Viscosity and Vortex Formation in a Liquid Placed in A Rotating Cylindrical Vessel

Keywords: liquid, cylindrical vessel, steady speed, viscosity, Stokes method, rotation, dynamic viscosity, vortex

Abstract

The free fall of steel balls of different diameters in viscous liquids placed in a cylindrical vessel at rest or rotating at a constant rate as well as the vortex generation in a liquid rotating in a cylindrical vessel were experimentally studied. To solve the problem a test stand including a cylindrical glass vessel mounted on the axis of a governed-speed electric engine shaft, monitoring and measuring devices as part of a digital laser tachometer, a digital USB microscope and a laptop was developed to visualize the processes under study. Experimental dependences of the instantaneous velocity of the balls on the distance traveled by them were obtained. It has been demonstrated, that there is a transition mode of the ball velocity variation when it enters the liquid. The transition mode was characterized by a damped, periodic variation of instantaneous velocity depending on a distance. It has been found that at a certain distance traveled by the ball, the transition mode becomes stationary when the ball moves at a constant velocity. The dependence of the liquid viscosity on the vessel rotation frequency was studied in the stationary mode using the Stokes method. It has been demonstrated that the common behavior of such processes is decreasing the time of balls falling and, consequently, the coefficient of a liquid dynamic viscosity with increasing the rotation frequency of the vessel. A periodic variation in the coefficient of the dynamic viscosity depending on the frequency of the vessel rotation was found experimentally. It has been found experimentally that several threadlike spiral flows of a colored liquid are formed parallel to the axis of the cylinder, when the cylindrical vessel rotates. At that, the velocity of the downward drift of the colored liquid increases with increasing its rotation rate and it increases from the periphery to the center of the vessel.

Downloads

Download data is not yet available.

References

L.D. Landau, and E.M. Lifshits, Теоретическая физика. Гидродинамика, T.6, [Theoretical physics. Hydrodynamics, Vol.6,] (Nauka, Moscow, 1986), pp. 736. (in Russian)

Е.G. Richardson, Proc. Phys. Soc. 61(4), 352-367 (1948), https://doi.org/10.1088/0959-5309/61/4/308.

M. Stephen, and Jr. Laverty, M.Sc. thesis, Massachusetts Institute of Technology, 2004, http://web.mit.edu/mhl/www/Impact%20Lab%20Page/Whole%20Thesis.pdf

А.B. Lotov, Uchenyie zapiski TsAGI, 2(4), 22-30 (1971). (in Russian).

I. Mirzaii, and M. Passandideh-Fard, in: 19th Annual Conference on Mechanical Engineering-ISME-2011, (The University of Birjand, Iran, 2011), pp. 1 4. https://www.researchgate.net/publication/307510320_The_Impact_of_a_Solid_Object_on_to_a_Liquid_Surface

H. Wagner, Math. Mech. 12, 193-215 (1932), http://dx.doi.org/10.1002/zamm.19320120402.

V. Fidleris, and R.L. Whitmore, Br. J. Appl. Phys. 12, 490-494 (1961), https://doi.org/10.1088/0508-3443/12/9/311.

P.P. Brown, and D.F. Lawler, Journal of Environmental Engineering, 129(3), 222 231 (2003), https://doi.org/10.1061/(ASCE)0733-9372(2003)129:3(222).

Rayleigh Lord, Proc. Roy. Soc. London, Series A, 93(648), pp. 148-154. Scientific papers, 6, 447-453, (Cambridge University Press, 1917), pp. 254, https://www.jstor.org/stable/93794.

S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, (Oxford University Press, 1970), pp. 657. https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/universal-stability-of-hydromagnetic-flows/826D62658D200A2DCE37F6006EE4390A

Y. Nakagawa, and P. Frenzen, Tellus. 7(1), 1 21 (1955), https://doi.org/10.3402/tellusa.v7i1.8773.

H.P. Grinspen, Теория вращающихся жидкостей [Rotating fluid theory], (Gidrometeoizdat, Leningrad, 1975), pp. 321, https://www.twirpx.com/file/243427/. (in Russian)

H. Bernard, Revue generale des Sciences, Pures et Appliques, 11, 1261-1271 and 1309-1328 (1900).

О.L. Patochkina, B.V. Borts, and V.I. Tkachenko, East Eur. J. Phys. 2(1), 23-31 (2015). https://periodicals.karazin.ua/eejp/article/view/2810

R. Skorer, Аэрогидродинамика окружающей среды [Aero-hydrodynamics of the environment], (Mir, Moscow, 1980), pp. 550. (in Russian)

M. Van-Dajk, Альбом течений жидкости и газа [Album of liquid and gas flows], (Mir, Moscow, 1986), pp. 184. (in Russian)

A.S. Monin, and G.M. Zhiharev, UFN, 160(5), 1-47 (1990), https://doi.org/10.3367/UFNr.0160.199005a.0001. (in Russian)

A.V. Tur, and V.V. Janovskij, Гидродинамические вихревые структуры [Hydrodynamic vortex structures], (Har'kov, NTK “Institut Monokristallov”, 2012), pp. 294. (in Russian)

O.L Andreeva, L.A. Bulavin, I.M. Kudrjavcev, R.S. Sokolenko, and V.I. Tkachenko, in: International scientific and technical conference “Physical And Technical Problems Of Energy And Their Solutions 2019”, (KhNU, Kharkіv, 2019), pp. 18-19, http://physics-energy.karazin.ua/resources/17c5203634424b2292944e8da8f6c686.pdf. (in Russian)

F. Sherman, editor, Эмульсии [Emulsions], (Himija, Leningrad, 1972), pp. 448, https://www.studmed.ru/sherman-f-red-emulsii_1553621cafe.html. (in Russian)

M.V. Krautsou, A.M. Krautsou, Izvestiâ vysših učebnyh zavedenij i ènergetičeskih obʺedinennij SNG. Ènergetika, 2, 80–87 (2011), https://energy.bntu.by/jour/article/download/301/296 (in Russian)

E.L. Koschmieder, Benard Cell and Taylor Vortices, (Cambridge University Press, 1993), pp. 337.

Published
2020-11-20
Cited
0 article
How to Cite
Andrieieva, O., Bulavin, L., Kudriavtsev, I., Sokolenko, R., & Tkachenko, V. (2020). Viscosity and Vortex Formation in a Liquid Placed in A Rotating Cylindrical Vessel. East European Journal of Physics, (4), 110-118. https://doi.org/10.26565/2312-4334-2020-4-14