Mixing properties of steady flow in thermocapillary driven droplets

We consider mixing via chaotic advection in microdroplets suspended at the free surface of a liquid substrate and driven along a straight line using the thermocapillary effect. With the help of a model derived by Grigoriev Phys. Fluids 17, 033601 2005 we show that the mixing properties of the flow inside the droplet can vary dramatically as a function of the physical properties of the fluids and the imposed temperature profile. Proper characterization of the mixing quality requires introduction of two different metrics. The first metric determines the relative volumes of the domain of chaotic streamlines and the domain of regular streamlines. The second metric describes the time for homogenization inside the chaotic domain. We compute both metrics using perturbation theory in the limit of weak temperature dependence of the surface tension coefficient at the free surface of the substrate. © 2007 American Institute of Physics. DOI: 10.1063/1.2738846