Effect of surfactants on the thermocapillary migration of a concentric compound drop

The quasi-steady thermocapillary motion of a concentric compound drop in the presence of an insoluble surfactant and an externally imposed constant temperature gradient is examined under conditions of negligible convective transport of momentum and energy. Surface tension is assumed to depend much more weakly on surfactant concentration than on temperature. For this case, the surface concentrations of surfactant are found exactly for all Peclet numbers, confirming the intuitively expected result that the surfactant tends to accumulate near the low temperature sides of the inner and outer drops. This, in turn, results in a decrease in the terminal migration velocities of the drops. The effect of surfactant on the shape of the inner and outer drops is also determined for small capillary numbers.