Spontaneous thermocapillary interaction of drops, bubbles and particles: Unsteady convective effects at low Peclet numbers

Mass and heat transfer between two adjacent droplets and the surrounding viscous fluid induce local variations in the surface properties of the drops. These may result in a self-induced surface flow and a subsequent motion of the droplets toward or away from each other. Previous studies of this spontaneous thermocapillary interaction were conducted under the limiting assumptions that inertia, convective effects, and interfacial deformation were negligible. In the present paper the effect of convective transport on the spontaneous interaction of droplets at small nonzero Peclet numbers is examined. It is shown that at large separation distances the motion maintains its quasi-steady nature and the correction to the approach velocity is of O(Pe). When the droplets are at closer proximity the temporal changes of the domain are dominant. They result in the appearance of a Basset type history term in the expansion of concentration field and, hence, in the force balance equation. The correction to the approach velocity is of O(Pe1/2) and it depends on the initial position and the evolution in time of the interaction process.