Numerical Study of the Regulatory Effects of Laser Heating on Thermocapillary-Buoyancy Convection in Two-Layer Fluid System
Abstract
1. Introduction
2. Physical and Mathematical Model
2.1. Physical Model
- (1)
- The flows in both the upper and lower fluid layers are laminar.
- (2)
- The left and right walls are maintained at constant temperatures, while the other walls are adiabatic.
- (3)
- The fluids are incompressible, and all properties except surface tension are independent of temperature.
- (4)
- Thermocapillary effects are considered at the free surface of the silicone oil layer and at the liquid–liquid interface, hereafter referred to as the fluid interface.
- (5)
- Deformation of the fluid interface is considered, while the free surface remains flat and undeformed.
- (6)
- Surface tension is a linear function of temperature, and the linear relationship is:
2.2. Governing Equations and Boundary Conditions
2.2.1. Governing Equations
2.2.2. Boundary Conditions
2.3. Material Parameters
2.4. Verification of Grid Independence
2.5. Computational Model Verification
3. Calculation Results and Analysis
3.1. The Influence of Laser on Multi-Vortex Cell Flow Patterns
3.2. The Influence of Laser on Thermal Fluid Waves
3.3. Steady-State Flow of Double-Layer Fluid System Under Laser Influence
4. Conclusions
- (1)
- As the laser power increases, the flow field exhibits an asymmetric response characteristic with the heating center as the dividing line. Convection intensity is significantly enhanced from the cold end to the laser region (left domain), while it is markedly reduced from the laser to the hot end (right domain).
- (2)
- Shifting the laser position significantly alters the temperature gradient distribution. When the laser moves toward the cold end, the temperature gradient in the right region decreases and weakens convection, while local convection near the laser is enhanced. When the laser moves toward the hot end, the temperature gradient in the left region increases and strengthens convection, and the weak-fluctuation region near the cold end of the fluid interface expands.
- (3)
- When the spot radius is w0 = 1 mm, temperatures at the heating regions of the free surface and the fluid interface increase markedly. At the fluid interface, temperature gradients decrease on both sides of the laser and increase in the heating region. At the free surface, an asymmetric pattern appears, with increased gradients on the left side of the laser and reduced gradients on the right side.
- (4)
- The laser builds a local high–temperature-gradient “barrier” and redistributes the axial heat flux. This barrier blocks and reshapes the propagation of hot-end disturbances toward the cold end. As a result, it enables active control of bilayer convection, driving a transition from oscillatory to steady flow.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Sui, Y.R.; Sui, Z.G.; Liang, G.D.; Wu, W. Superhydrophobic Microchannel Heat Exchanger for Electric Vehicle Heat Pump Performance Enhancement. Sustainability 2023, 15, 13998. [Google Scholar] [CrossRef] [Scilit]
- Zhao, Y.Z.; Qin, X.X.; Shi, X.Y. Heat Transfer Modeling on High-Temperature Charging and Discharging of Deep Borehole Heat Exchanger with Transient Strong Heat Flux. Sustainability 2022, 14, 9702. [Google Scholar] [CrossRef] [Scilit]
- Fan, D.; Zhu, X.; Xiang, Z.; Lu, Y.; Quan, L. Dimension-Reduction Many-Objective Optimization Design of Multimode Double-Stator Permanent Magnet Motor. IEEE Trans. Transp. Electrif. 2025, 11, 1984–1994. [Google Scholar] [CrossRef] [Scilit]
- Fan, D.; Miao, D.; Shan, W.; Xiang, Z.; Zhu, X. Short-Circuit Fault Demagnetization Assessment and Optimization of Double-Electrical-Port Vernier Permanent Magnet Motor. IEEE Trans. Ind. Appl. 2025, 1–10. [Google Scholar] [CrossRef] [Scilit]
- Zhang, J.; Qi, H.; Wu, J.J.; Mao, X.; Zhang, H.; Amin, N.; Xu, F.; Dong, C.; Wang, C.; Wang, P.; et al. Disposable Peptidoglycan-Specific Biosensor for Noninvasive Real-Time Detection of Broad-Spectrum Gram-Positive Bacteria in Exhaled Breath Condensates. Anal. Chem. 2024, 96, 9817–9825. [Google Scholar] [CrossRef] [Scilit]
- Liu, D.; Shen, Q.; Liu, J. The Health-Wealth Gradient in Labor Markets: Integrating Health, Insurance, and Social Metrics to Predict Employment Density. Computation 2026, 14, 22. [Google Scholar] [CrossRef] [Scilit]
- Shen, Q.; Zhang, J. MFTFormer: Meteorological-Frequency-Temporal Transformer with Block-Aligned Fusion for Traffic Flow Prediction. Res. Sq. 2026. [Google Scholar] [CrossRef] [Scilit]
- Guo, S.; Song, Y.; Wu, Y.; Hu, J.; Lu, J.; Wang, C.; Jia, Z.; Hua, L. Microscopic mechanism of enhanced strength-plasticity synergy in pre-damaged TC11 titanium alloys via novel electroshock treatment. J. Alloys Compd. 2026, 1052, 186139. [Google Scholar] [CrossRef] [Scilit]
- Liu, J.; Du, S.; Huang, Z.; Liu, N.; Shao, Z.; Qin, N.; Wang, Y.; Wang, H.; Ni, Z.; Yang, L. Enhanced Reduction of Nitrate to Ammonia at the Co-N Heteroatomic Interface in MOF-Derived Porous Carbon. Materials 2025, 18, 2976. [Google Scholar] [CrossRef] [Scilit]
- Zhang, H.R. Effect of Vertical Heat Transfer on Thermocapillary Convection in a Rectangular Liquid Pool. Ph.D. Thesis, Chongqing University, Chongqing, China, 2010. (In Chinese) [Google Scholar]
- Langlois, W.E. Buoyancy-driven flows in crystal-growth melts. Annu. Rev. Fluid Mech. 1985, 17, 191–215. [Google Scholar] [CrossRef]
- Kuhlmann, H.C. Thermocapillary Convection in Models of Crystal Growth; Springer: Berlin, Germany, 1999. [Google Scholar]
- Lu, Q.S.; Roux, B. Instability of Thermocapillary Convection in Multiple Superimposed Immiscible Liquid Layers. In Proceedings of the VIII European Symposium on Materials and Fluid Sciences in Microgravity, Paris, France, 12–16 April 1992; Volume 2, pp. 735–740. [Google Scholar]
- Ueno, I.; Tori, T. Thermocapillary-driven flow in a thin liquid film sustained in a rectangular hole with temperature gradient. Acta Astronaut. 2010, 66, 1017–1021. [Google Scholar] [CrossRef] [Scilit]
- Li, Y.R.; Zhang, W.J.; Wang, S.C. Numerical simulation of thermocapillary convection in an annular double-layer liquid system. J. Eng. Thermophys. 2008, 29, 1759–1761. (In Chinese) [Google Scholar]
- Li, H.M.; Shi, W.Y. Thermocapillary convection in a differentially heated two-layer annular system with and without rotation. Int. J. Heat Mass Transf. 2017, 105, 684–689. [Google Scholar] [CrossRef] [Scilit]
- Huang, H.L.; Zhou, X.M. The impact of normal magnetic fields on instability of thermocapillary convection in a two-layer fluid system. ASME J. Heat Transf. 2009, 131, 062502. [Google Scholar] [CrossRef] [Scilit]
- Zhou, X.M.; Huai, X.L.; Huang, H.L. MHD effects on thermocapillary-buoyant convection in an annular two-layer system. Heat Transf. Res. 2017, 48, 35–47. [Google Scholar] [CrossRef] [Scilit]
- Zhou, X.M.; Huang, H.L. MHD effects on the instability of thermocapillary convection in two-layer fluid system. Int. J. Heat Mass Transf. 2010, 53, 5827–5834. [Google Scholar] [CrossRef] [Scilit]
- Chen, G.; Lizee, A.; Roux, B. Bifurcation analysis of the thermocapillary convection in cylindrical liquid bridges. J. Cryst. Growth 1997, 180, 638–647. [Google Scholar] [CrossRef] [Scilit]
- Smith, M.K.; Davis, S.H. Instabilities of dynamic thermocapillary liquid layers. Part 1. convective instabilities. J. Fluid Mech. 1983, 132, 119–144. [Google Scholar] [CrossRef] [Scilit]
- Politano, O.; Baras, F. Thermocapillary convection in a laser-heated Ni melt pool: A molecular dynamics study. Appl. Phys. Lett. 2023, 134, 095301. [Google Scholar] [CrossRef] [Scilit]
- Gupta, N.R.; Haj-Hariri, H.; Borhan, A. Effect of free surface heat transfer on thermocapillary flow in double-layer fluid structures. Heat Mass Transf. 2014, 50, 333–339. [Google Scholar] [CrossRef] [Scilit]
- Shiomi, J.; Amberg, G. Active control of a global thermocapillary instability. Phys. Fluids 2002, 14, 1063–1073. [Google Scholar] [CrossRef] [Scilit]
- Shiomi, J.; Kudo, M.; Ueno, I.; Kawamura, H.; Amberg, G. Feedback control of oscillatory thermocapillary convection in a half-zone liquid bridge. J. Fluid Mech. 2003, 496, 193–211. [Google Scholar] [CrossRef] [Scilit]
- Muldoon, F.H. Numerical Study of Hydrothermal Wave Suppression in Thermocapillary Flow Using a Predictive Control Method. Comput. Math. Math. Phys. 2018, 58, 493–507. [Google Scholar] [CrossRef] [Scilit]
- Gelfgat, A. Effect of interface dynamic deformations on instabilities of buoyancy-thermocapillary convection in a two-fluid two-layer system. Phys. Rev. Fluids 2022, 7, 053503. [Google Scholar] [CrossRef] [Scilit]
- Bekezhanova, V.B.; Goncharova, O.N.; Ivanova, N.A.; Klyuev, D.S. Instability of a Two-layer System with Deformable Interfaces under Laser Beam Heating. J. Sib. Fed. Univ. Math. Phys. 2019, 12, 543–550. [Google Scholar] [CrossRef] [Scilit]
- Bekezhanova, V.; Fliagin, V.; Goncharova, O.; Ivanova, N.; Klyuev, D. Thermocapillary deformations of a two-layer system of liquids under laser beam heating. Int. J. Multiph. Flow 2020, 132, 103429. [Google Scholar] [CrossRef] [Scilit]
- Bekezhanova, V.; Goncharova, O.; Ovcharova, A. Numerical simulation of the dynamics of a locally heated bilayer system under weak evaporation. Int. J. Heat Mass Transf. 2022, 185, 122329. [Google Scholar] [CrossRef] [Scilit]
- Antonow, G.N. Sur la tension superficielle à la limite de deux couches. Chim. Phys. 1907, 5, 372–385. [Google Scholar] [CrossRef] [Scilit]
- Gupta, N.R. Double-Layer Thermocapillary Convection in a Differentially Heated Cavity. Ann. N. Y. Acad. Sci. 2006, 1077, 395–414. [Google Scholar]











| Physical Property Parameters | 0.65 cSt Silicone Oil | Water |
|---|---|---|
| Density ρ | 760 | 998 |
| Surface tension σ | 0.0159 | 0.719 |
| Surface tension temperature coefficient | 8 × 10−5 | |
| Dynamic viscosity μ Kg/(m·s) | 4.95 × 10−4 | 9.21 × 10−5 |
| Coefficient of thermal expansion β K−1 | 0.00134 | 0.000207 |
| Thermal conductivity λ W/(m·K) | 0.1 | 0.6083 |
| Specific heat capacity Cp J/(Kg·K) | 2000 | 4179 |
| Pr | 10.3 | 6.215 |
| Grid | Number of Grids | Flow Velocity × 10−3 (m/s) | Relative Error |
|---|---|---|---|
| A | 37,257 | 8.26 | 15.4% |
| B | 52,695 | 8.05 | 12.4% |
| C | 74,985 | 7.48 | 4.47% |
| D | 104,397 | 7.29 | 1.81% |
| E | 136,958 | 7.16 | 0 |
| F | 154,409 | 7.17 | 0.14% |
| G | 189,963 | 7.16 | / |
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© 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
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Yang, S.; Zhou, X.; Zheng, Y.; Duan, W. Numerical Study of the Regulatory Effects of Laser Heating on Thermocapillary-Buoyancy Convection in Two-Layer Fluid System. Appl. Sci. 2026, 16, 3186. https://doi.org/10.3390/app16073186
Yang S, Zhou X, Zheng Y, Duan W. Numerical Study of the Regulatory Effects of Laser Heating on Thermocapillary-Buoyancy Convection in Two-Layer Fluid System. Applied Sciences. 2026; 16(7):3186. https://doi.org/10.3390/app16073186
Chicago/Turabian StyleYang, Shuwen, Xiaoming Zhou, Yuhang Zheng, and Wenhao Duan. 2026. "Numerical Study of the Regulatory Effects of Laser Heating on Thermocapillary-Buoyancy Convection in Two-Layer Fluid System" Applied Sciences 16, no. 7: 3186. https://doi.org/10.3390/app16073186
APA StyleYang, S., Zhou, X., Zheng, Y., & Duan, W. (2026). Numerical Study of the Regulatory Effects of Laser Heating on Thermocapillary-Buoyancy Convection in Two-Layer Fluid System. Applied Sciences, 16(7), 3186. https://doi.org/10.3390/app16073186
