Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Abstract
When a very viscous fluid is drained out of a container through an axisymmetrically placed circular orifice a dip appears at the free surface. At later times, this dip develops into a cusp. The distance separating the tip of the dip and the bottom surface is measured and a scaling law is derived. We measured also the curvature versus the time and found that the curvature scales such that the viscous stress at the hole is always balanced by the surface tension of the free surface. Also we monitored the position of a passive tracer as a function the time before it reaches the hole and found that the cusped surface affects the flow both at the far field and close to the singularity. Finally, we investigated the encapsulation of a lighter and less viscous liquid when entrapped in the cusp at the final
stage of drainage
