In this chalk talk, we shall compare the stability of two distinct, equilibrium fluid configurations, viz., the pendent drop and the liquid bridge. Our main result is that the stability of these fluid bodies may be determined by knowing only their shapes. No eigenvalue problem is required to determine the neutral stability. Focusing, first on the pendent drop, we show that there are two different ways to create the drop- one by controlling the volume and the other by controlling its pressure. Our main result is easily obtained from the volume control case.
Extending the discussion to liquid bridges, we show that controlling pressure leads to a possible way to determine the interfacial tension between two fluids even when the density difference is zero.
As noted, this is a chalk talk- it is aimed at graduate students who have taken a first level transport phenomena and applied mathematics in chemical engineering course.
Ranga Narayanan has been a professor in the Department of Chemical Engineering at the University of Florida since 1981. His teaching interests include undergraduate mass and energy balances, fluid
mechanics, and thermodynamics and graduate courses in transport phenomena and applied mathematics. His research interests lie in all manners of hydrodynamic instability, pattern formation and nonlinear
dynamics. (Homepage: https://www.che.ufl.edu/faculty-staff/narayanan-ranga/)