Mixing immiscible fluids: drainage induced cusp formations

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

Experimental Study of Developable Cones

International audienceIn this paper we investigate developable cones (d-cones) topology. From profilometer measurements, we found that for a sample of a finite thickness the singularity is never pointlike but has a form of a crescent. Measurements of the sheet local curvature revealed that the d-cone tip is rejected by a distance which characterizes the singularity size. High deformations of the d-cone lead to a plastic regime equivalent to a decrease in the singularity size characterized from curvature and profile analysis. [S0031-9007(98)05464-7