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 arbitr ary equation of state are taken into account. In unconfined microgravity co nditions and for times much longer than the characteristic acoustic time, t he heat transfer becomes a convective-diffusive isobaric transient process. An asymptotic theory valid in the limit of very small ratio between the fl uid densities in the hot and cold regions is developed. The divergency of t he thermal conductivity kappa at the critical temperature controls the heat transfer to the cold region. In the present model it is shown that there e xists a well defined border, denoted by R(t), delimiting two distinguishabl e regions. The outer region extends from the far field down to R(t) where t he critical temperature T-c is reached. There, the temperature gradient van ishes 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 o f the initially cold fluid package takes place by the recession of the bord er R(t). The model predicts a temperature profile in the outer region which is quasisteady in a reference system receding with R(t). It is shown that R-2(t) decreases linearly with time. The recession velocity and thus the va porization time are obtained as a function of the geometry and of the far-f ield conditions. Furthermore, the restrictions imposed by the long-time iso baric hypothesis are analyzed. [S1063-651X(99)01009-0].