Transient displacement of a Newtonian fluid by air in straight or suddenly constricted tubes

We study the displacement of a viscous fluid by highly pressurized air in a straight or a suddenly constricted cylindrical tube of finite length. In contrast to previous efforts, the transient situation is examined. A long, narrower than the tube and round-ended bubble is created during the process. This is sometimes called "fingering instability" and is often encountered in several applications, but we will focus on process parameters that are relevant to the gas-assisted injection molding. For our numerical simulations we have combined the mixed finite element method with an appropriate system of elliptic partial differential equations and boundary conditions, capable of generating a boundary-fitted finite element mesh. The bubble front and the thickness of the deposited film on the tube wall are affected by the properties of the fluid being displaced and the flow conditions. Specifically, in straight tubes, the bubble keeps accelerating due to the decreasing fluid mass ahead of it. Increasing the Reynolds number decreases the film thickness and makes the bubble front steeper. When inertia becomes significant a tip-splitting instability arises. For sufficiently low Reynolds numbers, but still large applied pressures, a steady bubble shape is attained even in a straight tube and the fraction of the liquid deposited on the wall of the tube reaches the asymptotic value of 0.60, as observed by Taylor [J. Fluid Mech. 10, 161 (1961)] and Cox [J. Fluid Mech. 14, 81 (1962)]. In a constricted tube, the bubble temporarily attains a nearly constant velocity. When its front approaches the tube constriction it becomes pointed, due to the extensional flow that prevails there, but it reassumes its finger-like profile, after it goes through the constriction. (C) 2003 American Institute of Physics.