Marangoni convection instability in a sessile droplet with low volatility on heated substrate

Abstract

In order to investigate Marangoni convection in a sessile droplet on heated substrate, a series of three-dimensional numerical simulations are carried out in a wide range of Marangoni number. A low volatile silicone oil is adopted and the effect of evaporation is neglected. Bénard-Marangoni convection and thermocapillary convection may coexist in droplet because of its curve surface. When Marangoni number is low the flow is steady axisymmetric thermocapillary convection whereas the flow becomes to be asymmetric and loses its stability and Hopf bifurcation occurs when Marangoni number high. The oscillatory transition convection, steady Bénard-Marangoni convection and irregular oscillatory Bénard-Marangoni convection appear in sequence with increasing Marangoni number. The characteristics of each kind of convection modes are described and the critical Marangoni numbers for the incipience of them are determined in a wide range of contact angles. One of the most interesting phenomenon is that the shape of the Bénard-Marangoni convection cell in sessile droplet is circular, which is different from that of classical hexagonal cell in flat layer. With increasing contact angle, the critical Marangoni number for the onset of convection instabilities first decreases and then increases. Critical cell number of the steady Bénard-Marangoni convection keeps on only one for contact angle less than 15° whereas it increases sharply after angle lager than 15°. The numerical results are qualitatively verified by experiment.