Experiments in Fluids

, 56:6 | Cite as

Three-dimensional investigation of liquid slug Taylor flow inside a micro-capillary using holographic velocimetry

  • Dhananjay Kumar Singh
  • P. K. PanigrahiEmail author
Research Article


Digital holography is an optical technique which is capable of providing instantaneous three-components of fluid flow velocity in three-dimensions (3D-3C) using a single camera. Digital holographic microscopy has been implemented in the present study to analyze liquid slug Taylor flow in a micro-channel of cross-sectional dimensions of 1,000 × 1,000 µm2. The working fluids are water (liquid) and air (gas), with superficial velocities of liquid, U L = 0.6 mm/s and gas, U G = 1.2 mm/s, respectively. The corresponding Capillary number, Ca = 0.035 × 10−3 and Bond number, Bo = 0.144. The holographic velocimetry technique has been implemented and appropriately validated by comparing the velocity profile from present experiment with that from analytical velocity profile for single-phase flow. Complete flow field results, i.e., u-, v- and w-components of velocity inside the liquid slug volume, i.e., in both streamwise (xy) and cross-stream (yz) planes are presented. The present experiments on liquid slug Taylor flow show strong cross-stream velocity near the advancing and receding meniscus due to higher capillary pressure. The stream traces show converging and diverging radial flow in the cross-stream plane near the receding and advancing meniscus, respectively. Two three-dimensional recirculation bubbles are observed inside the liquid slug. Overall, this paper reports the complex three-dimensional flow field inside a liquid slug Taylor flow from the 3D-3C flow field measurements.


Capillary Number Particle Tracking Velocimetry Bubble Velocity Digital Holography Liquid Film Thickness 
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


Intensity distribution of hologram


Intensity distribution of magnified hologram


Magnification of microscope objective

\( h_{{z_{\text{r}} }} \)

Free space impulse response function at distance z r from hologram plane

x, y

x and y coordinates on hologram plane

xr, yr

x and y coordinates on reconstruction plane


Complex amplitude distribution on reconstruction plane


Complex amplitude distribution of plane collimated light


Wavelength of light


Distance of object particle from hologram plane


Distance of reconstructed particle from hologram plane


Intensity distribution on reconstruction plane


Time between two successive holograms


Liquid superficial velocity


Gas superficial velocity


Two-phase velocity


Channel cross-sectional area


Liquid flow rate


Gas flow rate


Width of channel along x-direction


Height of channel along y-direction


Depth of channel along z-direction


Length of the liquid slug


Non-dimensional coordinate along x-direction (x/W)


Non-dimensional coordinate along y-direction [y/(H/2)]


Non-dimensional coordinate along z-direction [z/(L/2)]


Bubble velocity


Dynamic viscosity


Density of fluid


Surface tension


Hydraulic radius


Liquid film thickness between the channel wall and the gas bubble


Streamwise velocity


Transverse velocity


Spanwise Velocity


Velocity on transverse plane


Absolute velocity


Relative velocity


Gravitational acceleration


Diameter of particle


Distance between microscope objective and hologram plane


Bond number, \( Bo = \frac{{(\rho_{\text{L}} - \rho_{\text{G}} )d_{\text{h}}^{2} g}}{\sigma } \)


Capillary number, \( Ca = \frac{{\mu_{\text{L}} U}}{\sigma } \)


Reynolds number, \( \text{Re} = \frac{{\rho_{\text{L}} Ud_{\text{h}} }}{{\mu_{\text{L}} }} \)


Weber number, \( We = \frac{{\rho_{\text{L}} U^{2} d_{\text{h}} }}{\sigma } \)



The authors thank Department of Science and Technology, Government of India for the financial support.

Supplementary material

Supplementary material 1 (WMV 2169 kb)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Technology KanpurKanpurIndia

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