## 4 Conclusions  
This paper presents a numerical investigation into the characteristics of oscillating thermo-solutocapillary convection in toluene/n-hexane mixed solutions. An improved level set method is employed to accurately track every displacement of the interface, while the surface tension is addressed using the CSF model. The study employs the mass conservation level set method to examine the flow and interface oscillation properties under various temperature differences and heat losses, as well as to analyze the temperature, concentration, velocity, and deformation at the interface. The main findings can be summarized as follows:  
1. In the study of the impact of temperature difference (\(\Delta T=1-6\)) on oscillatory flows in thermo-solutocapillary convection, the velocity of fluid at the liquid bridge interface increases as the temperature difference rises. Upon reaching a certain threshold (\(\Delta T=6\)), the fluid flow at the interface becomes disordered, and the oscillation becomes more intense. The interface deformation under different temperature differences presents an S-type distribution. The velocities at the upper and middle positions of the liquid bridge exhibit different oscillation forms. The transverse velocity at the upper end exhibits a sinusoidal oscillation at a small temperature difference (\(\Delta T=1-3\)), and this sinusoidal oscillation is a single-periodic oscillation. However, the longitudinal velocity exhibits the pulsating oscillation characteristic with a small amplitude and presents a double-periodic oscillation form. The transverse and longitudinal velocities at the intermediate position exhibit small-amplitude pulsation oscillation, both of which are single-periodic oscillations. The velocity oscillations at the upper and middle positions of the free interface are both pulsating oscillations with large amplitude under the condition of a large temperature disparity (\(\Delta T=6\)), and these pulsations are multi-periodic in nature. Figure 15: (**a**) Oscillation of longitudinal velocity at monitoring point “b” under different heat loss conditions; (**b**) power spectrum density of longitudinal velocity (\(R=5\) mm, \(Ar=1.0\), \(Pr=5.54\), \(Le=25.8\), \(Ca_{C}=-0.021\), \(\rho_{l}/\rho_{g}=597.9\)). 2. In the investigation on the impact of heat loss on the oscillatory behavior of thermovolutocapillary convection, the temperature contour distribution within the intermediate region of the liquid bridge (\(\kappa\) = 1.5 to 2.5) is relatively uniform, while near the interface, the temperature distribution is no longer uniform. The degree of unevenness increases as the \(Bi\) number ranges from 0.2 to 0.6. Furthermore, the concentration values within the concentration field are almost identical in the middle of the liquid bridge. However, the concentration contour near the free interface gradually approaches the upper end as the \(Bi\) number increases (\(Bi\) = 0.2 \(-\) 0.6), thus forming a large concentration gradient at the upper end. In comparison with the adiabatic conditions, the mean velocity, amplitude, and frequency at both the upper and middle positions of the free surface exhibit a gradual reduction as the intensity of heat loss increases. This decrease in dynamic response leads to a weakened oscillation intensity. 3. The simulation framework employed in this study makes certain assumptions and simplifications that may not accurately represent real-world conditions. The future research should aim to further explore relevant issues in this field by refining the models used and investigating factors such as different container sizes or shear airflows. Project administration, R.L. and S.Y. ; Conceptualization, R.L. ; Methodology, R.L. ; Validation, S.Z. and S.Y. ; Writing--original draft preparation, S.Z. ; Writing--review and editing, R.L. and S.Y. All authors have read and agreed to the published version of the manuscript.