Boiling‐Up Kinetics of Solutions of Cryogenic Liquids

Abstract

A kinetic theory of the process of boiling-up of superheated binary solutions is developed. In the framework of the Kramers-Zeldovich method, describing nucleation as a process of Brownian motion of the nucleus in the field of thermodynamic forces, an equation for the steady-state nucleation rate is derived. In the analysis of this kinetic problem, the whole spectrum of possible factors is included, which may limit the growth of the nucleus: the volatility of the solution, viscosity and inertia effects in the motion of the liquid, diffusion, and thermal conduction effects at the phase boundaries. For the determination of the work of critical cluster formation, the van der Waals theory of capillarity is utilized. This theory allows an account of the dependence of the properties of critical clusters on cluster size. The results of experiments on nucleation (the determination of the mean lifetimes of the solutions and the steady-state nucleation rates) in metastable solutions with full (Ar-Kr) and partial (He-O 2 ) solubility are given in dependence on temperature, pressure, and composition of the solutions. The results of the experiments are compared with the theoretical predictions. It is shown that a good agreement between experimental and theoretical results is reached when the curvature corrections to the surface tension, calculated via the van der Waals approach, are taken into account. IntroductionA first-order phase transition presupposes the existence of metastable states. It proceeds frequently via the formation and subsequent growth of critical nuclei of a new phase. In pure systems, in the absence of external factors initiating a phase transition, nuclei form via spontaneous fluctuations (homogeneous nucleation). The emergence of a new-phase fragment in a homogeneous metastable system is connected with the formation of a phase boundary and accompanied by an increase in the excess free energy . The competition of the surface and volume terms, entering the expression for the free energy with opposite signs, results in the existence of a finite maximum = W * . The fragments corresponding to the maximum of are called critical nuclei, and the quantity W * is the work of their formation. At each moment of time, the overwhelming majority of fragments has precritical sizes R < R * . Their existence is unfavorable from a thermodynamic point of view and they dissolve as a rule. However, due to fluctuations some of the fragments may grow up to sizes exceeding the critical one and then their further growth is thermodynamically irreversible.The discussed concepts form the basis of the classical nucleation theory formulated among others by Volmer [1], Döring [2], Zeldovich [3], and Frenkel [4]. For one-component systems, Nucleation Theory and Applications. edited by J. W. P. Schmelzer