Viscous Entrainment: Creating an Atomic-Sized Liquid Spout
by
Wendy W. Zhang
James Franck Institute, University of Chicago

A small air bubble rising in syrup remains spherical. A larger air bubbles deforms, developing an increasingly tapered trailing end. For an even larger air bubble, the tapered end is "broken". A thin tendril of air is deposited behind the rising bubble. This is a familiar example of viscous entrainment. Inspired by selective withdrawal experiments (Cohen & Nagel, PRL 2002) and the observation that the trailing tendril, or spout, is often far thinner than the air bubble radius, we study the shape transition associated with viscous entrainment via a long-wavelength model. We find that continuous and weakly discontinuous shape transitions at the onset of entrainment arise when a special class of boundary conditions are prescribed. Thus resulting in steady-state spouts above the entrainment onset whose radii is far smaller than the length-scale imposed by the boundary conditions. Spouts which are infinitely thin in the continuum approximation are also possible. If realized in practice, this would be a novel way to create objects which are microscopic in one dimension and macroscopic in other dimensions.

Date received: November 3, 2003