Minimal heating rate for isobaric nucleation at the spinodal in liquids

A thermodynamic model is developed that resolves the minimal heating rate required for rapid isobaric nucleation at the spinodal limit for both homogenous and heterogenous nucleaiton. For heterogeneous nucleation, a semi-empirical correlation for the heterogeneity factor is developed. The question of how fast should isobaric heating be in order for Onset of Nucleate Boiling (ONB) to occur at spinodal conditions can be answered currently for 1 atmosphere. For water at 1 atmosphere, it was found that the minimal heating rate for heterogeneous nucleation is about 10⁹ K/s, which is consistent with the available experimental results. The proposed model, however, allows to answer this question for a wide rage of pressure values. The effects of pressure, initial temperature, transition time into the metastable zone and heterogeneity factor are explored. It was found that the minimal heating rate decreases with the decrease of the degree of superheating and the increase in the degree of subcooling. It follows that the minimal heating rate required for reaching the spinodal decreases with the increase of pressure. For heterogeneous nucleation as a result of wall heating, it decreases with the decrease in the initial temperature. An explicit, analytical function is offered to correlate the minimal heating rate for water to the degree of subcooling at various pressure values, up to P_r∼0.5.