Transient Displacement of Newtonian Liquids By Gas in Periodically Constricted Tubes Yannis Dimakopoulos and John Tsamopoulos Laboratory of Computational Fluid Dynamics, Dept. of Chemical Engineering, University of Patras, Patras 26500, Greece DOI 10.1002/aic.10889 Published online June 2, 2006 in Wiley InterScience (www.interscience.wiley.com). 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 3 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, 52: 2707–2726, 2006 Keywords: Liquid displacement by gas; gas-assisted injection molding; oil recovery; flow in undulated tubes; moving boundary problems; elliptic mesh generation. Introduction The displacement of a viscous liquid by a gaseous phase is a problem of fundamental importance in the chemical and petrochemical industry. There are many practical applications and physical operations, such as the enhanced oil recovery, 1 the monolith reactors, 2 the pulmonary airway reopening, 3 the gas- assisted injection molding, 4 which have as a common basic feature the effective displacement of a liquid by gas. In the secondary oil recovery, air, steam or surfactants are introduced to displace oil lodged in rock pores. Monolith or honeycomb reactors are used for fast multiphase reactions, such as hydro- genations, due to the achieved enhancement in mass-transfer rates. During breathing, air or medication are driven into the lungs and the bronchioli, to expand them and retard or elimi- nate liquid bridging, which may lead to airway compliant collapse. The gas-assisted injection molding process (GAIM) is a modification of the conventional injection molding tech- nique 5 in which highly pressurized air or inert gas (usually N 2 ) is used to partially displace a molten polymer from a mold and produce hollow plastic articles. This leads to a reduction in the consumed energy for the process and improvement in the quality of the final product. Because of its importance, the liquid displacement by pres- surized gas from circular or noncircular tubes has attracted the interest of many researchers since early last century. 6-13 Invari- ably, in these theoretical or experimental studies the tube was much longer than its radius and the bubble that the gas formed while displacing the liquid was considered semi-infinite (that is, straight and open in its upstream side), making the motion steady. In particular, Taylor’s experiments 8 uncovered impor- tant aspects of this problem under creeping flow conditions, such as the three different flow patterns that can arise ahead of the bubble, and the variation of the thickness of the remaining liquid film as a function of the capillary number (Ca). Cox 9,10 extended Taylor’s measurements at higher capillary numbers © 2006 American Institute of Chemical Engineers AIChE Journal 2707 August 2006 Vol. 52, No. 8