Collective effects of temperature gradients and gravity on droplet coalescence
The interaction and coalescence of small spherical drops in dilute, homogeneous dispersions are considered theoretically under conditions, where drop motion results from gravity settling and thermocapillary migration acting simultaneously. A trajectory analysis is used to predict pairwise collision rates, and population dynamics equations are solved to predict the time evolution of the droplet size distribution. The rate of droplet collisions and growth may be reduced dramatically by antiparallel alignment of the gravitational and thermocapillary velocities. For such antiparallel alignment with the gravitational relative velocity exceeding the thermocapillary relative velocity for two widely separated drops, there is a 'collision-forbidden region' in parameter space. This occurs because the gravitational relative velocity decays more rapidly with decreasing separation distance between the drops than does the thermocapillary relative velocity, and so the resultant relative velocity along the line-of-centers from these two sources combined becomes zero at a finite separation and the drops are unable to collide. As a result, small drops which initially collide and coalesce due to thermocapillary motion will only grow until they reach a critical size for which the oppositely directed gravitational motion balances the thermocapillary motion.