# An Analysis of Bubble Migration in Horizontal Thermo-Capillarity Using the VOF Modeling
###### Abstract  
Due to various engineering applications, spontaneous bubble movement on the heated surface has brought huge attention. This work numerically studied the bubble migration driven by the thermo-capillary force under the temperature gradients perpendicular to the gravity direction. This problem is constructed in a two-dimensional domain, and the volume of fluid (VOF) method is adopted to capture the properties of the bubble interface between the vapor and the liquid. One still vapor bubble is initially positioned at the center of the liquid domain, and the temperature gradient is applied to two side walls. The results show that the bubble with a size greater than the capillary length can only oscillate near the initial position even with a larger temperature gradient. The deformation of the bubble such as spheroid and spherical cap can be found around this regime. However, the movement of the bubble with a size smaller than the capillary length is significant under a higher temperature gradient, and it remains a spherical shape. The coefficient of thermo-capillary force (\(C_{\text{Th}}\)) is defined within this work, and it is found that a larger Weber number (\(W_{e}\)) accomplishes a larger \(C_{\text{Th}}\). This work may provide more precise guidance for smart bubble manipulation and critical heat flux estimation for future nuclear reactor design.  
bubble; thermal-capillary force; surface tension; volume of fluid (VOF) 202220202022020220220220220220220220220220222022202  
et al. numerically investigated the bubble/droplet migration due to thermo-capillary force under uniform thermal radiation with the level set method [6]. [PERSON] and [PERSON] demonstrated the analytical solution of surface tension-driven flows for a droplet in a micro-gravity environment [7]. [PERSON] et al. numerically investigated the bubble migration driven by the thermo-capillary effect (temperature gradient parallel to the gravity direction) under variable buoyancy [8]. [PERSON] et al. showed the numerical simulations of the 3D thermo-capillary motion of deformable viscous drops under the influence of a constant temperature gradient within the liquid medium [9]. Using a finite difference method, [PERSON] analyzed the effect of bubble deformation while predicting thermo-capillary migration [10]. They found that decreased surface tension contributes to a higher deformation rate at higher temperatures. [PERSON] et al. showed the results from the experiments on the thermo-capillary migration of air bubbles and fluorinent drops in a Dow-Corning silicone oil aboard a NASA Space Shuttle mission [11]. The capillary-driven force also benefits the development of high-performance heat transfer devices, such as microscale heat pipes [12].  
Other than spontaneously manipulating the bubble movement, bubble behavior is also important to determine the heat flux. In a nuclear reactor, boiling can be found on the heating surface of the fuel rods. For safety, knowing the critical heat flux (CHF) of the fuel rods is vital for designing a nuclear reactor. Bubbles generated on the fuel rods will depart from the heating surface and migrate into the flow channel under lateral forces such as wall lubrication, dispersion, thermo-capillarity, etc. It is intuitive to imagine a more significant void fraction near the heating surface due to the heat and mass transfer. The CHF will decrease since the conductivity of vapor is smaller than liquid. Understanding the bubble dynamics near the heated surface is essential to determine the critical heat flux. Previous research mostly focused on the thermo-capillarity parallel to the gravity direction. However, this work investigates how a single bubble migrates under the temperature gradient perpendicular to gravity using the volume of fluid method (VOF). The primary goal of this work is to get a better understanding of the physics in a thermo-capillary bubble to pursue more precise critical heat flux estimation in the near future.