Effects of incompressible surfactant on thermocapillary interactions of spherical drops

Collision efficiencies are determined for two surfactant-covered spherical drops in the limit of nearly uniform surface coverage in thermocapillary motion. The problem is linearized by assuming dilute surfactant concentration, with the effect of surfactant controlled by a single retardation parameter A. The mobility function L A along the drops’ line of centers is much less than zero over a wide range of parameters, so that the smaller drop can move faster than the larger one at moderate to large separations. At surface Péclet numbers less than 10, the incompressible surfactant model agrees well with solution of the full convective-diffusion equation for the minimum separation between drops. With the exception of non-conducting drops, the collision efficiencies become zero at moderate values of A. A model system of contaminated ethyl salicylate (ES) drops in diethylene glycol (DEG) is studied in thermocapillary motion. Population dynamics simulations confirm the coalescence-inhibiting effect of incompressible surfactant on the evolution of the ES/DEG drop-size distribution.