Effect of surface-active contaminants on radial thermocapillary flows

TL;DR

This paper investigates how insoluble surfactants influence thermocapillary flows at liquid-air interfaces, revealing how surfactant distribution and flow patterns are affected by elasticity and diffusion in different regimes.

Contribution

It introduces a model for surfactant effects on thermocapillary flows, highlighting the impact of interfacial elasticity and diffusion on flow behavior and surfactant distribution.

Findings

Surfactants cause in-plane elastic effects altering flow patterns.

Depletion regions of surfactants are inversely related to interfacial elasticity.

Diffusion smooths out singularities in surfactant concentration and velocity fields.

Abstract

We study the thermocapillary creeping flow induced by a thermal gradient at the liquid-air interface in the presence of insoluble surfactants (impurities). Convective sweeping of the surfactants causes density inhomogeneities that confers in-plane elastic features to the interface. This mechanism is discussed for radially symmetric temperature fields, in both the deep and shallow water regimes. When mass transport is controlled by convection, it is found that surfactants are depleted from a region whose size is inversely proportional to the interfacial elasticity. Both the concentration and the velocity fields follow power laws at the border of the depleted region. Finally, it is shown that this singular behavior is smeared out when molecular diffusion is accounted for.