Dynamics of ensemble of gas bubbles with account of the Laplace pressure on the nucleation stage at degassing in a gas-liqiud mixture

Kuchma, A. E.; Щекин, А. К.; Martyukova, D. S.; Савин, А. В.

doi:10.1016/j.fluid.2017.09.022

Cited by 12 publications

(6 citation statements)

References 24 publications

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“…They were based either on highly simplified mathematical models 12,13 , or on a fairly complete system of classical equations as applied to the problem under consideration, solved numerically [14][15][16][17][18] . Similar studies can be found for gas bubbles [19][20][21][22][23][24] with the only difference that the mass transfer processes are the governing ones instead of the heat transfer processes.…”

supporting

confidence: 75%

New semi-analytical solution of the problem of vapor bubble growth in superheated liquid

Chernov

Pil’nik

Vladyko

et al. 2020

Sci Rep

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This paper presents a mathematical model of the vapor bubble growth in an initially uniformly superheated liquid. This model takes into account simultaneously the dynamic and thermal effects and includes the well-known classical equations: the Rayleigh equation and the heat conductivity equation, written with consideration of specifics associated with the process of liquid evaporation. We have obtained a semi-analytical solution to the problem, which consists in reducing the initial boundary value problem with a moving boundary to a system of ordinary differential equations of the first order, valid in a wide range of operating parameters of the process at all its stages: from inertial to thermal, including the transitional one. It is shown that at large times this solution is consistent with the known solutions of other authors obtained in the framework of the energy thermal model, in particular, for the high Jacob numbers, it is consistent with the Plesset–Zwick solution.

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supporting

confidence: 75%

New semi-analytical solution of the problem of vapor bubble growth in superheated liquid

Chernov

Pil’nik

Vladyko

et al. 2020

Sci Rep

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“…According to Refs. [17][18][19][20]29], it is convenient to introduce the volume V ex (R), which is excluded for nucleation around the selected growing overcritical bubble with radius R(t) by the integral relation:…”

Section: Excluded Volume For a Single Growing Overcritical Bubblementioning

confidence: 99%

“…Figure 1 illustrates the physical meaning of the quantities ex V and q. As is generally known [17][18][19][20], the ratio As is generally known [17][18][19][20], the ratio I(ρ, R)/I 0 can be expressed through the decline ϕ(ρ, R) as I(ρ, R)/I 0 = e −Γϕ(ρ,R) , where Γ ≡ −ζ 0 (∂∆F c /∂ζ 0 ) and ∆F c is the activation barrier for formation of the critical gas bubble. With the help of Equation (10), we can represent ratio q as…”

Section: Excluded Volume For a Single Growing Overcritical Bubblementioning

confidence: 99%

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The Effects of Viscosity and Capillarity on Nonequilibrium Distribution of Gas Bubbles in Swelling Liquid–Gas Solution

Щекин

Kuchma

Aksenova

2023

Colloids and Interfaces

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A detailed statistical description of the evolution of supersaturated-by-gas solution at degassing has been presented on the basis of finding the time-dependent distribution in radii of overcritical gas bubbles. The influence of solution viscosity and capillarity via internal pressure in the bubbles on this distribution has been considered until the moment when the gas supersaturation drops due to depletion and stops nucleation of new overcritical gas bubbles. This study aims to find the nonstationary growth rate of overcritical bubbles depending on gas supersaturation, diffusivity and solubility in solution, solution viscosity, and surface tension on bubble surface. Other important factors are linked with the initial rate of homogeneous gas bubble nucleation and coupling between diffusivity and viscosity in the solution. Here, we numerically studied how all these factors affect the time-dependent distribution function of overcritical bubbles in their radii, maximal and mean bubble radii, and the time-dependent swelling ratio of a supersaturated-by-gas solution in a wide range of solution viscosities.

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“…Binary nucleation covers a wide class of processes of phase transformations which can be divided into three groups: (i) gas-liquid (or solid) transformations, (ii) liquid-gas transformations, and (iii) transformations within a condensed state. The first group includes the binary droplet nucleation in a mixture of vapors of two substances [1][2][3][4], whereas the second group involves the bubble nucleation in binary fluids [5][6][7]. The third group includes liquid-liquid (LL), solid-solid (SS), and liquid-solid (LS) transformations.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics and kinetics of nucleation in binary solutions

Alekseechkin

2019

Chemical Physics

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A new approach that is a combination of classical thermodynamics and macroscopic kinetics is offered for studying the nucleation kinetics in condensed binary solutions. The theory covers the separation of liquid and solid solutions proceeding along the nucleation mechanism, as well as liquid-solid transformations, e.g., the crystallization of molten alloys. The cases of nucleation of both unary and binary precipitates are considered. Equations of equilibrium for a critical nucleus are derived and then employed in the macroscopic equations of nucleus growth; the steady state nucleation rate is calculated with the use of these equations. The present approach can be applied to the general case of non-ideal solution; the calculations are performed on the model of regular solution within the classical nucleation theory (CNT) approximation implying the bulk properties of a nucleus and constant surface tension. The way of extending the theory beyond the CNT approximation is shown in the framework of the finitethickness layer method. From equations of equilibrium of a surface layer with coexisting bulk phases, equations for adsorption and the dependences of surface tension on temperature, radius, and composition are derived. Surface effects on the thermodynamics and kinetics of nucleation are discussed.

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Dynamics of ensemble of gas bubbles with account of the Laplace pressure on the nucleation stage at degassing in a gas-liqiud mixture

Cited by 12 publications

References 24 publications

New semi-analytical solution of the problem of vapor bubble growth in superheated liquid

New semi-analytical solution of the problem of vapor bubble growth in superheated liquid

The Effects of Viscosity and Capillarity on Nonequilibrium Distribution of Gas Bubbles in Swelling Liquid–Gas Solution

Thermodynamics and kinetics of nucleation in binary solutions

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