Diffusion-controlled growth of multi-component gas bubbles

Cable, M.; Frade, J.R.

doi:10.1007/bf01103530

Cited by 32 publications

(19 citation statements)

References 10 publications

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“…The above system of equations comprises a closed problem which must be solved for the evolution of R. The problem of instantaneous decompression (step pressure reduction) leads to an autonomous problem for which an analytical solution exists (the so called self similar solution) for growth from zero initial radius [10,15]. In the present case where the pressure reduction is a function of time a numerical solution is necessary.…”

Section: Formulation Of 1-d Radial Symmetric Model For Isothermal Bubmentioning

confidence: 99%

Analysis of bubble growth on a hot plate during decompression in microgravity

Kostoglou

Karapantsios

Colin

et al. 2016

International Journal of Thermal Sciences

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The focus of the present work is the modeling of bubble growth on a hot plate during decompression (depressurization) of a volatile liquid at temperatures close to saturation and in the presence of dissolved gas. In particular, this work presents an organized attempt to analyze data obtained from an experiment under microgravity conditions. In this respect, a bubble growth mathematical model is developed and solved at three stages, all realistic under certain conditions but of increasing physical and mathematical complexity: At the first stage, the temperature variation both in time and space is ignored leading to a new semi analytical solution for the bubble growth problem. At the second stage, the assumption of spatial uniformity of temperature is relaxed and instead a steady linear temperature profile is assumed in the liquid surrounding the bubble from base to apex. The semi analytical solution is extended to account for the two dimensionality of the problem. As the predictions of the above models are not in agreement with the experimental data, at the third stage an inverse heat transfer problem is set up. The third stage model considers an arbitrary average bubble temperature time profile and it is solved numerically using a specifically designed numerical technique. The unknown bubble temperature temporal profile is estimated by matching theoretical and experimental bubble growth curves. A discussion follows on the physical mechanisms that may explain the evolution of the average bubble temperature in time.

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Section: Formulation Of 1-d Radial Symmetric Model For Isothermal Bubmentioning

confidence: 99%

Analysis of bubble growth on a hot plate during decompression in microgravity

Kostoglou

Karapantsios

Colin

et al. 2016

International Journal of Thermal Sciences

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“…As a result, the bubble grows under constant temperature and composition and its radius increases with the square root of time. Self-similar solutions have been reported for vapor bubble growth in a binary liquid (Scriven, 1959), multicomponent gas bubble growth (Cable and Frade, 1987a) and gas bubble growth with concentration-dependent diffusivity (Lastochkin and Favelukis, 1998). All these cases correspond to a single growth mechanism, either heat or mass transfer.…”

Section: Introductionmentioning

confidence: 96%

Self-similar growth of a gas bubble induced by localized heating: the effect of temperature-dependent transport properties

Divinis¹,

Kostoglou²,

Karapantsios³

et al. 2005

Chemical Engineering Science

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“…However, Ramos [15] reported a small effect of surface tension on bubble growth. Cable and Frade [16] neglected the effect of the surface tension initially. They solved the problem numerically for the arbitrary (but large enough to neglect Laplace pressure) initial radius and also presented an analytical description of the growth from the zero initial radius.…”

Section: Introductionmentioning

confidence: 99%

Steady-state composition of a two-component gas bubble growing in a liquid solution: Self-similar approach

Gor

Kuchma

2009

The Journal of Chemical Physics

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The paper presents an analytical description of the growth of a two-component bubble in a binary liquid-gas solution. We obtain asymptotic self-similar time dependence of the bubble radius and analytical expressions for the nonsteady profiles of dissolved gases around the bubble. We show that the necessary condition for the self-similar regime of bubble growth is the constant, steady-state composition of the bubble. The equation for the steady-state composition is obtained. We reveal the dependence of the steady-state composition on the solubility laws of the bubble components. Besides, the universal, independent from the solubility laws, expressions for the steady-state composition are obtained for the case of strong supersaturations, which are typical for the homogeneous nucleation of a bubble.

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Diffusion-controlled growth of multi-component gas bubbles

Cited by 32 publications

References 10 publications

Analysis of bubble growth on a hot plate during decompression in microgravity

Analysis of bubble growth on a hot plate during decompression in microgravity

Self-similar growth of a gas bubble induced by localized heating: the effect of temperature-dependent transport properties

Steady-state composition of a two-component gas bubble growing in a liquid solution: Self-similar approach

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