In this study, we investigate the steady propagation of a liquid plug within a two-dimensional channel lined by a uniform, thin liquid film. The Navier-Stokes equations with free-surface boundary conditions are solved using the finite volume numerical scheme. We examine the effect of varying plug propagation speed and plug length in both the Stokes flow limit and for finite Reynolds number (Re). For a fixed plug length, the trailing film thickness increases with plug propagation speed. If the plug length is greater than the channel width, the trailing film thickness agrees with previous theories for semi-infinite bubble propagation. As the plug length decreases below the channel width, the trailing film thickness decreases, and for finite Re there is significant interaction between the leading and trailing menisci and their local flow effects. A recirculation flow forms inside the plug core and is skewed towards the rear meniscus as Re increases. The recirculation velocity between both tips decreases with the plug length. The macroscopic pressure gradient, which is the pressure drop between the leading and trailing gas phases divided by the plug length, is a function of U and where U is the plug propagation speed, when the fluid property and the channel geometry are fixed. The term becomes dominant at small values of the plug length. A capillary wave develops at the front meniscus, with an amplitude that increases with Re, and this causes large local changes in wall shear stresses and pressures.
Steady Propagation of a Liquid Plug in a Two-Dimensional Channel
Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division March 4, 2004; revision received May 20, 2004. Associate Editor: C. R. Ethier.
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Fujioka , H., and Grotberg, J. B. (November 23, 2004). "Steady Propagation of a Liquid Plug in a Two-Dimensional Channel ." ASME. J Biomech Eng. October 2004; 126(5): 567–577. https://doi.org/10.1115/1.1798051
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