Blockage of thermocapillary flows by surface-active impurities

TL;DR

This paper develops a theoretical framework to quantify how surface-active impurities at the water-air interface hinder thermocapillary flows, with strong agreement between predictions and experiments, providing insights into interface contamination effects.

Contribution

It introduces a linearized model accounting for insoluble surfactants at the water-air interface, quantifying their impact on thermocapillary convection.

Findings

Surfactant concentration adapts to thermocapillary forcing to cancel viscous stress.

Model predictions agree quantitatively with experimental data.

Framework allows estimation of impurity concentration from flow measurements.

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.