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 vi scous 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 spon taneous thermocapillary interaction were conducted under the limiting assum ptions that inertia, convective effects, and interfacial deformation were n egligible. In the present paper the effect of convective transport on the s pontaneous interaction of droplets at small nonzero Peclet numbers is exami ned. It is shown that at large separation distances the motion maintains it s quasi-steady nature and the correction to the approach velocity is of O(P e). When the droplets are at closer proximity the temporal changes of the d omain are dominant. They result in the appearance of a Basset type history term in the expansion of concentration field and, hence, in the farce balan ce equation. The correction to the approach velocity is of O(Pe(1/2)) and i t depends on the initial position and the evolution in time of the interact ion process. (C) 1999 American Institute of Physics. [S1070-6631(99)04206-3 ].