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Motion of large bubbles in curved channels

Published online by Cambridge University Press:  14 October 2021

Metin Muradoglu  and
Howard A. Stone
Metin Muradoglu
Affiliation:
Department of Mechanical Engineering, Koc University, Rumelifeneri Yolu, Sariyer 34450 Istanbul, [email protected]
Howard A. Stone
Affiliation:
Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, [email protected]
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Abstract

We study the motion of large bubbles in curved channels both semi-analytically using the lubrication approximation and computationally using a finite-volume/front-tracking method. The steady film thickness is governed by the classical Landau–Levich–Derjaguin–Bretherton (LLDB) equation in the low-capillary-number limit but with the boundary conditions modified to account for the channel curvature. The lubrication results show that the film is thinner on the inside of a bend than on the outside of a bend. They also indicate that the bubble velocity relative to the average liquid velocity is always larger in a curved channel than that in a corresponding straight channel and increases monotonically with increasing channel curvature. Numerical computations are performed for two-dimensional cases and the computational results are found to be in a good agreement with the lubrication theory for small capillary numbers and small or moderate channel curvatures. For moderate capillary numbers the numerical results for the film thickness, when rescaled to account for channel curvature as suggested in the lubrication calculation, essentially collapse onto the corresponding results for a bubble in a straight tube. The lubrication theory is also extended to the motion of large bubbles in a curved channel of circular cross-section.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 570 , 10 January 2007 , pp. 455 - 466
Copyright
Copyright © Cambridge University Press 2007

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