Understanding the Terminal Velocity of Particle Motion in Fluids at the Senior High School Level with Numerical Experiments
Abstract
Investigating the motion of solid particles in fluids analyzes the drag force experienced by the particles, depending on parameters such as particle diameter, fluid velocity, density, and viscosity. The Reynolds number, which expresses a fluid's inertia relative to its viscosity, governs the dimensionless drag coefficient, which is critical to understanding drag forces. Terminal velocity, achieved when the force of gravity equals the buoyancy and drag forces of the fluid, is a critical concept often analyzed using the Stokes model. However, differences between theoretical and experimental terminal velocities arise due to oversight of the model's application conditions. Numerical experiments offer controlled conditions to address this, helping predictions align with theoretical models. This research explores the influence of density ratio and particulate diameter on terminal velocity, aiming to support research-based learning for teachers and conceptual understanding for students. Numerical experiments designed by Arbie et al. (2021) investigated two-dimensional particulate configurations, allowing controlled manipulation of parameters. The results show a strong influence of the density ratio and diameter to the terminal velocity, with larger parameter values influencing the Reynolds number and giving rise to differences between theoretical and experimental values. Therefore, careful parameter selection is essential for viscosity experiments, aligning with the objectives and comparability of theoretical models.
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Arbie, M. R., Fauzi, U., & Latief, F. D. (2019). Dynamics of two disks in a counter-flow using Immersed Boundary-Lattice Boltzmann method. Computers & Fluids, 179, 265-276.
Arbie, M. R., Fauzi, U., Latief, F. D. E., & Mustopa, E. J. (2021). Two-Solid Deposition in Fluid Column using Immersed Boundary-Lattice Boltzmann Method. Journal of Applied and Computational Mechanics, 7(3), 1814–1825. https://doi.org/10.22055/jacm.2021.37140.2969
Ardiansyah, D. (2017). PERANCANGAN DAN PENERAPAN SENSOR KUMPARAN UNTUK PERCOBAAN VISKOSITAS DENGAN METODE BOLA JATUH. Jurnal Inovasi Fisika Indonesia, 06(01), 5–9.
Bagheri, G., & Bonadonna, C. (2016). On the drag of freely falling non-spherical particles. Powder Technology, 301, 526–544. https://doi.org/10.1016/j.powtec.2016.06.015
Baker, L. J., & Coletti, F. (2021). Particle–fluid–wall interaction of inertial spherical particles in a turbulent boundary layer. Journal of Fluid Mechanics, 908, A39. https://doi.org/10.1017/jfm.2020.934
Bergougnoux, L., Bouchet, G., Lopez, D., & Guazzelli, É. (2014). The motion of solid spherical particles falling in a cellular flow field at low Stokes number. Physics of Fluids, 26(9). https://doi.org/10.1063/1.4895736
Budiyono, B., Sutrisno, E., & Wibowo, T. U. (2022). Design of a Falling Ball Speed Measuring Instrument in Viscosity Experiment Using Arduino UNO ATmega. BERKALA SAINSTEK, 10(1), 10. https://doi.org/10.19184/bst.v10i1.27315
Chau, T., Ghazali, I., Nguyen, H., Nguyen, D., Ly, H., & Nguyen, T. (2023). A low-cost pitot tube-based experimental model for active teaching-learning of applied fluid mechanics: A demonstration from NTTU. Engineering Science Letter, 2(03), 84–91. https://doi.org/10.56741/esl.v2i03.432
Chen, D. L., Schonger, M., & Wickens, C. (2016). oTree—An open-source platform for laboratory, online, and field experiments. Journal of Behavioral and Experimental Finance, 9, 88–97. https://doi.org/10.1016/j.jbef.2015.12.001
Chen, H., Liu, W., Chen, Z., & Zheng, Z. (2021). A numerical study on the sedimentation of adhesive particles in viscous fluids using LBM-LES-DEM. Powder Technology, 391, 467–478. https://doi.org/10.1016/j.powtec.2021.06.031
Chukwuneke, J. L., Aniemene, C. P., Okolie, P. C., Obele, C. M., & Chukwuma, E. C. (2022). Analysis of the Dynamics of a Freely Falling Body in a Viscous Fluid: Computational Fluid Dynamics Approach. International Journal of Thermofluids, 14. https://doi.org/10.1016/j.ijft.2022.100157
Dan, P., Miao, L., Linfang, S., Zhiliang, W., & Zhenquan, L. (2023). The effects of channel width on particle sedimentation in fluids using a coupled lattice Boltzmann-discrete element model. Physics of Fluids, 35(5). https://doi.org/10.1063/5.0147826
De Bézenac, E., Pajot, A., & Gallinari, P. (2019). Deep learning for physical processes: incorporating prior scientific knowledge. Journal of Statistical Mechanics: Theory and Experiment, 2019(12), 124009. https://doi.org/10.1088/1742-5468/ab3195
Dey, S., Zeeshan Ali, S., & Padhi, E. (2019). Terminal fall velocity: the legacy of Stokes from the perspective of fluvial hydraulics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2228), 20190277. https://doi.org/10.1098/rspa.2019.0277
Dioguardi, M., Di Gioia, G., Illuzzi, G., Laneve, E., Cocco, A., & Troiano, G. (2018). Endodontic irrigants: Different methods to improve efficacy and related problems. European journal of dentistry, 12(03), 459-466.
Ershadnia, R., Amooie, M. A., Shams, R., Hajirezaie, S., Liu, Y., Jamshidi, S., & Soltanian, M. R. (2020). Non-Newtonian fluid flow dynamics in rotating annular media: Physics-based and data-driven modeling. Journal of Petroleum Science and Engineering, 185, 106641. https://doi.org/10.1016/j.petrol.2019.106641
Fahrudin, A. (2022). Pengaruh Penggunaan Software Treker Terhadap Hasil Belajar Fisika Mahasiswa Pada Pokok Bahasan Viskositas Fluida. Jurnal Pendidikan Sains Dan Komputer, 2(01), 41–48. https://doi.org/10.47709/jpsk.v2i01.1357
Fornari, W., Zade, S., Brandt, L., & Picano, F. (2019). Settling of finite-size particles in turbulence at different volume fractions. Acta Mechanica, 230(2), 413–430. https://doi.org/10.1007/s00707-018-2269-1
Kaiser, D., Kowalski, N., & Waniek, J. J. (2017). Effects of biofouling on the sinking behavior of microplastics. Environmental Research Letters, 12(12), 124003. https://doi.org/10.1088/1748-9326/aa8e8b
Kantas, N., Beskos, A., & Jasra, A. (2014). Sequential Monte Carlo Methods for High-Dimensional Inverse Problems: A Case Study for the Navier--Stokes Equations. SIAM/ASA Journal on Uncertainty Quantification, 2(1), 464–489. https://doi.org/10.1137/130930364
Li, X., Liu, G., Zhao, J., Yin, X., & Lu, H. (2022). IBM-LBM-DEM Study of Two-Particle Sedimentation: Drafting-Kissing-Tumbling and Effects of Particle Reynolds Number and Initial Positions of Particles. Energies, 15(9), 3297. https://doi.org/10.3390/en15093297
Liu, L., Yan, H., Zhao, G., & Zhuang, J. (2016). Experimental studies on the terminal velocity of air bubbles in water and glycerol aqueous solution. Experimental Thermal and Fluid Science, 78, 254–265. https://doi.org/10.1016/j.expthermflusci.2016.06.011
Liu, Y., & Yu, X. (2022). General formulation of drag force on assemblage of spherical particles in fluids: A critical review and a new empirical formula. Physics of Fluids, 34(6). https://doi.org/10.1063/5.0096069
Lubis, N. (2018). PENGARUH KEKENTALAN CAIRAN TERHADAP WAKTU JATUH BENDA MENGGUNAKAN FALLING BALL METHOD THE INFLUENCE OF LIQUID VISCOSITY ON FALLING TIME BY FALLING BALL METHOD. 2(2), 26–32.
Lv, K., Min, F., Zhu, J., Ren, B., Bai, X., & Wang, C. (2021). Experiments and CFD-DEM simulations of fine kaolinite particle sedimentation dynamic characteristics in a water environment. Powder Technology, 382, 60–69. https://doi.org/10.1016/j.powtec.2020.12.057
Maxey, M. (2017). Simulation Methods for Particulate Flows and Concentrated Suspensions. Annual Review of Fluid Mechanics, 49(1), 171–193. https://doi.org/10.1146/annurev-fluid-122414-034408
Michna, J., & Rogowski, K. (2022). Numerical Study of the Effect of the Reynolds Number and the Turbulence Intensity on the Performance of the NACA 0018 Airfoil at the Low Reynolds Number Regime. Processes, 10(5), 1004. https://doi.org/10.3390/pr10051004
Mirzaee, H., Rafee, R., & Ahmadi, G. (2019). Inertial impaction of particles on a circular cylinder for a wide range of Reynolds and P numbers: A comparative study. Journal of Aerosol Science, 135, 86–102. https://doi.org/10.1016/j.jaerosci.2019.06.001
Momenifar, M., Dhariwal, R., & Bragg, A. D. (2019). Influence of Reynolds number on the motion of settling, bidisperse inertial particles in turbulence. Physical Review Fluids, 4(5), 054301. https://doi.org/10.1103/PhysRevFluids.4.054301
Ouchene, R., Khalij, M., Tanière, A., & Arcen, B. (2015). Drag, lift and torque coefficients for ellipsoidal particles: From low to moderate particle Reynolds numbers. Computers and Fluids, 113, 53–64. https://doi.org/10.1016/j.compfluid.2014.12.005
Putra, B. E. (2022). The IMPLEMENTATION OF PHYSICS LEARNING MEDIA IN VISCOSITY TUBE WITH VIDEO ANALYSIS USING SOFTWARE TRACKER. Jurnal Pendidikan Fisika Dan Sains (JPFS), 5(1), 10–15. https://doi.org/10.52188/jpfs.v5i1.207
Rao, Y., Liu, C., Wang, H., Ni, Y., Lv, C., Liu, S., Lan, Y., & Wang, S. (2018). Density ratio effect on particle sedimentation in a vertical channel. Chinese Journal of Physics, 56(4), 1427–1438. https://doi.org/10.1016/j.cjph.2018.06.007
Rauter, M. (2021). The compressible granular collapse in a fluid as a continuum: validity of a Navier–Stokes model with , -rheology. Journal of Fluid Mechanics, 915, A87. https://doi.org/10.1017/jfm.2021.107
Romadhon, N., Pratiwi, U., & Al Hakim, Y. (2019). KEEFEKTIFAN ALAT PERAGA VISKOSITAS DENGAN SENSOR MINI REED SWITCH MAGNETIC BERBASIS ARDUINO UNTUK MENINGKATKAN KEMAMPUAN ANALYZEPESERTA DIDIK. Muslim Heritage, 4(2). https://doi.org/10.21154/muslimheritage.v4i2.1765
Setiawati, D., & Yohanes, R. (2017). Analisis Hubungan Kecepatan Terminal dengan Viskositas Zat Cair Menggunakan Software Tracker. Jurnal Materi Dan Pembelajaran Fisika, 17, 1–6. https://doi.org/https://doi.org/10.20961/jmpf.v7i2.31378
Shen, J., Lu, Z., Wang, L.-P., & Peng, C. (2021). Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows. Physical Review E, 104(2), 025109. https://doi.org/10.1103/PhysRevE.104.025109
Shen, J., Peng, C., Lu, Z., & Wang, L. P. (2024). The influence of particle density and diameter on the interactions between the finite-size particles and the turbulent channel flow. International Journal of Multiphase Flow, 170. https://doi.org/10.1016/j.ijmultiphaseflow.2023.104659
Syifa, N. H., Hartono, H., & Sulhadi, S. (2022). DETERMINATION OF TERMINAL VELOCITY AND FLUID VISCOSITY USING FALLING BALL VISCOMETER WITH VIDEO TRACKER APLICATION. JPF (Jurnal Pendidikan Fisika) Universitas Islam Negeri Alauddin Makassar, 10(2), 75–80. https://doi.org/10.24252/jpf.v10i2.22242
Vowinckel, B., Withers, J., Luzzatto-Fegiz, P., & Meiburg, E. (2019). Settling of cohesive sediment: particle-resolved simulations. Journal of Fluid Mechanics, 858, 5–44. https://doi.org/10.1017/jfm.2018.757
Wang, D., Qian, Q., Zhong, A., Lu, M., & Zhang, Z. (2023). Numerical modeling of micro-particle migration in channels. Advances in Geo-Energy Research, 10(2), 117–132. https://doi.org/10.46690/ager.2023.11.06
Wang, D., & Wang, Z. (2022). 3D Lattice Boltzmann Method-Discrete-Element Method with Immersed Moving Boundary Scheme Numerical Modeling of Microparticles Migration Carried by a Fluid in Fracture. SPE Journal, 27(05), 2841–2862. https://doi.org/10.2118/209822-PA
Wang, L., Zheng, K., Ding, Z., Yan, X., Zhang, H., Cao, Y., & Guo, C. (2020). Drag coefficient and settling velocity of fine particles with varying surface wettability. Powder Technology, 372, 8–14. https://doi.org/10.1016/j.powtec.2020.05.102
Wang, Y., Zhou, L., Wu, Y., & Yang, Q. (2018). New simple correlation formula for the drag coefficient of calcareous sand particles of highly irregular shape. Powder Technology, 326, 379–392. https://doi.org/10.1016/j.powtec.2017.12.004
White, F. (2011). Fluid Mechanics. 7th Edition. McGraw-Hill.
Zhang, P., & Mohseni, K. (2019). Viscous drag force model for dynamic Wilhelmy plate experiments. Physical Review Fluids, 4(8), 084004. https://doi.org/10.1103/PhysRevFluids.4.084004
Zhao, R., Zhou, Y., Zhang, D., & Gao, X. (2022). Numerical investigation of the hydraulic transport of coarse particles in a vertical pipe based on a fully-coupled numerical model. International Journal of Multiphase Flow, 155, 104094. https://doi.org/10.1016/j.ijmultiphaseflow.2022.104094
Zhou, C., Su, J., Chen, H., & Shi, Z. (2022). Terminal velocity and drag coefficient models for disc-shaped particles based on the imaging experiment. Powder Technology, 398, 117062. https://doi.org/10.1016/j.powtec.2021.117062
DOI: https://doi.org/10.53889/ijses.v4i2.389
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