## 3 Results and Discussion
### Simulation Analysis of the Migration Tank
#### 3.1.1 Model Construction  
(1) Physical Model of the Electromigration Tank [18; 19]  
All currents flowed through the anode and cathode. The influence of the voltage drop of the cathode on the electric field was ignored. The anode was uniformly consumed in the height direction, and the amount of liquid cathode was uniformly increased. The electrolytic cell was symmetrical, and one half of it was used as the research object. The diameters of the cathode and anode were 25 mm; the insertion depths of the cathode and anode were 12 mm; the depth of the molten pool was 30 mm. The process conditions included (1) a working current of 2 A, electrolysis temperature of 1035 \({}^{\circ}\)C, AlF\({}_{3}\)-AlF\({}_{3}\)-LiF-Y\({}_{2}\)O\({}_{3}\) electrolysis system, molten salt density of 6.20 g/cm\({}^{3}\), molten salt viscosity of 0.020 Pa\(\bullet\)S, surface tension of 0.28 N/m, and conductivity of 2.30 S/cm. Unstructured mesh was used to densify the chemical reaction boundary and contact area, mainly including the contact surface between graphite anode and electrolyte, the contact surface between tungsten cathode and electrolyte, and the top of tungsten cathode. The grid parameters are as follows:  
The number of vertex units is 20, the number of side elements is 1600, and the number of boundary elements is 112586. Special encryption location (maximum unit is 0.003 m and minimum unit is 1.5) \(\times\) 10\({}^{-5}\) m, the maximum unit growth rate is 1.1, the curvature factor is 0.2, and narrow area resolution (0.6). Location of ordinary grid (maximum unit is 0.016 m and minimum unit is 7) \(\times\) 10\({}^{-4}\) m, the maximum unit growth rate is 1.1, the curvature factor is 0.3, and narrow area (resolution 0.90). (2) Preset Conditions [20]  
The driving force of the electrolyte flow was the buoyancy of bubbles; the interaction force between different bubbles was ignored, and the bubble size was uniform. The electrolytic cell had no leakage. The current flowed from the anode to the cathode, and the electrolyte was an incompressible fluid with a uniform temperature. The anode surfacegenerated the bubbles at a gas production rate of 0.21 m\({}^{3}\)/(s\(\bullet\)m\({}^{2}\)). The electrolyte surface was in contact with the atmosphere, and the graphite crucible had no-slip walls. Control Equations [21; 22; 23]  
Equation (1), continuity equation:  
\[\frac{\partial\rho}{\partial t}+\frac{\partial(\rho u_{x})}{\partial x}+\frac{ \partial(\rho u_{y})}{\partial y}=0 \tag{2}\]  
where \(u_{x}\) is the velocity component in the X direction, m\(\bullet\)s\({}^{-1}\); \(u_{y}\) is the velocity component in the Y direction, m\(\bullet\)s\({}^{-1}\); is the time, s.  
Equation (2), momentum equations:  
\[\frac{\partial\rho u_{x}}{\partial t}+\bigtriangledown\bullet(\rho u_{x} \overrightarrow{u})=\frac{\partial\rho}{\partial x}+\frac{\partial\tau_{xx} }{\partial x}+\frac{\partial\tau_{xy}}{\partial y}+\rho f_{x} \tag{3}\]  
\[\frac{\partial\rho u_{y}}{\partial t}+\bigtriangledown\bullet(\rho u_{y} \overrightarrow{u})=\frac{\partial\rho}{\partial y}+\frac{\partial\tau_{xx} }{\partial x}+\frac{\partial\tau_{yy}}{\partial y}+\rho f_{y} \tag{4}\]  
where \(u_{x}\) is the velocity component in the X direction, \(u_{y}\) is the velocity component in the Y direction, m\(\bullet\)s\({}^{-1}\); t is the time, s; \(\rho\) is the density, kg\(\bullet\)m\({}^{-3}\); \(f_{x}\), and \(f_{y}\) are the X- and Y-directional mass forces, respectively, m\(\bullet\)s\({}^{-2}\); \(\tau_{xx}\) and \(\tau_{yy}\) are the components of the viscous stress generated on the surface of an infinitesimal body, Pa.