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

Gor, Gennady Y.; Kuchma, A. E.

doi:10.1063/1.3276708

Cited by 11 publications

(5 citation statements)

References 27 publications

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“…At the equilibrium state, the bulk concentration ( C 0 ) is equal to the interfacial concentration ( C i ) . Substituting eq into eq , we can obtain the critical supersaturation requirement for the bubble nucleus in a supersaturated solution ζ = 2 σ P 0 R b which can also be expressed as C 0 − C sat = 2 σ C sat P 0 R b = 2 σ k H R normalb …”

Section: Model and Methodsmentioning

confidence: 99%

“…According to eqs 8 and 10, the concentration of dissolved gas adjacent to the bubble−liquid interface C i can be expressed as At the equilibrium state, the bulk concentration (C 0 ) is equal to the interfacial concentration (C i ). 29 Substituting eq 11 into eq 9, we can obtain the critical supersaturation requirement for the bubble nucleus in a supersaturated solution 21 = P R…”

Section: ■ Model and Methodsmentioning

confidence: 99%

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Size Ranges of Effective Nucleation Cavities on Gas-Evolving Surfaces

Zhao,

Zhang,

Gong

2023

Langmuir

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Bubble nucleation has a significant influence on mass transfer and energy conversion in electrochemical gas-evolving reactions. In this work, we establish a theoretical model for bubble nucleation from gas cavities on gas-evolving surfaces. Based on analyses of transient gas diffusion within the concentration boundary layer and supersaturation equation for stable bubble nuclei, we determined the size ranges of effective nucleation cavities on gas-evolving surfaces under different levels of supersaturation conditions. In addition, a criterion for the incipience of bubble nucleation on gasevolving surfaces is proposed. We investigate the effects of the contact angle, cone angle, concentration boundary layer thickness, ambient pressure, and temperature on the size ranges of effective nucleation cavities, respectively. We demonstrate that a larger contact angle or a smaller cone angle can broaden the size range of effective cavities, thereby promoting bubble nucleation from cavities. We also show that increasing the concentration boundary layer thickness causes larger cavities to become effective nucleation sites, which significantly expands the size range of effective cavities. In contrast, increasing the ambient pressure enables smaller cavities to become effective nucleation sites, resulting in an expansion in the size range of effective cavities. Results of this work will contribute to the manipulation of bubble nucleation densities and the optimal design of gas-evolving electrodes in various electrochemical gas-evolving reactions.

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Section: Model and Methodsmentioning

confidence: 99%

Section: ■ Model and Methodsmentioning

confidence: 99%

Size Ranges of Effective Nucleation Cavities on Gas-Evolving Surfaces

Zhao,

Zhang,

Gong

2023

Langmuir

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“…Various effects of non stationary growth of single and multicomponent droplets and bubbles were studied in [7][8][9][10][11][12][13][14][15][16]. In this study, we will focus on description of the nonstationary diffusion growth of a substantially supercritical droplet (i.e., a droplet for which the saturation vapor pressure can be taken equal to the pressure over a planar surface of the liquid) in a vapor-gas medium with allowance for the Stefan flux of the vapor-gas medium toward the condensing droplet, the motion of the surface of the growing droplet, and the concentration depen dence of the diffusion coefficient of the condensing vapor in the medium.…”

Section: Introductionmentioning

confidence: 99%

A self-similar regime of droplet growth with allowance for the Stefan flux and dependence of diffusion coefficient on vapor-gas medium composition

Kuchma

Щекин

2012

Colloid J

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An analytical self similar description is formulated for the problem of nonstationary diffusion droplet growth in a vapor-gas medium with allowance for the Stefan flux of the medium, themotion of the surface of a growing droplet, and an arbitrary concentration dependence of the diffusion coefficient of a con densing vapor in the medium. Analytical expressions are found for the diffusion profile of condensing vapor concentration and for the droplet growth rate at a constant diffusion coefficient of the vapor and at a coeffi cient linearly dependent on vapor concentration. The combined allowance for the Stefan flux of the medium, the motion of the surface of the growing droplet, and the dependence of the vapor diffusion coefficient in the medium on the vapor concentration is shown to result in renormalization of the rate of droplet growth related to the stationary diffusion regime. At small deviations from the stationarity, the Stefan flux, nonstationary dif fusion, and dependence of the diffusion coefficient on the vapor-gas mixture composition lead to corrections of the same order of magnitude.

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“…In particular, it was reported in [15,16] that large enough bubbles reach a state of stationary growth with fixed composition and growth rate and may demonstrate a nonmonotonic change in their radius during the initial stage of their evolution. Formulation of the theory of non-stationary self-similar growth of a binary bubble with stationary composition in the case of high supersaturation had been done by Gor and Kuchma [17].…”

Section: Introductionmentioning

confidence: 99%

Evolution of size and composition of a multicomponent gas bubble in liquid solution

Kuchma¹,

Щекин²

2015

Nanosist.: fiz. him. mat.

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The equations describing the transient and steady stages of size and composition evolution for a gas bubble which grows or shrinks due to the diffusion of several gases dissolved in liquid solution have been derived. The diffusion fluxes for gases in the liquid mixture caused by the bubble growth or dissolution were assumed to be quasistationary and the mixture of the gases in the bubble was treated as ideal. The analytical solutions for the obtained evolution equations have been found for bubbles of any size with an arbitrary number of components in the case of equal products of diffusivities and solubilities of dissolved gases in the liquid solution, and for sufficiently large binary bubbles for which capillary effects can be neglected.

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

Cited by 11 publications

References 27 publications

Size Ranges of Effective Nucleation Cavities on Gas-Evolving Surfaces

Size Ranges of Effective Nucleation Cavities on Gas-Evolving Surfaces

A self-similar regime of droplet growth with allowance for the Stefan flux and dependence of diffusion coefficient on vapor-gas medium composition

Evolution of size and composition of a multicomponent gas bubble in liquid solution

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