. Figure 1 shows the geometry and mesh of the model.

Fig. 1
figure 1

Model geometry and mesh. (Color figure online)

Full size image

The quality of the geometry and mesh are listed in Table 1.

Table 1 Geometry and mesh data
Full size table

We selected the “Electrical potential” model. The steady-state and incompressible flow was assumed. And, the methods and equations used in this model are listed in Eqs. (1–9). In general, the electric field E can be written as:

$$ E = - \Delta \varphi - \frac{\partial A}{{\partial t}} $$
(1)

where \(\varphi\) and A are the scalar potential and vector potential.

Ohm’s law can be described as:

$$ j = \sigma E $$
(2)

Here, j = current density, \(\sigma\) = electrical conductivity of media. If U = velocity field and B = magnetic field, it also can be written as:

$$ j = \sigma \left( {E + U \times B} \right) $$
(3)

As in the steady-state,

$$ \frac{\partial A}{{\partial t}} = 0 $$
(4)

Ohm’s law can be written as:

$$ j = \sigma \left( { - \Delta \varphi + \left( {U \times B} \right)} \right) $$
(5)

For sufficiently conducting media, the principle of conservation of electric charge gives:

$$ \nabla \cdot j = 0 $$
(6)

Therefore,

$$ \nabla^{2} \varphi = \nabla \left( {U \times B} \right) $$
(7)

The potential on the boundary can be defined as:

$$ \frac{\partial \varphi }{{\partial n}} = (B \times U)_{{{\text{boundary}}}} \cdot n $$
(8)

where n = vector normal to the boundary, and

$$ \varphi = \varphi_{0} $$
(9)

\(\varphi_{0}\) is a specific potential on the boundary.

Properties of the electrolyte were defined, which is from our previous experimental results [11]. Properties of the anode (Al) and the cathode (Cu) were built-in with the software.

After defining the properties of the electrolyte, thermal and potential conditions and values of those boundaries were set rational and compared to the real experiment. For the final calculation process, we chose solution methods, such as Gauss–Seidel or ILU methods, set reference and initialization values.

Results and Discussion

Current Density Distribution

The vector of the electric current density magnitude is shown in Figs. 2 and 3. In this case we considered, applied Voltage = 1.5 V, distance of electrodes = 2.3 cm, Stirring speed = 12.57 rad/s (120 rpm). Viscosity and electrical conductivity of the electrolyte at 100°C were used. Contact resistance at cathode and anode were both set as 0 ohm-m2 for the first simulation.

Fig. 2
figure 2

Distribution of electric current density in the X–Z plane (left side is Cu cathode and right side is Al anode). (Color figure online)

Full size image
Fig. 3
figure 3

Distribution of electric current density in the X–Y plane, 0.005 m from the top of the ionic liquid (left side is Cu cathode and the right side is Al anode). (Color figure online)

Full size image

As shown in Figs. 2 and 3, the current density is larger at the bottom and edge of the Cu electrode. That might be one of the reasons for the easy formation of Al dendrite at the bottom and the edge parts of the electrode [11]. Also, the backside of the Cu electrode, which is face to the beaker boundary, has a lower current density than the front side. That is why there is more deposition at the front side than the backside of the electrode in the experiment.

Calculation of Secondary Resistances (Rc + Rct)

In this modeling approach, we calculated Rc + Rct based on the experimental current density as a function of applied potential, temperature, and surface roughness. In Table 2, the Rc + Rct was given for different applied potential values (Deposition temperature: 100°C; stirring rate: 120 rpm; deposition time: 2 h; surface roughness of Cu electrode: 543.1 ± 59.7 nm; electrode distance: 23 mm; electrolyte BMIC: AlCl3 at a molar ratio of 1: 2).

Table 2 Rc + Rct as a function of the applied potential
Full size table

The relationship between Rc + Rct and the temperature was also simulated. During the simulation, a variation of temperature has changed the conductivity and viscosity of the ionic liquid. Thus, we set the different conductivities and viscosities of ionic liquid to simulate the secondary resistances at different temperatures.

The variables and results for the study of deposition temperature effect on Rc + Rct are given below (stirring rate: 120 rpm; applied potential 1.5 V; deposition time: 2 h; surface roughness of Cu electrode: 543.1 ± 59.7 nm; electrode distance: 23 mm) (Table 3).

Table 3 Secondary resistances as a function of temperature
Full size table

The effect of cathode surface roughness as a function of Rc + Rct is given in Table 4 (deposition temperature: 100 °C; stirring rate: 120 rpm; applied potential 1.5 V; deposition time: 2 h; electrode distance: 23 mm).

Table 4 Rc + Rct as a function of surface roughness
Full size table

In the last part of the study, the effect of electrolyte composition was investigated. The molar ratio of AlCl3 was changed to 1.4, 1.6, 1.8, and 2 where the molar ratio of BMIMCl was fixed to 1. The Rc + Rct decreased with an increasing AlCl3 molar ratio. With the increasing molar ratio of AlCl3, the concentration of Al2Cl7− ion increases [14]. Al2Cl7 ion raises the electrical conductivity and reduces the viscosity [15,16,17]. Because of this, Rc + Rct decreases. The values of secondary resistances are listed in Table 5 (temperature: 100 °C; stirring rate: 120 rpm; applied potential 1.5 V; deposition time: 2 h; surface roughness of Cu electrode: 543.1 ± 59.7 nm; electrode distance: 23 mm).

Table 5 Rc + Rct as a function of AlCl3 molar ratio
Full size table

The correlation between these parameters and surface roughness is given in Fig. 4.

Fig. 4
figure 4

Variation of secondary resistances in the cell with a applied potential, b temperature, c surface roughness, and d AlCl3 molar ratio

Full size image

As shown in Fig. 4, the Rs + Rct decreased as applied potential and temperature increased, while increased as surface roughness increased. On the other hand, the redox reaction of Al species is easier to take place at higher potential, temperature, and AlCl3 molar ratio as well as lower surface roughness. So, the contact resistance response to change these variables is expected.

Conclusions

A 3-D numerical model of aluminum electrodeposition from chloroaluminate-based electrolyte was developed in ANSYS Fluent. The potential distribution and contact resistance in the electrochemical cell were determined. The result showed that electrode potential is uniform in the electrodes. The contact resistance between the electrode and electrolyte decreased with increasing applied voltage, temperature, and AlCl3 molar ratio. In contrast, increasing surface roughness increased the contact resistance.