Investigation of geometric effects on fluid viscosity using the falling ball method

Amnur Akhyan; Mustaza Maâ€™a; Fortinov Akbar Irdam; Alvin Alvarez; Nurcahya Nugraha; Nurkhamdi Nurkhamdi

doi:10.30811/jpl.v23i5.7347

Investigation of geometric effects on fluid viscosity using the falling ball method

Amnur Akhyan, Mustaza Maâ€™a, Fortinov Akbar Irdam, Alvin Alvarez, Nurcahya Nugraha, Nurkhamdi Nurkhamdi

Abstract

The falling ball method, based on Stokes law, is a simple yet accurate technique for determining fluid viscosity, though its precision is influenced by factors such as wall, Reynolds, end, memory, and off-center effects. This study aims to determine the effect of spherical geometry on the fluid viscosity value represented by the sphericity factor ï™. An experimental study was conducted to examine its accuracy of viscosity values to produce the correction factor. The sphericity factors studied were 0.993, 0.976, and 0.949. To reduce the uncertainty caused by the wall effect, the ratio db/Dt was 0.071, using a 5.8mm diameter plastic ball and SAE 40 oil fluid at 32.4Â°C. Terminal velocity (ð‘‰ð‘¡) was obtained by analyzing the video of the ball falling in the fluid, which was displayed on the tracker software. The video was taken using a 1080p, 60 fps camera. Wall and Reynolds effect correction factors were used to amend experimental viscosity values. The result indicates the viscosity will be accurately determined by selecting a larger sphericity value of the ball during the experimental process. It will reduce the necessity of correction factors to obtain the value of fluid viscosity.

Keywords

Falling Ball Viscosity; Sphericity; Sphericity Correction Factor

Full Text:

PDF

References

R. MacÃasâ€Salinas and I. Romero-Rueda, "Density and viscosity modeling of three deep eutectic solvents using a volume-shifted cubic equation of state coupled with the friction theory", Industrial & Engineering Chemistry Research, vol. 63, no. 1, p. 718-730, 2023. https://doi.org/10.1021/acs.iecr.3c03478

X. Li, X. Lv, G. Yao, Y. Zhao, & F. Gao, "Study on measurement of liquid viscosity coefficient", Journal of Physics Conference Series, vol. 2660, no. 1, p. 012021, 2023. https://doi.org/10.1088/1742-6596/2660/1/012021

L. Cardona, L. Forero, & J. VelÃ¡squez, "Extension of a group contribution method to predict viscosity based on momentum transport theory using a modified pengâ€“robinson eos", Industrial & Engineering Chemistry Research, vol. 60, no. 41, p. 14903-14926, 2021. https://doi.org/10.1021/acs.iecr.1c02146

M. Delina, D. Anugrah, A. Hussaan, A. Harlastputra, P. Akbar, & P. Renaldi, "Optimizing viscosity measurement: an automated solution with yolov3", Journal of Physics Conference Series, vol. 2596, no. 1, p. 012022, 2023. https://doi.org/10.1088/1742-6596/2596/1/012022

A. Lesmono, E. Ramadhan, R. Handayani, & S. Prastowo, "Design of student worksheet teaching materials for viscosity of biodiesel, dexlite, and pertamina dex with falling ball measurement technique", Jurnal Pendidikan Fisika Indonesia, vol. 19, no. 2, p. 145-153, 2023. https://doi.org/10.15294/jpfi.v19i2.46714

S. Neuhaus, H. Bissig, B. Bircher, & M. Huu, "Traceability of the micro scale pipe viscometer for traceable calibration of dynamic viscosity", Applied Sciences, vol. 13, no. 10, p. 5984, 2023. https://doi.org/10.3390/app13105984.

M. Brizard, M. Megharfi, and C. Verdier, â€œAbsolute falling-ball viscometer: Evaluation of measurement uncertainty,â€ Metrologia, vol. 42, no. 4, pp. 298â€“303, 2005, doi: 10.1088/0026-1394/42/4/015.

X. Yang, A. Aramiâ€“Niya, X. Xiao, D. Kim, S. Ghafri, T. Tsujiet al., "Viscosity measurements of binary and multicomponent refrigerant mixtures containing hfc-32, hfc-125, hfc-134a, hfo-1234yf, and co2", Journal of Chemical & Engineering Data, vol. 65, no. 9, p. 4252-4262, 2020. https://doi.org/10.1021/acs.jced.0c00228

Y. Wu and K. Li, "Experimental study and numerical simulation of viscosity measurement of solid propellant slurry by press barâ€fall ball viscometer", Propellants Explosives Pyrotechnics, vol. 46, no. 4, p. 663-669, 2021. https://doi.org/10.1002/prep.202000286

D. Sagdeev, I. Gabitov, Ð’. Ð¥Ð°Ð¹Ñ€ÑƒÑ‚Ð´Ð¸Ð½Ð¾Ð², M. Fomina, V. Alyaev, Ð . Ð¡Ð°Ð»ÑŒÐ¼Ð°Ð½Ð¾Ð²et al., "New design of the falling-body rheoviscometer for high and extra-high viscous liquid measurements. viscosity of vacuum oils", Journal of Chemical & Engineering Data, vol. 65, no. 4, p. 1773-1786, 2020. https://doi.org/10.1021/acs.jced.9b01071

SH Ali, AAD Al- Zuky, AH Al-Saleh, and HJ Mohamad, "Measure liquid viscosity by tracking falling ball automatically depending on image processing algorithm," J Phys Conf Ser, vol. 1294, no. 2, 2019, doi: 10.1088/1742-6596/1294/2/022002

S. Choi, M. Lee, C. Roh, & D. Kim, "Freely falling sphere with a rigid rear-side filament", Journal of Fluid Mechanics, vol. 1010, 2025. https://doi.org/10.1017/jfm.2025.271

D. Nie, J. Wang, S. Li, & J. Lin, "Freely rising or falling of a sphere in a square tube at intermediate reynolds numbers", Journal of Fluid Mechanics, vol. 1000, 2024. https://doi.org/10.1017/jfm.2024.1004

A. Mayme and C. Mungan, "Vertical fall of a sphere opposed by fluid buoyancy and drag", European Journal of Physics, vol. 46, no. 3, p. 035004, 2025. https://doi.org/10.1088/1361-6404/adca14

P. Billa, T. Josyula, C. Tropea, & P. Mahapatra, "Motion of a rigid sphere penetrating a deep pool", Journal of Fluid Mechanics, vol. 1012, 2025. https://doi.org/10.1017/jfm.2025.10166

M. Sequeira, H. Avelino, F. Caetano, & J. Fareleira, "Viscosity and density of two 1-alkyl-3-methyl-imidazolium triflate ionic liquids at high pressures: experimental measurements and the effect of alkyl chain length", Journal of Chemical & Engineering Data, vol. 66, no. 4, p. 1763-1772, 2021. https://doi.org/10.1021/acs.jced.0c01057

J. Xue, J. Cai, H. Ding, Z. Mao, & Z. Jin, "Comparative analysis of viscosity measurement techniques poiseuille method versus falling ball method", Highlights in Science Engineering and Technology, vol. 93, p. 270-278, 2024. https://doi.org/10.54097/n187sw27

R. Wang, Q. Zhang, S. Xu, L. Cui, and H. Jiang, â€œTheoretical Correction of Viscosity Coefficient Measurement by Falling Ball Method,â€ International Transactions on Electrical Energy Systems, vol. 2022, 2022, doi: 10.1155/2022/3897120

E. Hemingway and S. Fielding, "Interplay of edge fracture and shear banding in complex fluids", Journal of Rheology, vol. 64, no. 5, p. 1147-1159, 2020. https://doi.org/10.1122/8.0000086

D. Frank, A. Penko, M. Palmsten, & J. Calantoni, "Vortex trapping of suspended sand grains over ripples", Journal of Geophysical Research Earth Surface, vol. 129, no. 10, 2024. https://doi.org/10.1029/2023jf007620

WS Janna, Introduction to Fluid Mechanics, Sixth Edition. 2020

M. Lifi, J. Bazile, N. MuÃ±oz-Rujas, G. GalliÃ©ro, F. Aguilar, & J. Daridon, "Density, viscosity, and derivative properties of diethylene glycol monoethyl ether under high pressure and temperature", Journal of Chemical & Engineering Data, vol. 66, no. 3, p. 1457-1465, 2021. https://doi.org/10.1021/acs.jced.0c01055

A. Semenov, V. Drevetskyi, A. Rudyk, O. Semenova, & P. Komada, "Developing and investigating the analyzers of kinematic viscosity and density of petroleum products on throttle bridge transducers", Inventions, vol. 7, no. 1, p. 6, 2021. https://doi.org/10.3390/inventions7010006

M. Kaneko, "High pressure rheology of lubricants (part 5)", Tribology Online, vol. 17, no. 4, p. 257-275, 2022. https://doi.org/10.2474/trol.17.257

N. Cuong, L. Thinh, P. Truong, T. Thang, N. ThÃ nh, & L. Cuong, "Investigation on effect of surface roughness pattern to dynamic performance of mems resonators in various types of gases and gas rarefaction", Vietnam Journal of Science and Technology, vol. 59, no. 5, 2021. https://doi.org/10.15625/2525-2518/59/5/15478

J. Slapnik, R. Lorber, I. Pulko, M. HuskiÄ‡, & K. ÄŒreÅ¡nar, "Overprinting of tpu onto pa6 substrates: the influences of the interfacial area, surface roughness and processing parameters on the adhesion between components", Polymers, vol. 16, no. 5, p. 650, 2024. https://doi.org/10.3390/polym16050650

A. Polo, C. Toro, E. Echeverri, C. Aguirre, L. MartÃnez, & J. Barba-Ortega, "Theoretical comparison of the motions of two spheres falling independently in a viscous fluid", Journal of Southwest Jiaotong University, vol. 59, no. 1, 2024. https://doi.org/10.35741/issn.0258-2724.59.1.16

P. Ballereau, D. Truong, and A. Matias, â€œAbsolute falling ball viscometer, adapted to the low viscosities of liquids,â€ International Journal of Metrology and Quality Engineering, vol. 7, no. 3, pp. 1â€“8, 2016, doi: 10.1051/ ijmqe /2016015.

M. Brizard, M. Megharfi, and C. Verdier, â€œDesign of a High Precision Falling Ball,â€ Review of Scientific Instruments, vol. 2, no. 1, pp. 1â€“13, 2005. https://doi.org/10.1063/1.1851471

E. Oberg, FD Jones, HL Horton, HH Ryffel, CJ McCauley, and L. Brengelman, Machinery's Handbook: A reference book for the Mechanical Engineer, Designer, Drafter, Metalworker, Toolmaker, Machinist, Hobbyist, Educator, and Student. 2020.

S. Feng, A.L. Graham, P.T. Reardon, J. Abbotti, and L. Mondy, â€œImproving falling ball tests for viscosity determination,â€ Journal of Fluids Engineering, Transactions of the ASME, vol. 128, no. 1, pp. 157â€“163, 2006, doi: 10.1115/1.2137345.

DOI: http://dx.doi.org/10.30811/jpl.v23i5.7347