Droplet vaporization at critical conditions: Long-time convective-diffusive profiles along the critical isobar

The heating of a cold fluid package introduced, at critical conditions, in a hotter environment of the same fluid at the critical pressure is analyzed. Critical anomalies of the fluid transport properties as well as an arbitrary equation of state are taken into account. In unconfined microgravity conditions and for times much longer than the characteristic acoustic time, the heat transfer becomes a convective-diffusive isobaric transient process. An asymptotic theory valid in the limit of very small ratio between the fluid densities in the hot and cold regions is developed. The divergency of the thermal conductivity $\kappa$ at the critical temperature controls the heat transfer to the cold region. In the present model it is shown that there exists a well defined border, denoted by $R\left(t\right),$ delimiting two distinguishable regions. The outer region extends from the far field down to $R\left(t\right)\mathrm{}$ where the critical temperature $T_c$ is reached. There, the temperature gradient vanishes due to the divergency of $\kappa .$ Thus, heat does not penetrate in the inner cold region where the temperature remains equal to $T_c.$ The heating of the initially cold fluid package takes place by the recession of the border $R\left(t\right).$ The model predicts a temperature profile in the outer region which is quasisteady in a reference system receding with $R\left(t\right).$ It is shown that $R^2\mathrm{}\left(t\right)\mathrm{}$ decreases linearly with time. The recession velocity and thus the vaporization time are obtained as a function of the geometry and of the far-field conditions. Furthermore, the restrictions imposed by the long-time isobaric hypothesis are analyzed.