Thermocapillary migration of interfacial droplets

We study the thermocapillary driven motion of a droplet suspended at an interface of two fluid layers subjected to an imposed temperature gradient parallel to the interface. We compute the temperature and velocity fields inside and outside of the droplet using a boundary collocation numerical scheme in the limit of small capillary and thermal Péclet numbers and compare the results with the classical problem of thermocapillary migration of a droplet in the bulk. In particular, we find that, for typical values of parameters, interfacial droplets migrate in the direction opposite to the temperature gradient, while in the classical problem migration is always in the direction of the gradient. Furthermore, we find that a rich variety of flow structures can emerge inside interfacial droplets. We also confirm that for parameters matching a recent experimental study of mixing inside interfacial microdroplets R. O. Grigoriev, V. Sharma, and M. F. Schatz, Lab Chip 6, 1369 (2006) the interior flow can be approximated with reasonable accuracy by assuming the droplet to be completely submerged in the bottom layer.