Surface tension can markedly affect the growth or dissolution of small gas bubbles but, even when spherical symmetry is maintained and the interfacial concentration assumed constant, generally valid analytical solutions for the change of size with time cannot be obtained; approximations of limited validity are therefore often used. However, accurate and efficient methods for computing the diffusion-controlled growth or dissolution of spheres in such conditions have recently been developed; the results obtained when interfacial solute concentration is assumed constant have been published and validated by comparing them, where possible, with the equivalent analytical solutions. This paper extends that work to include the effects of a constant surface tension, for both Henry’s and Sievert’s laws. The numerical results are valid for as wide a range of parameters as is likely to be needed and are compared with the few analytical solutions available for particular cases. It is shown that, when surface tension is introduced, a complete description of the problem requires an additional saturation parameter as well as the dimensionless surface tension. It is also shown that Henry’s and Sievert’s laws can have very different effects on dissolving bubbles: when Sievert’s law applies a higher surface tension can increase time for a bubble to dissolve but this paradox can be resolved by examining the competing effects involved.

The equations properly describing the diffusion-controlled reaction of a spherical particle to form a concentric spherical shell of product are set up then solved numerically and their predictions compared with those of the commonly used approximate models due to Jander, Ginstling and Brounshtein, and Valensi or Carter. It is shown that the quasi-steady-state Ginstling and Brounshtein model correctly describes the kinetics of the process when the solute is of low solubility but becomes increasingly inaccurate as solubility increases; the Jander model gives almost identical predictions up to about 60% degree of conversion. There is thus a range of problems of practical interest for which either the Jander or Ginstling and Brounshtein model gives an acceptable description of the shape of at least the early stages of the degree of reaction versus time curve, but these simple models do not then give the correct values of, for example, diffusivity from such curve fitting. The simple models are nevertheless suitable for determining whether a reaction is controlled by diffusion through the product layer or by reaction at the interface, provided that some important assumptions are satisfied. [

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This article reviews the progress in studies devoted to the understanding of glassmelting made since the foundation of The American Ceramic Society. After briefly considering some of the necessary preliminaries, the article briefly discusses studies in melting reactions, redox control, refining, homogenizing, volatilization, refractory corrosion, and flow in furnaces. Knowledge of all of these has advanced significantly in the period considered. However, although many aspects of glassmelting can be discussed on a reasonably sound theoretical foundation, the actual behavior of real, multicomponent systems can be predicted only rarely with confidence from the generally available data base. Computers now make it possible to store much more data than ever before and to analyze information in much more sophisticated ways. Nevertheless, there is often a need to continue carefully conducted basic work. The article concentrates on the older work not readily recovered by computer database searches.

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