_{1}

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The phase transitions and the effect on this process of two factors: relative motion and the external influence of the carrier flow (pressure perturbation) are investigated. A mathematical model describing all the stages of the phenomenon is constructed. The model includes mass, momentum and energy balance equations (both for the vapor and for the liquid) or their first integrals.

The study of the dynamics and heat and mass city transfer of an individual bubble is of independent interests and, at the same time, one of the steps in the investigations of bubbly mixtures [

The corresponding spherically symmetric problem is studied in [

We assume that the bubble always preserves a spherical shape. For estimating the validity of this assumption, it is possible to employ the Weber number test [

We assume that the flow is potential and that there is no boundary layer separation. In [

In this formulation the momentum equation for the liquid has as its first integral a Gauchy-Lagrange integral. With allowance for the balance conditions imposed on the mass and momentum at the bubble surface, this integral can be written in the form of Rayleigh-Pleset equation [

We assume that all the thermophysical parameters of the vapor in the bubble depend only on time. If the specific heat of the liquid and its thermal conductivity are assumed to be constant, the energy equation for the liquid can be written in terms of the temperature. The local heat fluxes vary with the angle; as a result, at the surface of the bubble the evaporation (condensation) rate has different values depending on the angle. In the framework of quasi-equilibrium phase transition scheme the phase transition rate can be determined from the condition of energy balance at the bubble surface.

The system loses equilibrium as a result of a change in the pressure in the liquid at infinity. In relation to these processes it is possible to distinguish two stages in the variation of the bubble radius [

It is shown that the investigated process has seven similarity criteria, each of which plays definite role. The Peclet number (together with the Jacob number) is the principal dimensionless number. The value Pe = 0 corresponds to the case in which there is no flow over the bubble. Then the system of basic equations corresponds to the formulation problem of the spherically symmetric oscillations a vapor bubble [

The system of basic equations contains one nondimensional non-steady equation and four ordinary differential equations. For numerically solving heat transfer equation we used the method of alternating interaction proposed in [

In order to test the correctness of the model we compared the results with the experimental data. In the experiments the following phenomenon was investigated [

In

In

The temperature distribution in the liquid near the bubble at the moment at which the bubble radius reaches a local maximum is shown in

the radius either cease completely or decrease considerably in amplitude, i.e. after the dynamic stage. The assumption that the pressure in the bubble adjusts itself instantaneously to the pressure in the liquid at infinity turns out to be inaccurate (see

The effect of translatory motion on the dynamics of radial oscillations and heat and mass transfer of vapor bubble was investigated. Earlier this problem was studied with many simplifications particularly that translatory motion of bubble is constant. Results of numerical investigation of this problem are presented. The results obtained agree well with experimental data. In future studies would be interesting to study dynamics of vapor-gas bubbles with diffusion in gaseous and liquid phases.

Earlier similar problem was studied in [

The latest detailed review devoted to dynamics of vapor bubbles was done in [

The author declares no conflicts of interest regarding the publication of this paper.

Khabeev, N.S. (2019) Effect of Translatory Motion on Dynamics Heat and Mass Transfer of Vapor Bubble Radially Oscillating in a Liquid. Journal of Applied Mathematics and Physics, 7, 942-947. https://doi.org/10.4236/jamp.2019.74063

R-bubble radius, m

r-radius coordinate, m

τ-nondimensional time