(316j) Thermocapillary Induced Motion of a Drop with Simultaneous Effect of Surface Viscosity

Surface viscosity may arise when surface active substances are absorbed on the interface separating immiscible fluid phases. The idea that surface viscosity may retards the motion of drops of various sizes was introduced by Boussinesq in 1913, and it was later followed by an invariant formulation for the surface stress balance by Scriven in 1960. This formulation facilitated the development of several methods to measure the surface viscosity as well as a few analytic studies such as, e.g., by Levan in 1980. In this work we present a study of the thermocapillary induced motion of a droplet in a viscous fluid under the additional effect of surface viscosity. In this study the surface tension and the surface viscosity depend on the thermodynamic state variables, such as temperature or concentration of the absorbed species, and they vary along the surface. When deformation and convective effects are neglected it was found that, for drop size in microns scale, the Marangoni effect is stronger than the surface viscosity effect. However, when the scale is submicron the surface viscosity effect becomes increasingly significant. We have also studies the effect of convection when the Peclet number is small. The magnitude of this effect can vary. It is shown that, if the source of active substance or heat driving the flow is steady with time the convective effect is small, of O(Pe). However, when the source is time dependent the leading order correction is enhanced and become of O(Pe1/2).