Experiment and Data Analysis of Spheres Falling in Bounded System

Abstract:

In an open or unbounded system, when a solid sphere freely falls into a liquid, it accelerates until it reaches a terminal velocity. At this point, the gravitational force, buoyant force, and viscous drag acting on the sphere are balanced. Stokes' law describes that in a laminar flow state, the viscous drag on the sphere is proportional to its radius, velocity, and viscosity coefficient. In this paper, an experimental system was constructed and the vertical and horizontal positions of spheres were measured with different sizes and densities in liquids of different diameters and viscosities, and the vertical and horizontal positions, velocities, and accelerations of spheres were analyzed. The data analysis shows that the sphere is not only subjected to the viscous drag and but also the boundary forces from the system. This work will have a significance in modeling and computer simulation of accurate measurement of liquid viscosity.

• Periodical: Advances in Science and Technology (Volume 166)
• Pages: 83-90
• DOI: https://doi.org/10.4028/p-KmD8tG
• Online since: June 2025
• Authors: Rui Yang He, Chun Jiang*
• Keywords: Bounded System, Data Analysis, Dynamics, Sphere

References

[1] N. Srivastava, R.D. Davenport, and M.A. Burns, "Nanoliter viscometer for analyzing blood plasma and other liquid samples," Anal. Chem. 77(2), 383–392 (2005).

DOI: 10.1021/ac0494681

[2] Y.I. Cho, J.P. Hartnett, and W.Y. Lee, "Non-Newtonian viscosity measurements in the intermediate shear rate range with the falling-ball viscometer," J. Non-Newtonian Fluid Mech. 15, 61–74 (1984).

DOI: 10.1016/0377-0257(84)80028-2

[3] M. Gottlieb, "Zero shear rate viscosity measurements for polymer solutions by falling ball viscometer," J. Non-Newtonian Fluid Mech. 6, 97–109 (1979).

DOI: 10.1016/0377-0257(79)87008-1

[4] N. V. Paniker, I. Ben-Bassat, and E. Beutler, "Evaluation of sickle hemoglobin and desickling agents by falling ball viscometer," J. Lab. Clin. Med. 80(2), 282–290 (1972).

[5] T.D. Pollard, "A falling ball apparatus to measure filament cross-linking," Methods Cell Biol. 24(Pt. A), 301–311 (1982).

DOI: 10.1016/s0091-679x(08)60663-9

[6] O. Wagner, H. Schuler, P. Hofmann, D. Langer, P. Dancker, and J. Bereiter-Hahn, "Sound attenuation of polymerizing actin reflects supramolecular structures: Viscoelastic properties of actin gels modified by cytochalasin D, profilin and alpha-actinin," Biochem. J. 355(Pt. 3), 771–778 (2001).

DOI: 10.1042/bj3550771

[7] M. Brizard, M. Megharfi, E. Mahe, and C. Verdier, "Design of a high precision falling-ball viscometer," Rev. Sci. Instrum. 76(2), 025109 (2005).

DOI: 10.1063/1.1851471

[8] A. Ambari, B. Gauthier-Manuel, and E. Guyon, "Direct measurement of tube wall effect on the Stokes force," Phys. Fluids 85, 1559–1561 (1985).

DOI: 10.1063/1.864990

[9] P. Yuan and B.-Y. Lin, "Measurement of viscosity in a vertical falling ball viscometer," Am. Lab. 40(18) (2008).

[10] Jay X. Tang, Measurements of fluid viscosity using a miniature ball drop device, Rev. Sci. Instrum. 87, 054301 (2016).