Measurements of copper droplet oscillations on tungsten substrate and the angular dependence of the oscillation frequency
Abstract
The study of droplet impingement and subsequent oscillations on solid substrates is critical for understanding wetting dynamics and heat transfer in applications such as spray cooling and metal coating. However, existing experimental approaches often rely on low-speed imaging or manual analysis, which limits their ability to capture rapid, transient oscillations and achieve high precision, particularly under extreme high-temperature and vacuum conditions. Moreover, conventional methods face challenges in automatically extracting key dynamic parameters like contact spot diameter and oscillation frequencies without user intervention. Novel methods for the computer processing of high-speed video images from experiments on droplet impingement and subsequent oscillations on a solid substrate were developed and validated. The image analysis algorithms, implemented in the Python programming language utilizing the OpenCV computer vision library, enable automated, high-precision tracking of dynamic droplet parameters. These methods were successfully applied to real high-temperature experiments involving molten copper droplets falling onto a polished tungsten substrate under vacuum conditions. Through automated image processing, time-dependent evolutions of the droplet center-of-mass coordinates, the diameter of the contact spot with the solid surface, and the dynamic contact wetting angles for the Cu/W system were obtained. The analysis reveals that upon impact, the droplet undergoes damped shape oscillations. The fundamental oscillation frequencies of the droplets and their dependence on mass were determined with high accuracy. Furthermore, by integrating data from other experimental systems, a generalized angular dependence of the oscillation frequency for sessile droplets was established and compared with existing theoretical models.
Document Type: Original article
Cited as: Zhevnenko, S., Slinkin, M. Measurements of copper droplet oscillations on tungsten substrate and the angular dependence of the oscillation frequency. Capillarity,
2026, 19(2): 39-47. https://doi.org/10.46690/capi.2026.05.01
DOI:
https://doi.org/10.46690/capi.2026.05.01Keywords:
Copper melt, tungsten, high-speed imaging, droplet oscillations, contact angleReferences
Adam, N. K. Use of the term ‘Young’s Equation’ for contact angles. Nature, 1957, 180(4590): 809-810.
Amberg, G. Detailed modelling of contact line motion in oscillatory wetting. npj Microgravity, 2022, 8: 1.
Assael, M. J., Kalyva, A. E., Antoniadis, K. D., et al. Reference data for the density and viscosity of liquid copper and liquid tin. Journal of Physical and Chemical Reference Data, 2010, 39(3): 033105.
Barsoum, M. W., Radovic, M. Elastic and mechanical properties of the MAX phases. Annual Review of Materials Research, 2011, 41: 195-227.
Bostwick, J. B., Steen, P. H. Dynamics of sessile drops. Part 1. Inviscid theory. Journal of Fluid Mechanics, 2014, 760: 5-38.
Brenn, G., Frohn, A. An experimental method for the investigation of droplet oscillations in a gaseous medium. Experiments in Fluids, 1993, 15(2): 85-90.
Brillo, J., Egry, I. Surface tension of nickel, copper, iron and their binary alloys. Journal of Materials Science, 2005, 40(8): 2213-2216.
Brunet, P., Baudoin, M., Bou Matar, O., et al. Droplet displacements and oscillations induced by ultrasonic surface acoustic waves: A quantitative study. Physical Review E, 2010, 81(3): 036315.
Castrejon-Pita, J. R., Baxter, W. R. S., Morgan, J., et al. Future, opportunities and challenges of inkjet technologies. Atomization and Sprays, 2013, 23(6): 541-565.
Chandrasekhar, S. On the stability of a spinning liquid drop. Proceedings of the London Mathematical Society, 1959, 3(9): 141-149.
Dai, X., Sun, N., Nielsen, S. O., et al. Hydrophilic directional slippery rough surfaces for water harvesting. Science Advances, 2018, 4: eaaq0919.
Daniel, S., Chaudhury, M. K., Chen, J. C. Fast drop movements resulting from the phase change on a gradient surface. Science, 2001, 291(5504): 633-636.
Dupré, A. Thermodynamic theory. Paris, France, Gauthier-Villars, 1869. (in French)
Egry, I., Giffard, H., Schneider, S. The oscillating drop technique revisited. Measurement Science and Technology, 2005, 16(2): 426-431.
Fahimi, K., Mädler, L., Ellendt, N. Measurement of surface tension with free-falling oscillating molten metal droplets: A numerical and experimental investigation. Experiments in Fluids, 2023, 64: 133.
Harrison, D. A., Yan, D., Blairs, S. The surface tension of liquid copper. Journal of Chemical Thermodynamics, 1977, 9: 1111-1119.
Ji, S., Gu, Q., Xia, B. Porosity dependence of mechanical properties of solid materials. Journal of Materials Science, 2006, 41: 1757-1768.
Kasama, A., McLean, A., Miller, W. A. Temperature dependence of the surface tension of liquid copper. Canadian Metallurgical Quarterly, 1980, 19(4): 399-401.
Lamb, H. Hydrodynamics. Cambridge, United Kingdom, Cambridge University Press, 1932.
Li, S., Yu, W., Zhai, H., et al. Mechanical properties of low-temperature synthesized dense and fine-grained Cr2AlC ceramics. Journal of the European Ceramic Society, 2011, 31(1-2): 217-224.
Noblin, X., Buguin, A., Brochard-Wyart, F. Vibrations of sessile drops. European Physical Journal E, 2004, 14: 395-404.
Pittoni, P. G., Chang, Y., Lin, S. The effect of interfacial morphology on wetting of graphite by molten silver at high temperature. Journal of Materials Science, 2012, 47: 8395-8403.
Protsenko, P. V., Gorshenkov, M. V., Zhevnenko, S. N., et al. Wetting and spreading of Pb, Pb-Cu, and Ag-Cu melts on a polycrystalline copper surface with cobalt particles. Journal of Alloys and Compounds, 2023, 948: 169785.
Qi, A., Yeo, L., Friend, J., Ho, J. The extraction of liquid, protein molecules and yeast cells from paper through surface acoustic wave atomization. Lab on a Chip, 2010, 10: 470-476.
Rayleigh, R. W. S. On the capillary phenomena of jets. Proceedings of the Royal Society of London, 1879, 29: 71-97.
Sakakeeny, J., Ling, Y. Numerical study of natural oscillations of supported drops with free and pinned contact lines. Physics of Fluids, 2021, 33(6): 062109.
Sarina, B. A. O., Tang, K., Kvithyld, A., et al. Wetting of pure aluminium on graphite, SiC, and Al2O3 in aluminium filtration. Transactions of Nonferrous Metals Society of China, 2012, 22(8): 1930-1938.
Sharp, J. S. Resonant properties of sessile droplets; contact angle dependence of the resonant frequency and width in glycerol/water mixtures. Soft Matter, 2012, 8(2): 399-407.
Sharp, J. S., Farmer, D. J., Kelly, J. Contact angle dependence of the resonant frequency of sessile water droplets. Langmuir, 2011, 27: 9367-9371.
Shilton, R., Tan, M. K., Yeo, L. Y., et al. Particle concentration and mixing in microdrops driven by focused surface acoustic waves. Journal of Applied Physics, 2008, 104(1): 014910.
Silze, F., Wiehl, G., Kaban, I., et al. Wetting behaviour of CuGa alloys on 304L steel. Materials & Design, 2016, 91: 11-18.
Soda, H., McLean, A., Miller, W. A. Surface tension measurements of liquid copper droplets in the temperature range 1000 to 1330°C. Transactions of the Japan Institute of Metals, 1978, 18: 614-619.
Strani, M., Sabetta, F. Free vibrations of a drop in partial contact with a solid support. Journal of Fluid Mechanics, 1984, 141: 233-247.
Subramanian, P. R., Laughlin, D. E. Cu-W (Copper-tungsten). In: Phase Diagrams of Binary Tungsten Alloys, 1991: 76-79.
Sun, S., Zhang, L., Jahanshahi, S. From viscosity and surface tension to Marangoni flow in melts. Metallurgical and Materials Transactions B, 2003, 34(5): 517-523.
Tian, Y., Holt, R. G., Apfel, R. E. Investigation of liquid surface rheology of surfactant solutions by droplet shape oscillations: Experiments. Journal of Colloid and Interface Science, 1997, 187(1): 1-10.
Whitehill, J., Neild, A., Ng, T. W., et al. Collection of suspended particles in a drop using low frequency vibration. Applied Physics Letters, 2010, 96(5): 053501.
Wright, P. H., Saylor, J. R. Patterning of particulate films using Faraday waves. Review of Scientific Instruments, 2003, 74(9): 4063-4070.
Yao, C.-W., Lai, C.-L., Alvarado, J. L., et al. Experimental study on effect of surface vibration on micro textured surfaces with hydrophobic and hydrophilic materials. Applied Surface Science, 2017, 412: 45-51.
Yasuri, K. A. Energy dissipation mechanisms in droplet dynamics: Implications for wetting phenomena. Microfluidics and Nanofluidics, 2025, 29(11): 71.
Young, T. An essay on the cohesion of fluids. Philosophical Transactions of the Royal Society of London, 1805, 95: 65-87.
Zhevnenko, S., Gorshenkov, M., Petrov, I. Effect of B on improving wetting and imbibition of sintered porous Ta by Cu melt. Journal of Alloys and Compounds, 2021, 860: 157886.
Downloads
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Author(s)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.