## 3 Results and Discussions
Figure 10: (**a**) Oscillation of longitudinal velocity at monitoring point “b” under different temperature difference conditions; (**b**) power spectrum density of longitudinal velocity (\(R=5\) mm, \(Ar=1.0\), \(Pr=5.54\), \(Le=25.8\), \(Ca_{C}=-0.021\), \(\rho_{1}/\rho_{g}=597.9\)). Effect of Heat Loss on Flow Structure and Interfacial Oscillation Characteristics of Thermo-Solutocapillary Convection  
Figure 11a exhibits the contour plot of the internal temperature of the liquid bridge under different heat loss conditions. The results show that the heat loss has little influence on the temperature change in the center vicinity of the system (x = 1.5 to 2.5) via comparing the temperature contours under three heat loss conditions. The temperature profile in this region is almost straight, indicating that the heat transfer pattern near the center is mainly in the form of heat conduction. However, there are some subtle changes in the temperature field of the area due to heat loss in close proximity to the free interface. The temperature near the free interface no longer remains uniform compared to that in the central portion. The non-uniformity increases as the \(Bi\) number increases. The closer to the interface, the more apparent the temperature variations. The heat transfer method near the free interface is mainly conducted by convection under the influence of the surface flow, which results in a certain unevenness in the temperature distribution of the region compared with the central part. The heat loss of the liquid bridge magnifies when the \(Bi\) number increases. The temperature value at a fixed distance from the interface exhibits a continuously decreasing trend, resulting in a gradual increase in the non-uniformity of temperature distribution near the interface. Figure 11b exhibits the contour plot of the internal concentration under different heat loss conditions. Generally, the concentration value on the interface is smaller than the concentration value at the rest of the same height, and a large concentration gradient is formed at the upper end. Compared with the temperature contour, the concentration contour shows greater heterogeneity. Under the three heat loss conditions, most of the concentration values in the middle part remain almost unchanged. However, the concentration profile near the free interface gradually approaches the upper end of the interface as the \(Bi\) number increases, and a large concentration gradient is formed in this region. Figure 11: (**a,b**) Temperature and concentration contours under different heat loss conditions (\(R\) = 5 mm, \(Ar\) = 1.0, \(Pr\) = 5.54, \(Le\) = 25.8, \(Ca_{C}\) = \(-\)0.021, \(\rho_{l}\)/\(\rho_{S}\) = 597.9). entering the high-frequency stable oscillation stage. The yellow area is the selected high-frequency stable oscillation stage, and the arrow refers to an enlarged area map of the area. Figure 12b shows that the monitoring points have only one main frequency under different heat losses, and they all have a single-periodic oscillation. When \(Bi=0.2\), the average velocity is \(-0.00227\), the average amplitude is \(1.2\times 10^{-4}\), and the main frequency is \(f_{1}=0.053\). At \(Bi=0.4\), the velocity, amplitude, and frequency are \(-0.00198\), \(1.1\times 10^{-4}\), and \(0.053\), respectively. At \(Bi=0.6\), the velocity, amplitude, and frequency are \(-0.00174\), \(8\times 10^{-5}\), and \(0.047\), respectively. The transverse velocity value and amplitude gradually decrease, while the average oscillation period gradually increases as the \(Bi\) number increases. Because the upper monitoring point is located in a region of high temperature and concentration, the fluid flow experiences significant influence from the thermo-solutocapillary convection. Meanwhile, the temperature and concentration of the monitoring point \"a\" decrease as the degree of heat loss increases (see Figure 11).