Sufficiency of initial surface-area minimization for dynamic relaxation

Determine whether minimizing the initial liquid surface area at fixed volume is sufficient to minimize the subsequent relaxation time of a drop generated by capillary auto-ejection, accounting for inertia, viscosity, and capillary forces.

Background

The paper studies capillary auto-ejection as a rapid method for generating nearly spherical, centimeter-sized liquid drops in the brief microgravity intervals available in drop-tower experiments. Because the ejected drop must both form and relax rapidly, the authors examine how the geometry of the supporting cavity affects the post-ejection relaxation time.

A natural geometric hypothesis is that the cavity producing the smallest initial liquid surface area for a fixed liquid volume will also produce the shortest relaxation time. The paper identifies and verifies this correspondence for a one-parameter family of parabolic troughs, but the introduction explicitly presents the general sufficiency of this criterion as unresolved because relaxation is governed by fully dynamic fluid effects. The later double-well simulations show that the correspondence fails when an additional geometric degree of freedom is introduced.