On hydrothermal waves observed during evaporation of sessile droplets

Pattern formation driven by the spontaneous evaporation of sessile drops of methanol, ethanol, and FC-72 using infrared thermography have been recently observed and, interpreted in terms of hydrothermal waves. New results are presented showing the influence of the temperature and the thermal conductivity of the substrate on the number of waves observed at the free surface of evaporating pinned droplets. Another correlation shows the influence of the liquid volatility on the number of waves. Additional experimental data are presented in this paper that corroborates the original findings as well as the interpretation given of the phenomenon. The experimental data seem to reveal the presence of travelling waves that could be the result of a surface oscillatory instability. To rationalize these results, from the theoretical perspective, a three-dimensional stability analysis in spherical coordinates is required that defines new scaling factors and dimensionless numbers in order to take account of the thermal diffusivity in the substrate as well as the evaporation rate. A formulation of the problem described above is attempted including the appropriate scaling and relevant dimensionless numbers. The Marangoni number deduced from the scaling of the problem is found to be function of the Evaporation number. This latter is in turn function of position, time as well as the nature of system studied. A parametric analysis allowed the deduction of analysis of the form of the solutions giving rise to the experimentally observed waves. This theoretical analysis represents a first step toward a further more complete description of experimental observations.