Transient displacement of Newtonian liquids by gas in periodically constricted tubes

Abstract The displacement of viscous liquids by pressurized gas from harmonically undulated tubes of finite length is examined. This unsteady process gives rise to a long open bubble of varying radius, increasing length and surrounded by the liquid. In general, the thickness of the liquid film that remains on the tube wall is nonuniform. Under creeping flow conditions, it varies periodically, but with a phase difference from the tube radius. The liquid fraction remaining in each periodic segment of the tube increases as the ratio between the minimum and maximum of the tube radius S decreases, whereas it tends to the well‐known asymptotic value for straight tubes as S → 1, or as the wavelength of the tube undulation increases, although here the flow is accelerating. At high‐values of the Reynolds number, the film thickness increases with the axial distance, and the periodicity of the flow field ahead of the bubble tip, which exists under creeping flow conditions, is broken. At even higher Reynolds numbers, recirculating vortices develop inside each tube expansion and when S also decreases significantly, nearly isolated bubbles are formed in each tube segment. The location of the bubble tip can be monitored by examining the time variation of the pressure at the tube wall. © 2006 American Institute of Chemical Engineers AIChE J, 2006