  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.
