Effect of thermal convection on frequency response of a perturbed vaporizing pastille-shaped droplet

Abstract

We study the dynamic response to small acoustic oscillations of a vaporizing droplet in shape of a pastille (a small liquid cylinder, called “pastille” in the sequel, the height of which being smaller than the radius of the base). Contrary to some previously proposed models, where the thermal convection effect inside the droplet is often neglected, the continuously fed pastille-shaped model takes into account the effects of both thermal convection and conduction. Curves related to different heat exchange coefficients are presented for the frequency response of the vaporization rate. The case where the feeding process at the bottom of the pastille is assumed isothermal (isothermal bottom regime) is compared to the one where the feeding process at the bottom of the pastille is adiabatic (adiabatic bottom regime). The response factor curves for the pure conduction model of the spherical droplet and for the present model of the “equivalent pastille” are also compared. The temperature field perturbation is then examined. As well as for the evaporation mass flow rate perturbation, comparisons are made between the regime with an isothermal bottom and the one with an adiabatic bottom. We find that, in spite of some divergences observed between the various cases, the frequency response of a droplet submitted to acoustic oscillations presents also some common points. It is shown that the life time (or residence time), the thermal diffusion time, and the period of the harmonic perturbation do intervene strongly in the behaviour of the vaporizing pastille. The liquid propulsion is a possible application of this basic study conducted as part of a thesis.