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.
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