Analysis of local pressure gradient inversion and form of bubbles in Taylor flow in microchannels

Analysis of local pressure gradient inversion and pressure 'jumps' at gas-liquid Taylor flow in microchannels, which has been previously observed, but not explained by Kreutzer et al. (2005b) and Duran Martinez et al. (2015) is carried out. The new understanding originates from a mathematical model of two-phase flow developed before (Abiev (2008) for circular capillaries, Falconi et al. (2016) for micro channels with square cross-section). It is shown that the inverse flow of the fluid in the film around the bubble is caused by the inverse pressure gradient in the film. The key factors determining the Taylor bubble surface deformation near its ends are found. The deformation occurring at the nose and tail ellipsoidal surfaces and on the cylindrical surface near the tail of the bubble is caused by the balance of pressure in the liquid film along the bubble, the pressure level in the bubble and capillary pressure. It was shown that pressure difference in the liquid film along the bubble caused by peculiar properties of Taylor flow in micro channels is the prime cause of non-hemispherical form of the bubble ends, not vice versa. The obtained results are applicable to micro channels both with circular and square crosssection (in the latter case to the so-called axisymmetric form of the bubble or close to it). The wavy form of the bubble near its tail observed by Kreutzer et al. (2005b), Abadie et al. (2013), Hayashi et al. (2014), and Falconi et al. (2016) is shown herein to be governed by the balance between the capillary forces at the interface and wave-like pressure field near the ends of the bubble. The performed analysis provides a quite simple understanding of previously unexplored features of Taylor flow hydrodynamics (pressure oscillations near the ends of the bubble found by Kreutzer et al. (2005a, 2005b)) and allows a characterization of the shape of the bubble ends in general (concave or almost planar, convex, elongated convex). The results obtained will allow a more accurate modeling of developing gas-liquid slug flow and a calculation of the surface area of the bubbles in the description of mass transfer processes. Besides, the results of this paper are important for better understanding of bubbles' formation process driving forces, thus giving a tool to engineers for better design of microreactors and micro heat exchangers. The bubble's nose elongation results in a significant change in the liquid film thickness in this area, influencing thus mass transfer characteristics by the change in the gas-liquid interface and the velocity in the liquid film. The observed form of the bubbles could also be used in experimental praxis as a detector indicating pressure drop and two-phase flow rate in the Taylor flow. (C) 2017 Elsevier Ltd. All rights reserved.