Spontaneous boiling-up of gas-saturated liquids: Attainable superheating of ethane–helium and ethane–hydrogen solutions

Abstract

The fluctuation growth of a vapor-gas bubble is described as a diffusion process in the space of three variables: the bubble volume V and the partial pressures P1 and P2 of the mixture components in the bubble. The dynamics of the nucleus growth takes into account the viscosity, the solvent volatility and the diffusion supply of the substance dissolved. An equation has been obtained for nucleation rate J expressed as a function of temperature, pressure, and solution concentration. Nucleation in superheated ethane–helium and ethane–hydrogen solutions was studied by the lifetime measurement method. Temperature and pressure dependencies of the nucleation rate have been established at pressures p = 1.6 and 2.0 MPa in solutions containing up to 0.05 mol% of helium and up to 0.31 mol% of hydrogen. The range of nucleation rates studied was J = (2.3·106 – 1.4·108) m−3s−1. The experimental results were compared to classical nucleation theory (CNT). Similarly to pure ethane, there is systematic “underheating” of the solutions as compared to the temperatures predicted by the CNT. The discrepancy found between theory and experiment is explained by the size-dependence of the surface tension of critical bubbles. It is noted that although, unlike hydrogen, helium in ethane acts as a surface-inactive component, this does not lead to an excess of the attainable superheating temperature of the ethane–helium solution over the superheating temperature of the ethane–hydrogen solution.