## 3 Results and Discussions  
This paper mainly studies the influence of temperature difference and heat loss on the flow structure and surface oscillation of the coupled thermo-solutocapillary convection. The calculation conditions are exhibited in Tables 3 and 4, respectively. Two fixed monitoring points \"a\" and \"b\" are installed at the upper end (\(R\), \(0.9H\)) and the intermediate position (\(R\), \(0.5H\)) of the right interface to monitor the oscillation characteristics of the free interface. \begin{table}
\begin{tabular}{c c c c c} \hline
**Grids** & \
\begin{tabular}{c} **Longitudinal** \\ **Velocity** \\ \end{tabular} &
\begin{tabular}{c} **Transverse** \\ **Velocity** \\ \end{tabular} & **Temperature** & **Concentration** \\ \hline \(41\times 21\) & \(0.005382\) & \(-0.000136\) & \(0.265457\) & \(0.316837\) \\ \(81\times 41\) & \(0.005194\) & \(-0.000129\) & \(0.265165\) & \(0.313024\) \\ \(101\times 51\) & \(0.005234\) & \(-0.000131\) & \(0.265960\) & \(0.314206\) \\ \(121\times 61\) & \(0.005162\) & \(-0.000127\) & \(0.264634\) & \(0.312122\) \\ \hline \end{tabular}
\end{table} 
Table 2: Dimensionless velocity, temperature, and concentration distributions at the intermediate height surface point of the right liquid bridge (\(\Delta T=1\), \(\Delta C=1\), \(Pr=5.54\), \(Le=25.8\), \(R=5\) mm, \(Ar=1.0\)). \begin{table}
\begin{tabular}{c c c c c} \hline \(\Delta T\)**(-)** & \(\Delta C\)**(-)** & \(Ca_{T}\) & \(Ca_{C}\) & \(Ma\) \\ \hline \(1\) & \(1\) & \(0.00045\) & \(-0.021\) & \(372\) \\ \(2\) & \(1\) & \(0.0009\) & \(-0.021\) & \(744\) \\ \(3\) & \(1\) & \(0.00135\) & \(-0.021\) & \(1116\) \\ \(6\) & \(1\) & \(0.0027\) & \(-0.021\) & \(2232\) \\ \hline \end{tabular}
\end{table} 
Table 3: Calculation conditions (corresponding to Section 3.1). Figure 2: **(a,b)** Comparison of longitudinal velocity and deformation at free surface (\(R_{\sigma}=-10\), \(Le=100\), \(Pr=1\), \(A_{r}=1\)). Effect of Temperature Difference on Flow Structure and Interfacial Oscillation Characteristics of Thermo-Solutocapillary  
Figure 3 shows the velocity vector under different temperature differences at the same time. It can be found in Figure 3 that the adjustment of temperature difference has little effect on the velocity vector in the vicinity of the central axis of the liquid bridge (x = 1.75 to 2.25), but the velocity vector in other areas has changed greatly due to the change in temperature difference. It can be clearly examined from Figure 3a-d that the flow velocity of the fluid near the interface on both sides of the liquid bridge escalates with an augmentation in temperature difference. The fluid flow near the interface is relatively stable when the temperature difference is 1 to 3. However, when the temperature difference increases to 6, the fluid flow near the interface is no longer stable and fluctuates intensively, resulting in the interface fluid flow becoming disordered, thereby promoting the absorption of liquid bridge surface materials. Because the interface vicinity is the principal surface recirculation area, the increase in the flow rate indicates that the conversion speed between volume reflow and surface reflow is accelerated. By comparing the velocity vector diagrams under different temperature differences, it indicates that the velocity of fluid in the vicinity of the interface increases with the increase in temperature difference. When the temperature difference is aggravated to a particular extent, the interface flow becomes disordered. The conversion speed of surface reflow and volume reflow also increases as the temperature difference increases. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{\Delta T}\)(-) & \(\mathbf{\Delta C}\)(-) & \(\mathbf{Ca_{T}}\) & \(\mathbf{Ca_{C}}\) & \(\mathbf{Ma}\) & \(\mathbf{Bi}\) \\ \hline \(1\) & \(1\) & \(0.00045\) & \(-0.021\) & \(372\) & \(0.2\) \\ \(1\) & \(1\) & \(0.00045\) & \(-0.021\) & \(372\) & \(0.4\) \\ \(1\) & \(1\) & \(0.00045\) & \(-0.021\) & \(372\) & \(0.6\) \\ \hline \hline \end{tabular}
\end{table}