Effect of surface-active contaminants on radial thermocapillary flows

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.

References in corpus (3)

• Thermally driven Marangoni surfers
• Migration of a surfactant-laden droplet in non-isothermal Poiseuille flow
• Thermocapillary flows and interface deformations produced by localized laser heating in confined environment

Cited by in corpus (7)

• Microscale Marangoni Surfers
• Azimuthal instability of the radial thermocapillary flow around a hot bead trapped at the water-air interface
• Competition between thermocapillary and solutocapillary flows in thin liquid films
• Surfactant-driven instability of a divergent flow
• Blockage of thermocapillary flows by surface-active impurities
• Stokes equation in a semi-infinite region: generalization of Lamb solution and applications to Marangoni flows
• Exact solutions for viscous Marangoni spreading