Advertisement

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

Abstract

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.

Keywords

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

IH

Intensity distribution of hologram

IH,image

Intensity distribution of magnified hologram

M

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

Er

Complex amplitude distribution on reconstruction plane

E

Complex amplitude distribution of plane collimated light

λ

Wavelength of light

zo

Distance of object particle from hologram plane

zr

Distance of reconstructed particle from hologram plane

Ir

Intensity distribution on reconstruction plane

t

Time between two successive holograms

UL

Liquid superficial velocity

UG

Gas superficial velocity

UTP

Two-phase velocity

Ach

Channel cross-sectional area

QL

Liquid flow rate

QG

Gas flow rate

W

Width of channel along x-direction

H

Height of channel along y-direction

L

Depth of channel along z-direction

Ls

Length of the liquid slug

x*

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

y*

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

z*

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

UB

Bubble velocity

μL

Dynamic viscosity

ρ

Density of fluid

σ

Surface tension

rh

Hydraulic radius

δ

Liquid film thickness between the channel wall and the gas bubble

u

Streamwise velocity

v

Transverse velocity

w

Spanwise Velocity

Uvw

Velocity on transverse plane

Uabs

Absolute velocity

Urel

Relative velocity

g

Gravitational acceleration

dp

Diameter of particle

D

Distance between microscope objective and hologram plane

Bo

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

Ca

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

Re

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

We

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

Notes

Acknowledgments

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

Supplementary material

Supplementary material 1 (WMV 2169 kb)

References

  1. Abadie T, Aubin J, Legendre D, Xuereb C (2012) Hydrodynamics of gas–liquid Taylor flow in rectangular micro channels. Microfluid Nanofluid 12:355–369CrossRefGoogle Scholar
  2. Akbar MK, Plummer DA, Ghiaasiaan SM (2003) On gas–liquid two-phase flow regimes in microchannels. Int J Multiphase Flow 29:855–865CrossRefzbMATHGoogle Scholar
  3. Choi YS, Lee SJ (2009) Three-dimensional volumetric measurement of red blood cell motion using digital holographic microscopy. Appl Opt 48(16):2983–2990CrossRefGoogle Scholar
  4. Choi YS, Lee SJ (2010) Holographic analysis of three-dimensional inertial migration of spherical particles in micro-scale pipe flow. Microfluid Nanofluid 9:819–829CrossRefGoogle Scholar
  5. Goodman JW (1968) Introduction to fourier optics. McGraw-Hill, New YorkGoogle Scholar
  6. Ishikawa M, Murai Y, Wada A, Iguchi M, Okamoto K, Yamamoto F (2000) A novel algorithm for particle tracking velocimetry using the velocity gradient tensor. Exp Fluids 29:519–531CrossRefGoogle Scholar
  7. Kim S, Lee SJ (2008) Effect of particle number density in in-line digital holographic particle velocimetry. Exp Fluids 44:623–631CrossRefGoogle Scholar
  8. Kinoshita H, Kaneda S, Fujii T, Oshima M (2007) Three-dimensional measurement and visualization of internal flow of a moving droplet using confocal micro-PIV. Lab Chip 7:338–346CrossRefGoogle Scholar
  9. Kreis T (2005) Handbook of holographic interferometry optical and digital methods. Wiley-VCH Verlag GmbH and Co. KGaA, WeinheimGoogle Scholar
  10. Ooms T, Lindken AR, Westerweel J (2009) Digital holographic microscopy applied to measurement of a flow in a T-shaped micromixer. Exp Fluids 47:941–955CrossRefGoogle Scholar
  11. Qian D, Lawal A (2006) Numerical study on gas and liquid slugs for Taylor flow in a T-junction microchannel. Chem Eng Sci 61:7609–7625CrossRefGoogle Scholar
  12. Satake S, Kunugi T, Sato K, Ito T, Taniguchi J (2005) Three-dimensional flow tracking in a micro channel with high time resolution using micro digital-holographic particle-tracking velocimetry. Opt Rev 12(6):442–444CrossRefGoogle Scholar
  13. Satake S, Kunugi T, Sato K, Ito T, Kanamori H, Taniguchi J (2006) Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry. Meas Sci Technol 17:1647–1651CrossRefGoogle Scholar
  14. Sheng J, Malkiel E, Katz J (2006) Digital holographic microscope for measuring three-dimensional particle distributions and motions. Appl Opt 45(16):3893–3901CrossRefGoogle Scholar
  15. Sheng J, Malkiel E, Katz J (2008) Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer. Exp Fluids 44(6):1023–1035CrossRefGoogle Scholar
  16. Singh DK, Panigrahi PK (2010) Improved digital holographic reconstruction algorithm for depth error reduction and elimination of out-of-focus particles. Opt Express 18(3):2426–2448CrossRefGoogle Scholar
  17. Singh DK, Panigrahi PK (2012) Automatic threshold technique for holographic particle field characterization. Appl Opt 51(17):3874–3887CrossRefGoogle Scholar
  18. Xu W, Jericho MH, Meinertzhagen IA, Kreuzer HJ (2002) Digital in-line holography of microspheres. Appl Opt 41(25):5367–5375CrossRefGoogle Scholar
  19. Zaloha P, Kristal J, Jiricny V, Volkel N, Xuereb C, Aubin J (2012) Characteristics of liquid slugs in gas-liquid Taylor flow in microchannels. Chem Eng Sci 68(1):640–649CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

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

Personalised recommendations