Development of a Tracer Fluid in a Vertical Tube With Gravity-Assisted and Resisted Motions

This study provides procedural tools that can be used in concert with a computer algorithm to simulate the two-phase flow development of a higher density, tracer fluid inside a vertical tube. The problem arises in the context of a tracer fluid (e.g., a contrast agent) being injected into a neutral fluid such as blood. Based on cell fractions of tracer fluid obtained numerically, absorbency profiles are extrapolated. These are shown to compare favorably with laboratory x-ray samples realized under similar flow conditions. At low Reynolds numbers, one finds that a downward profile exhibits a more elongated frontal boundary than predicted by laminar flow theory of a single-phase, Newtonian fluid. The observed stretching of the denser fluid is confirmed experimentally and can be attributed to the combined effects of gravity assistance near the core and viscous resistance near the wall. In gravity-resisted flow, a reverse behavior is observed. A blunter frontal boundary is established during upward motion. In both cases, the role of gravity is weakened with successive increases in the Reynolds number. This behavior suggests the existence of a Reynolds number above which gravitational bias can be neglected in any flow orientation. It is hoped that this study will set the pace for a broader investigation of two-phase motion characterization of a tracer fluid under various flow conditions and orientations.