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Applied Mathematics Research eXpress (2006) Vol. 2006 : article ID 36283, 11 pages, doi:10.1155/AMRX/2006/36283
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Confined motion of a long bubble through a power-law fluid

A. Nadim and A. Borhan

Departments of Mathematics & Bioengineering, Claremont Graduate University and Keck Graduate Institute Claremont, CA 91711, USA E-mail address: nadim{at}kgi.edu
Department of Chemical Engineering, The Pennsylvania State University University Park, PA 16802, USA E-mail address: borhan{at}psu.edu

Understanding the movement of drops and bubbles in microchannels is increasingly important in the design and operation of microfluidic devices that involve two-phase flows. Thus, Bretherton's analysis of the motion of long bubbles in tubes and the associated profile of the wetting film around it are relevant. In this work, steady motion of a long bubble through a cylindrical tube is revisited in the case where the wetting film between the bubble interface and the capillary wall is non-Newtonian and described by the power-law constitutive relation. Using the standard lubrication analysis, the equation for the thickness of the wetting film as a function of axial distance is derived and integrated to find the film thickness. The film thickness and pressure drop across the bubble are found to scale with the capillary number as Ca2/3, with a proportionality factor that depends on the power-law index.



References

  1. Bird R. B., Armstrong R. C., Hassager O. Dynamics of Polymeric Liquids, Vol. 1 (1987) 2nd. New York, NY, USA: Wiley-Interscience.
  2. Borhan A., Mao C. F. Effect of surfactants on the motion of drops through circular tubes. Physics of Fluids A: Fluid Dynamics (1992) 4(12):2628–2640.[CrossRef][Web of Science]
  3. Brenner H. Pressure drop due to the motion of neutrally buoyant particles in duct flows: II. Spherical droplets and bubbles. Industrial and Engineering Chemistry Fundamentals (1971) 10(4):537–543.[CrossRef]
  4. Bretherton F. P. The motion of long bubbles in tubes. Journal of Fluid Mechanics (1961) 10:166–188.[CrossRef][Web of Science]
  5. Chang H.-C. Bubble/drop transport in microchannels. In: The MEMS Handbook—Gad-el-Hak M., ed. (2001) Florida: CRC Press. chapter 11.
  6. Hetsroni G., Haber S., Wacholder E. The flow fields in and around a droplet moving axially within a tube. Journal of Fluid Mechanics (1970) 41:689–705.[CrossRef][Web of Science]
  7. Hyman W. A., Skalak R. Non-Newtonian behavior of a suspension of liquid drops in tube flow. AIChE Journal (1972) 18(1):149–154.[CrossRef][Web of Science]
  8. Hyman W. A., Skalak R. Viscous flow of a suspension of liquid drops in a cylindrical tube. Applied Scientific Research (1972) 26(1-2):27–52.[CrossRef][Web of Science]
  9. Martinez M. J., Udell K. S. Boundary integral analysis of the creeping flow of long bubbles in capillaries. Journal of Applied Mechanics, Transactions ASME (1989) 56(1):211–217.
  10. Olbricht W. L. Pore-scale prototypes of multiphase flow in porous media. Annual Review of Fluid Mechanics (1996) 28:187–213.[Web of Science]
  11. Reinelt D. A., Saffman P. G. The penetration of a finger into a viscous fluid in a channel and tube. SIAM Journal on Scientific and Statistical Computing (1985) 6(3):542–561.[CrossRef][Web of Science]
  12. Ro J. S., Homsy G. M. Viscoelastic free surface flows: thin film hydrodynamics of Hele-Shaw and dip coating flows. Journal of Non-Newtonian Fluid Mechanics (1995) 57(2-3):203–225.[CrossRef]
  13. Shen E. I., Udell K. S. A finite element study of low Reynolds number two-phase flow in cylindrical tubes. Journal of Applied Mechanics, Transactions ASME (1985) 52(2):253–256.
  14. Westborg H., Hassager O. Creeping motion of long bubbles and drops in capillary tubes. Journal of Colloid and Interface Science (1989) 133(1):135–147.[CrossRef][Web of Science]

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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
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Google Scholar
Right arrow Articles by Nadim, A.
Right arrow Articles by Borhan, A.
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