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Steady Flows Excited by Local Oscillations of Flexible Boundary of a Container with Fluid

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Abstract

Viscous fluid flow near an oscillating deformable boundary of a cylindrical container is studied experimentally. The container is fixed horizontally, filled with a fluid and hermetically closed. On the top of the cylindrical boundary, a longitudinal activator is fixed, transmitting the vibrations from a linear motor to the boundary. The latter vibrates as a whole along its length, with an exception of short regions near the end faces. Under vibrations, in the Stokes boundary layers on the inner boundary surface, the steady streaming is generated. In the fluid, a system of rolls, extended parallel to the activator and mirror-symmetric with respect to the vibration axis, is formed. Their position is linked to the coordinates of boundary oscillation nodes. The flows are localized near the activator. The dynamics of the primary and the secondary steady flows is compared. The obtained results are important for the description of the flows in multiphase systems with an interface or in closed containers with an elastic boundary.

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References

  • Batchelor, G.: Introduction to Fluid Dynamics. University Press, Cambridge (1967)

    MATH  Google Scholar 

  • Gershuni, G.Z., Lyubimov, D.V.: Thermal Vibrational Convection. Wiley, New York (1998)

    Google Scholar 

  • Hanson, C.: Recent Advances in Liquid-Liquid Extraction. Elsevier Science, Amsterdam (2013)

    Google Scholar 

  • Ivanova, A.A., Kozlov, V.G.: Vibrational convection in nontranslationally oscillating cavity (isothermal case). Fluid Dyn. 38, 186–192 (2003)

    Article  Google Scholar 

  • Ivanova, A.A., Kozlov, V.G., Selin, N.V.: Average fluid flow in the end regions of a long channel subjected to rotational vibration. Fluid Dyn. 40, 369–375 (2005)

    Article  Google Scholar 

  • Klimenko, L.S., Lyubimov, D.V.: Generation of an average flow by a pulsating stream near a curved free surface. Fluid Dyn. 47(1), 26–36 (2012). https://doi.org/10.1134/S0015462812010048

    Article  MathSciNet  MATH  Google Scholar 

  • Klimenko, L.S., Lyubimov, D.V.: Average flow generation by a pulsating flow near a curved interface. Eur. Phys. J. E 40(1), 6 (2017). https://doi.org/10.1140/epje/i2017-11494-7

    Article  Google Scholar 

  • Klimenko, L., Lyubimov, D.: Surfactant effect on the average flow generation near curved interface. Microgravity Sci. Technol. 30(1), 77–84 (2018). https://doi.org/10.1007/s12217-017-9577-2

    Article  Google Scholar 

  • Kozlov, V.G., Kozlov, N.V., Schipitsyn, V.D.: Steady flows in an oscillating deformable container: effect of the dimensionless frequency. Phys. Rev. Fluids 2, 094501 (2017)

    Article  Google Scholar 

  • Kozlov, V.G., Sabirov, R.R., Subbotin, S.V.: Steady flows in oscillating spheroidal cavity with elastic wall. Fluid Dyn. 53, 189–199 (2018)

    Article  Google Scholar 

  • Murtsovkin, V.A., Muller, V.M.: Steady-state flows induced by oscillations of a drop with an adsorption layer. J. Colloid Interf. Sci. 151, 150–156 (1992)

    Article  Google Scholar 

  • Riley, N.: Steady streaming. Ann. Rev. Fluid Mech. 33, 43–65 (2001)

    Article  MathSciNet  Google Scholar 

  • Schlichting, H.: Boundary Layer Theory. McGraw-Hill, New York (1968)

    MATH  Google Scholar 

  • Shitanishi, K., Hasegawa, K., Kaneko, A., Abe, Y.: Study on heat transfer and flow characteristic under phase-change process of an acoustically levitated droplet. Microgravity Sci. Technol. 26(5), 305–312 (2014). https://doi.org/10.1007/s12217-014-9401-1

    Article  Google Scholar 

  • Sznitman, J., Rösgen, T.: Acoustic streaming flows in a cavity: an illustration of small-scale inviscid flow. Physica D 237, 2240–2246 (2008)

    Article  Google Scholar 

  • Thielicke, W., Stamhuis, E.J.: Pivlab—towards user-friendly, affordable and accurate digital particle image velocimetry in matlab. J. Open Res. Softw. 2, e30 (2014)

    Article  Google Scholar 

  • Trinh, E., Wang, T.G.: Large-amplitude free and driven drop-shape oscillations: experimental observations. J. Fluid Mech. 122, 315–338 (1982)

    Article  Google Scholar 

  • Trinh, E., Zwern, A., Wang, T.G.: An experimental study of small-amplitude drop oscillations in immiscible liquid systems. J. Fluid Mech. 115, 453–474 (1982)

    Article  Google Scholar 

  • Wegener, M., Paul, N., Kraume, M.: Fluid dynamics and mass transfer at single droplets in liquid/liquid systems. Int. J. Heat Mass Transf. 71, 475–495 (2014)

    Article  Google Scholar 

  • Yamamoto, Y., Abe, Y., Fujiwara, A., Hasegawa, K., Aoki, K.: Internal flow of acoustically levitated droplet. Microgravity Sci. Technol. 20(3), 277 (2008). https://doi.org/10.1007/s12217-008-9070-z

    Article  Google Scholar 

  • Yarin, A.L.: Stationary d.c. streaming due to shape oscillations of a droplet and its effect on mass transfer in liquid–liquid systems. J. Fluid Mech. 444, 321–342 (2001)

    Article  Google Scholar 

  • Yarin, A.L., Brenn, G., Kastner, O., Rensink, D., Tropea, C.: Evaporation of acoustically levitated droplets. J. Fluid Mech. 399, 151–204 (1999)

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to Professor V. G. Kozlov for fruitful discussions.

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Correspondence to Nikolai Kozlov.

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This article belongs to the Topical Collection: Multiphase Fluid Dynamics in Microgravity

Guest Editors: Tatyana P. Lyubimova, Jian-Fu Zhao

The research was supported by the Russian Science Foundation (project 17-71-10189).

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Kozlov, N., Vjatkin, A., Schipitsyn, V. et al. Steady Flows Excited by Local Oscillations of Flexible Boundary of a Container with Fluid. Microgravity Sci. Technol. 31, 821–831 (2019). https://doi.org/10.1007/s12217-019-09719-5

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