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

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## Abstract

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.

## Keywords

Liquid Bridge Camera Calibration Oscillatory Flow Marangoni Number Particle Tracking Velocimetry## List of symbols

*H*height of the liquid bridge [mm]

*m*azimuthal wave number [-]

*R*radius of the liquid bridge [mm]

*T*temperature [°C]

- Δ
*T* temperature difference [K]

- Δ
*T*_{c} critical temperature difference [K]

## Greek symbols

*β*coefficient of thermal expansion [1/K]

*Γ*aspect ratio

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

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

*κ*thermal diffusivity [mm

^{2}/s]*ν*kinematic viscosity [mm

^{2}/s]*ρ*density [kg/mm

^{3}]*σ*surface tension [N/mm]

*σ*_{T}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

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

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

- Ma
_{c} critical Marangoni number

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

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