Skip to main content
SpringerLink
Log in

Numerical Investigation of the Effects of High Reynolds and Marangoni Numbers on Thermocapillary Droplet Migration

  • Original Article
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

Abstract

This paper presents the results of the thermocapillary motion of a spherical droplet under Marangoni flow conditions, which takes place in a zero-gravity environment where buoyancy effects become insignificant. In such an environment the droplet moves from the cold region to the warm region due to the variation of surface tension induced by the temperature gradient. This two-phase flow problem is formulated using a 3D CFD model linked with four user-defined functions (UDFs) where the liquid–liquid interface is tracked using the “volume of fluid (VOF)” method and the “geometric reconstruction” scheme. The droplet interface was captured using the “Piece-wise Linear Interface Calculation (PLIC)” approach as a part of the VOF method. A constant temperature gradient was assumed in the stagnant liquid bounded medium. The results obtained cover low, intermediate, and high thermal Marangoni numbers (MaT ≤ 105), which were not covered before in numerical or space onboard experimental results. It was found that the droplet deforms as it elongates in the direction of the temperature gradient. The scaled droplet velocity decreases as the thermal Marangoni number increases for the full range of MaT. In addition, the scaled droplet velocity has been correlated with the thermal Marangoni number of a single droplet migrating in the zero-gravity condition, based on the results of the present work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Alhendal, Y., Turan, A., Kalendar, A.: Thermocapillary Bubble Migration at High Reynolds and Marangoni Numbers: 3D Numerical Study. Microgravity Sci. Technol. 30, 561–569 (2018). https://doi.org/10.1007/s12217-018-9643-4

    Article  Google Scholar 

  • Alhendal, Y., Turan, A.: Thermocapillary bubble dynamics in a 2d axis swirl domain. Heat Mass Transf. 51, 529–542 (2015)

    Article  Google Scholar 

  • Alhendal, Y., Turan, A.: Microgravity Sci. Technol. 28, 639 (2016). https://doi.org/10.1007/s12217-016-9521-x

    Article  Google Scholar 

  • Alhendal, Y., Turan, A., Hollingsworth, P.: Thermocapillary simulation of single bubble dynamics in zero gravity. Acta Astronaut. 88, 108–115 (2013)

    Article  Google Scholar 

  • Alhendal, Y., Turan, A., Al-mazidi, M.: Thermocapillary bubble flow and coalescence in a rotating cylinder: a 3D study. Acta Astronaut. 117, 484–496 (2015)

    Article  Google Scholar 

  • ANSYS-FLUENT 2011. Users Guide

  • Balasubramaniam, R., Subramanian, R.S.: The migration of a drop in a uniform temperature gradient at large Marangoni numbers. Phys. Fluids 12, 733–743 (2000)

    Article  Google Scholar 

  • Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354 (1992)

    Article  MathSciNet  Google Scholar 

  • Colin, C., Riou, X., Fabre, J.: Bubble coalescence in gas–liquid flow at microgravity conditions. Microgravity Sci. Technol. 20(3), 243–246 (2008)

    Article  Google Scholar 

  • Hadland, P.H., Balasubramaniam, R., Wozniak, G., Subramanian, R.S.: Thermocapillary migration of bubbles and drops at moderate to large Marangoni number and moderate Reynolds number in reduced gravity. Exp. Fluids 26, 240–248 (1999)

    Article  Google Scholar 

  • Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225 (1981)

    Article  Google Scholar 

  • Kang, Q., Cui, H.L., Hu, L., Duan, L.: On-board Experimental Study of Bubble Thermocapillary Migration in a Recoverable Satellite. Microgravity Science and Technology 20, 67–71 (2008)

    Article  Google Scholar 

  • Kawaji, M., Dejesus, J.M., Tudose, G.: Investigation of flow structures in vertical slug flow. Nucl. Eng. Des. 175, 37–48 (1997)

    Article  Google Scholar 

  • Larkin, B.K.: Thermocapillary flow around hemispherical bubble. AICHEJ 16, 101–107 (1970)

    Google Scholar 

  • MA, X. : Numerical simulation of thermocapillary drop motion with internal circulation. Numerical Heat Transfer, Part A: Applications 35, 291–309 (1999)

    Article  Google Scholar 

  • O’Shaughnessy, S.M., Robinson, A.J.: Numerical investigation of bubble induced marangoni convection: some aspects of bubble geometry. Microgravity Sci. Technol. 20(3), 319–325 (2008)

    Article  Google Scholar 

  • Radulescu, C., Robinson, A.J.: The influence of gravity and confinement on marangoni flow and heat transfer around a bubble in a cavity: a numerical study. Microgravity Sci. Technol. 20(3), 253–259 (2008)

    Article  Google Scholar 

  • Subramanian, K., Paschke, S., Repke, J., Wozny, G.: Drag force modelling in CFD simulation to gain insight of packed columns. AIDIC Conference Series 09, 299–308 (2009)

    Google Scholar 

  • Tomiyama, A., Sou, A., Minagawa, H., Sakaguchi, T.: Numerical Analysis of a Single Bubble by VOF Method. JSME International Journal Series B 36, 51–56 (1993)

    Article  Google Scholar 

  • Treuner, M., Galindo, V., Gerbeth, G., Langbein, D., Rath, H.J.: Thermocapillary Bubble Migration at High Reynolds and Marangoni Numbers under Low Gravity. J. Colloid Interface Sci. 179, 114–127 (1996)

    Article  Google Scholar 

  • Wölk, G., Dreyer, M., Rath, H.J.: Flow patterns in small diameter vertical non-circular channels. Int. J. Multiph. Flow 26, 1037–1061 (2000)

    Article  Google Scholar 

  • Xie, J.C., Lin, H., Zhang, P., Liu, F., Hu, W.R.: Experimental investigation on thermocapillary drop migration at large Marangoni number in reduced gravity. J. Colloid Interface Sci. 285, 737–743 (2005)

    Article  Google Scholar 

  • Yin, Z.H., Chang, L., Hu, W.R., Gao, P.: Thermocapillary migration and interaction of two nondeformable drops. Applied Mathematics and Mechanics 32, 811–824 (2011)

    Article  MathSciNet  Google Scholar 

  • Young, N.O., Goldstein, J.S., Block, M.J.: The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6, 350–356 (1959)

    Article  Google Scholar 

  • YOUNGS, D. L. : Time-dependent multi-material flow with large fluid distortion, pp. 273–285. Academic Press, Numerical Methods for Fluid Dynamics (1982)

    MATH  Google Scholar 

  • Zhao, J.F., Li, Z.D., Li, H.X., Li, J.: Thermocapillary migration of deformable bubbles at moderate to large Marangoni number in microgravity. Microgravity Sci. Technol. 22, 295–303 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Technological Studies (CTS), Public Authority for Applied Education and Training, Adailiyah, Kuwait

    Abdulrahim Kalendar, Yousuf Alhendal & Hosny Abou-Ziyan

  2. Manchester, UK

    Ali Turan

  3. Mechanical Power Engineering Department, Faculty of Engineering, Helwan University, Cairo, Egypt

    Hosny Abou-Ziyan

Authors
  1. Abdulrahim Kalendar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yousuf Alhendal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ali Turan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hosny Abou-Ziyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yousuf Alhendal.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalendar, A., Alhendal, Y., Turan, A. et al. Numerical Investigation of the Effects of High Reynolds and Marangoni Numbers on Thermocapillary Droplet Migration. Microgravity Sci. Technol. 33, 23 (2021). https://doi.org/10.1007/s12217-021-09874-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12217-021-09874-8

Keywords

Search

Navigation