Blockage of thermocapillary flows by surface-active impurities

Abstract

Thermocapillary convection is particularly effective for the control of thin liquid film topography or for the actuation of microparticles at the liquid-air interface. Experiments with water are challenging, however, as its interface is prone to contamination by surface-active impurities that profoundly alter its hydrodynamic response. Despite numerous reports highlighting the hindrance of thermocapillary flows, quantitative information on interface contamination is definitely lacking. We therefore introduce a general framework in order to account for the presence of a low concentration of insoluble surfactants at the water-air interface. Focusing on the low-compressibility limit, we identify the inverse Marangoni number as the appropriate small parameter in the modeling. The transport equations can then be linearized without any further assumption regarding the other dimensionless groups. It is shown in particular that the surfactant concentration adapts to the thermocapillary forcing in order to cancel the interfacial viscous stress. Several experimentally relevant situations are discussed with emphasis on physical observables. Besides the excellent agreement between theory and experiment, our predictions provide a quantitative assessment of the impurity concentration.

References in corpus (8)

• Azimuthal instability of the radial thermocapillary flow around a hot bead trapped at the water-air interface
• Effect of surface-active contaminants on radial thermocapillary flows
• Hydrodynamic response of a surfactant-laden interface to a radial flow
• Laminar drag reduction in surfactant-contaminated superhydrophobic channels
• Modification of the fluctuation dynamics of ultra-thin wetting films
• Surfactant-driven instability of a divergent flow
• Probing interfacial effects with thermocapillary flows
• Stokes equation in a semi-infinite region: generalization of Lamb solution and applications to Marangoni flows

Cited by in corpus (1)

• Competition between thermocapillary and solutocapillary flows in thin liquid films