Self-organised Marangoni motion at evaporating drops or in capillary menisci - thermohydrodynamical model

Thermocapillary convection has been observed both in capillaries and at the surface of evaporating sessile droplets. The present paper aims to give a model of the onset of these convective patterns. The model accounts for the self-induced surface gradient of temperature linked to the stronger mass transfer observed near the triple line region. The role of the apparent contact angle is also evidenced. Dimensionless quantities such as the Marangoni number and the partition coefficient are the key factors of the present analysis. The calculations show that for the same environmental conditions the convection can be influenced by the geometrical considerations. Indeed the calculated Marangoni numbers are found to be greater in the capillary than in the drop for a wetting contact angle of less than pi/4; for an angle greater than pi/4, the results are inverted.