Transient free‐surface flows: Motion of a fluid advancing in a tube

The fluid motion at a free surface advancing into a mold or duct is appreciably different from its steady state behavior in well‐developed flow; this affects the residence time distribution and structure of macromolecular fluids as they are frozen in injection molding processes. In this work such motion is treated numerically and measured precisely for Newtonian fluids. While the three‐phase contact line represents a special problem conceptually and analytically, a very simple algorithm is seen to represent the fluid motion in this region accurately. Good agreement is found over wide ranges of the governing dimensionless groups (the Reynolds, Jeffrey, and capillary numbers). Since viscous forces are dominant under the circumstances studied, this finding is not surprising but it confirms the applicability of the numerical methods developed herein to the modeling of these flows under conditions of actual interest. As a result, simulations may be made with confidence to predict flow patterns encountered in practice but difficult to reproduce in laboratory experiments.