Skip to main content
SpringerLink
Log in

Experimental study of the free surface deformation due to thermal convection in liquid bridges

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

Optical imaging was used to measure the free surface deformation due to thermal (Marangoni-buoyant) convection in liquid bridges of 5-cSt silicone oil. We obtained the free surface position averaged over time in both the steady and oscillatory regimes. The deviation of the free surface contour from the corresponding equilibrium shape was determined with an uncertainty of about 2 μm. This deviation grew linearly with the applied temperature difference with a proportionality coefficient depending on the liquid bridge volume at equilibrium. Shrinkage at the upper part of the liquid bridge was slightly greater than bulging at the lower with the sum of the maximum deviations at both parts being about 30 μm near the onset of oscillations. This sum, normalized with the radius of the supporting disks, was of the same order of magnitude as the Capillary number. We observed the influence of thermal expansion, surface tension variation over the free surface, and fluid motion separately. The local mean curvature was also calculated and compared with its value at equilibrium, showing that the hydrodynamic effects were important.

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

Access this article

Log in via an institution

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
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Anastasiadis SH, Chen JK, Koberstein JT, Siegel AF, Sohn JE, Emerson JA (1987) The determination of interfacial tension by video image processing of pendant fluid drops. J Colloid Interface Sci 184:77–91

    Google Scholar 

  • Cabezas MG, Bateni A, Montanero JM, Neumann AW (2006) Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces without use of apex coordinates. Langmuir 22:10053–10060

    Article  Google Scholar 

  • Cabezas MG, Ferrera C, Montanero JM (2007) Computational evaluation of the Theoretical Image Fitting Analysis-Axisymmetric Interfaces (TIFA-AI) method of measuring interfacial tension. Meas Sci Technol 119:55–66

    Google Scholar 

  • Canny JA (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 8:679–698

    Google Scholar 

  • Chen QS, Hu WR (1998) Influence of liquid bridge volume on instability of floating half zone convection. Int J Heat Mass Transf 41:825–837

    Article  MathSciNet  MATH  Google Scholar 

  • Ermakov MK, Ermakova MS (2004) Linear-stability analysis of thermocapillary convection in liquid bridges with highly deformed free surface. J Cryst Growth 266:160–166

    Article  Google Scholar 

  • Ferrera C, Cabezas MG, Montanero JM (2006) An experimental analysis of the linear vibration of axisymmetric liquid bridges. Phys Fluids 18:082105.1–082105.16

    Article  Google Scholar 

  • Ferrera C, Montanero JM, Cabezas MG (2007) An analysis of the sensitivity of pendant drops and liquid bridges to measure the interfacial tension. Meas Sci Technol 18:3713–3723

    Article  Google Scholar 

  • Ferrera C, Montanero JM, Mialdun A, Shevtsova V, Cabezas MG (2008) A new experimental technique for measuring the dynamical free surface deformation in liquid bridges due to thermal convection. Meas Sci Technol 19:015410.1–015410.10

    Article  Google Scholar 

  • Han JH, Sun ZW, Dai LR, Xie JC, Hu WR (1996) Experiment on the thermocapillary convection of a mercury liquid bridge in a floating half zone. J Cryst Growth 169:129–135

    Article  Google Scholar 

  • Hu WR, Shu JZ, Zhou R, Tang ZM (1994) Influence of liquid bridge volume on the onset of oscillation in floating zone convection. J Cryst Growth 142:379–384

    Article  Google Scholar 

  • Kamotani Y, Ostrach S, Masud J (2000) Microgravity experiments and analysis of oscillatory thermo-capillary flows in cylindrical containers. J Fluid Mech 410:211–233

    Article  MATH  Google Scholar 

  • Kamotani Y, Matsumoto S, Yoda S (2007) Recent developments in oscillatory Marangoni convection. Fluid Dyn Mater Process 2:147–160

    Google Scholar 

  • Kuhlmann HC (1999) Thermocapillary convection in models of crystal growth. Springer, Berlin

    Google Scholar 

  • Lappa M (2004) Fluids, materials and microgravity: numerical techniques and insights into the physics. Elsevier Science, Oxford

    Google Scholar 

  • Lappa M, Savino R, Monti R (2001) Three-dimensional numerical simulation of Marangoni instabilities in non-cylindrical liquid bridges in microgravity. Int J Heat Mass Transfer 44:1983–2003

    Article  MATH  Google Scholar 

  • Lappa M, Yasuhiro S, Imaishi N (2003) 3D numerical simulation of on ground Marangoni flow instabilities in liquid bridges of low Prandtl number fluid. Int J Num Meth Heat Fluid Flow 13:309–340

    Article  MATH  Google Scholar 

  • Li X, Nishino K, Yoda S (2004) Temporal speckle pattern interferometry for measuring micron-order surface motion of a liquid bridge. Meas Sci Technol 18:2284–2294

    Article  Google Scholar 

  • Lowry BJ (1996) Pressure and stress measurement via image analysis (P-SIA) of axisymmetric drops and liquid bridges. J Colloid Interface Sci 176:284–297

    Article  Google Scholar 

  • Montanero JM, Cabezas MG, Acero J, Perales, JM (2002) Theoretical and experimental analysis of the equilibrium contours of liquid bridges of arbitrary shape. Phys Fluids 14:682–693

    Article  MathSciNet  Google Scholar 

  • Nienhüser C, Kuhlmann HC (2002) Stability of thermocapillary flows in non-cylindrical liquid bridges. J Fluid Mech 458:35–73

    Article  MathSciNet  MATH  Google Scholar 

  • Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans SMC 9:62–66

    Google Scholar 

  • Sakurai M, Onishi N, Hirata A (1999) Oscillatory thermocapillary convection features in a liquid bridge under normal gravity and microgravity conditions—drop shaft experiments. Adv Space Res 24:1379–1384

    Article  Google Scholar 

  • Schatz MF, Neitzel GP (2001) Experiments on thermocapillary instabilities. Annu Rev Fluid Mech 33:93–127

    Article  Google Scholar 

  • Schwabe D (2006) Marangoni instability in small circular containers under microgravity. Exp Fluids 40:942–950

    Article  Google Scholar 

  • Shevtsova V (2005) Thermal convection in liquid bridges with curved free surfaces: benchmark of numerical solutions. J Crystal Growth 280:632–651

    Article  Google Scholar 

  • Shevtsova VM, Legros JC (1998) Thermocapillary motion and stability of strongly deformed liquid bridges. Phys Fluids 10:1621–1634

    Article  MathSciNet  MATH  Google Scholar 

  • Shevtsova VM, Mojahed M, Legros JC (1999) The loss of stability in ground based experiments in liquid bridges. Acta Astronaut 44:625–634

    Article  Google Scholar 

  • Shevtsova VM, Mialdun A, Mojahed M (2005) A study of heat transfer from liquid bridge interfaces to surroundings. J Non-Equilib Thermodyn 30:261–281

    Article  Google Scholar 

  • Shevtsova V, Mialdun A, Ferrera C, Ermakov M, Cabezas MG, Montanero JM (2008) Subcritical and oscillatory dynamic surface deformations in non-cylindrical liquid bridges. Fluid Dyn Mater Process 4:43–45

    Google Scholar 

  • Shu JZ, Yao YL, Zhou R, Hu WR (1994) Experimental study of free surface oscillations of a liquid bridge by optical diagnostics. Micrograv Sci Technol VII/2:83–89

    Google Scholar 

  • Sim BC, Zebib A (2002) Thermocapillary convection with underformable curved surfaces in open cylinders. J Thermophys Heat Transf 16(4):553–561

    Article  Google Scholar 

  • Song B, Springer J (1996) Determination of interfacial tension from the profile of a pendant drop using computer-aided image processing. 2. Experimental. J Colloid Interface Sci 184:77–91

    Google Scholar 

  • Tang ZM, Hu WR, Imaishi N (2001) Two bifurcation transitions of the floating zone convection in a fat liquid bridge of larger Pr. Int J Heat Mass Transf 44:1299–1307

    Article  MATH  Google Scholar 

Download references

Acknowledgments

We are indebted to Prof. J.C. Legros for helpful discussions and creating the academic environment that made this research possible. J.M.M. acknowledges partial support from the Ministerio de Educación y Ciencia (Spain) through Grant No. PR2007-0510.

Author information

Author notes

  1. J. M. Montanero

    Present address: Department of Mechanical, Energetic and Materials Engineering, University of Extremadura, Avda De Elvas s/n, 06071, Badajoz, Spain

Authors and Affiliations

  1. Microgravity Research Center, CP-165/62, Université Libre de Bruxelles, 50, av. F. D. Roosevelt, 1050, Brussels, Belgium

    J. M. Montanero, C. Ferrera & V. M. Shevtsova

Authors
  1. J. M. Montanero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Ferrera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. M. Shevtsova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. M. Montanero.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Montanero, J.M., Ferrera, C. & Shevtsova, V.M. Experimental study of the free surface deformation due to thermal convection in liquid bridges. Exp Fluids 45, 1087–1101 (2008). https://doi.org/10.1007/s00348-008-0529-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-008-0529-x

Keywords

Search

Navigation