Transient displacement of a viscoplastic material by air in straight and suddenly constricted tubes

TLDR: In this article, the authors examine the transient displacement of a viscoplastic material from straight or suddenly constricted cylindrical tubes of finite length and develop accurate and efficient numerical methods for the fundamental study of processes in which a gas is displacing a liquid from prototype geometries under various operating conditions.

Abstract: We examine the transient displacement of a viscoplastic material from straight or suddenly constricted cylindrical tubes of finite length. Our general goal is to develop accurate and efficient numerical methods for the fundamental study of processes in which a gas is displacing a liquid from prototype geometries under various operating conditions. Such processes can be part of the Gas Assisted Injection Molding (GAIM) or enhanced oil recovery. To this end, we use the mixed finite element method coupled with a quasi-elliptic mesh generation scheme in order to follow the very large deformations of the fluid volume. The displacing fluid is gas at high pressure, which forms a bubble of increasing length and a shape that depends on the fluid properties, the flow conditions, and the tube geometry. The cross-section of the bubble is always smaller than that of the tube due to adherence of fluid on the tube walls. The thickness of the remaining film depends on the same parameters and for most of its length it behaves as unyielded material. Unyielded material also arises in front of the bubble, around the axis of symmetry of the tube(s) and in the case of a constricted tube near the recirculation corner, but not around the entrance of the secondary tube. The rate of growth of the ‘tip splitting’ instability, that arises at relatively large values of the Reynolds number for Newtonian fluids in straight tubes, decreases as the Bingham number increases and, eventually, the instability disappears. The resistance provided by the constricted tube downstream makes the bubble move at a nearly constant velocity only when the Bingham number is not large. When the bubble approaches the constriction it becomes more pointed, but after entering it, the bubble reassumes its well-developed profile. Depending on parameter values, the bubble in the secondary tube may periodically split, thus forming a train of smaller bubbles directed towards the exit of the tube, a phenomenon for which experimental evidence exists.