Experiments in Fluids

, Volume 38, Issue 3, pp 285–290 | Cite as

3D PTV measurement of oscillatory thermocapillary convection in half-zone liquid bridge

  • M. Nishimura
  • I. UenoEmail author
  • K. Nishino
  • H. Kawamura


Three-dimensional (3D) reconstruction of a unique particle motion in oscillatory thermocapillary convections in a small-sized half-zone liquid bridge with a radius of O (1 mm) was carried out by applying 3D particle tracking velocimetry (PTV). By placing a small cubic beam splitter above a transparent top rod, simultaneous observation of the particles in the bridge by use of two CCD cameras was realized. Reconstruction of the 3D trajectories and the particle velocity fields in several types of oscillatory flow regimes was conducted successfully for a sufficiently long period without losing particle tracking.


Liquid Bridge Camera Calibration Oscillatory Flow Marangoni Number Particle Tracking Velocimetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


height of the liquid bridge [mm]


azimuthal wave number [-]


radius of the liquid bridge [mm]


temperature [°C]


temperature difference [K]


critical temperature difference [K]

Greek symbols


coefficient of thermal expansion [1/K]


aspect ratio

\( \Gamma = H{\text{/}}R{\left[ - \right]} \)


overcritical parameter, where\(\varepsilon = {\left( {{\text{Ma}} - {\text{Ma}}_{{\text{c}}} } \right)}/{\text{Ma}}_{{\text{c}}}\)


thermal diffusivity [mm2/s]


kinematic viscosity [mm2/s]


density [kg/mm3]


surface tension [N/mm]


temperature coefficient of surface tension, where \( \sigma _{{\text{T}}} = {\left| {\partial \sigma {\text{/}}\partial {\text{T}}} \right|}\;\;{\left[ {{\text{N/mm}} \cdot {\text{K}}} \right]} \)

Non-dimensional numbers


Grashof number, where \( {\text{Gr}} = \beta g\Delta TL^{3} /\nu ^{2} \)


Marangoni number; where \( {\text{Ma}} = \sigma _{{\text{{\rm T}}}} \Delta T \cdot H{\text{/}}{\left( {\rho \nu \kappa } \right)} \)


critical Marangoni number


Prandtl number, where\(\Pr = \nu /\kappa\)


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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • M. Nishimura
    • 1
  • I. Ueno
    • 1
    Email author
  • K. Nishino
    • 2
  • H. Kawamura
    • 1
  1. 1.Department of Mechanical EngineeringTokyo University of ScienceNodaJapan
  2. 2.Department of Mechanical EngineeringYokohama National UniversityYokohamaJapan

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