Unsteady propagation of a liquid plug in a liquid-lined straight tube.

This paper considers the propagation of a liquid plug driven by a constant pressure within a rigid axisymmetric tube whose inner surface is coated by a thin liquid film. The Navier-Stokes equations are solved using the finite-volume method and the SIMPLEST algorithm. The effects of precursor film thickness, initial plug length, pressure drop across the plug, and constant surface tension on the plug behavior and tube wall mechanical stresses are investigated. As a plug propagates through a liquid-lined tube, the plug gains liquid from the leading front film, and it deposits liquid into the trailing film. If the trailing film is thicker (thinner) than the precursor film, the plug volume decreases (increases) as it propagates. For a decreasing volume, eventually the plug ruptures. Under a specific set of conditions, the trailing film thickness equals the precursor film thickness, which leads to steady state results. The plug speed decreases as the precursor film thins because the resistance to the moving front meniscus increases. As the pressure drop across the plug decreases, the plug speed decreases resulting in thinning of the trailing film. As the plug length becomes longer, the viscous resistance in the plug core region increases, which slows the plug and causes the trailing film to become even thinner. The magnitude of the pressure and shear stress at the tube inner wall is maximum in the front meniscus region, and it increases with a thinner precursor film. As the surface tension increases, the plug propagation speed decreases, the strength of the wall pressure in the front meniscus region increases, and the pressure gradient around the peak pressure becomes steeper.