Chaotic mixing in thermocapillary-driven microdroplets

Liquid microdroplets represent a convenient system for studies of mixing by chaotic advection in discrete microscopic volumes. The mixing properties of the flows in microdroplets are governed by their symmetries, which give rise to invariant surfaces serving as barriers to transport. Thorough mixing via chaotic advection requires destruction of all such invariant surfaces. To illustrate this idea, we demonstrate that quick and thorough mixing inside a spherical microdroplet suspended in a layer of substrate fluid can be obtained by moving the droplet along a two-dimensional path using temperature-induced surface tension gradients. The use of flow invariants also provides a convenient way to analyze the mixing properties of flows in many other experimental implementations.