The growth rate of vapour bubbles in superheated pure liquids and binary mixtures: Part I: Theory

Abstract

A survey is given of the theories concerning spherically symmetric growth of free bubbles in initially uniformly superheated pure liquids. The physical basis of the Bos̆njaković model is developed from experiments by Jakob and Fritz, giving the temperature distribution in boiling liquids, and by Heidrich and Prüger, showing that thermodynamic equilibrium exists at the vapour-liquid interface during stationary evaporation of superheated liquids without ebullition. According to Forster and Zuber, and Plesset and Zwick, bubble growth in a superheated pure liquid following from Rayleigh's dynamic equation of isothermal motion [ R ≅ ( 2Δp 3p 1 ) 1 2t for an expanding spherical cavity with a constant excess pressure Δp]is slowed down by heat diffusion towards the bubble boundary to satisfy the latent heat requirement of evaporation. For asymptotic growth ( R p ≅ C 1,pΔθ ot 1 2 ), bubble dynamics and the influence of viscosity and surface tension are neglible since Δp → 0 as t → ∞ (isobaric growth). Thermodynamic equilibrium at the bubble boundary follows from the extended Rayleigh equation in accordance with Prüger's results. In superheated binary mixtures, bubble growth is further decreased due to the analogous mass diffusion of the more volatile component according to van Wijk, Vos and van Stralen, Scriven, Bruijn, van Stralen and Skinner and Bankoff. Van Stralen's modification shows the physical equivalence of the various theories. The dew temperature of the vapour is increased with an amount ΔT with respect to the boiling temperature of the original liquid. As a consequence, the occurrence of a minimal bubble growth rate (corresponding with a maximal ΔT G d ) is predicted at a certain low concentration of the more volatile component. This leads to the “broiling paradox”, which can be explained by van Stralen's “relaxation microlayer” theory.