Convective bubble growth

Bubble size at departure. At departure from a heated surface, the bubble size may theoretically be obtained from a dynamic force balance on the bubble. This should include allowance for surface forces, buoyancy, liquid inertia due to bubble growth, viscous forces, and forces due to the liquid convection around the bubble. For a horizontally heated surface, the maximum static bubble size can be determined analytically as a function of contact angle, surface tension, and... 

For liquid metals the superiority of nucleate boiling heat transfer coefficients over those for forced-convection liquid-phase heat transfer is not as great as for ordinary liquids, primarily because the liquid-phase coefficients for liquid metals are already high, and the bubble growth period for liquid metals is a relatively short fraction of the total ebullition cycle compared with that for ordinary fluids. In the case of liquid metals, the initial shape of the bubbles is hemispheric, and it becomes spherical before leaving the heating surface. This is because of very rapid... 

Diffusion-Controlled Bubble Growth S. G. Bankoff Evaporative Convection... 

Diffusion-Controlled Bubble Growth S. G. Bankoff Evaporative Convection John C. Berg, Andreas Acrivos, and Michel Boudart... 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

This section follows Zhang and Xu (2008). In most liquids, a bubble rises rapidly under buoyancy, which induces forced convection. For rising bubbles, two factors cause the bubble to become larger mass increase in the bubble and the pressure decrease as the bubble rises. The second factor is significant only when rising distance is large (e.g., >10 m). For clarity of discussion, CO2 bubble growth in water is considered. The mass in the bubble increases as... 

Various mathematical models have been put forth to describe the rate of bubble growth and the threshold pressure for rectified diffusion.f ° The most widely used model quantifies the extent of rectified diffusion (i.e., the convection effect and bubble wall motion) by separately solving the equation of motion, the equation of state for the gas, and the diffusion equation. To further simplify the derivation, Crum and others made two assumptions 1) the amplitude of the pressure oscillation is small, i.e., the solution is restricted to small sinusoidal oscillations, and 2) the gas in the bubble remains isothermal throughout the oscillations.Given these assumptions, the wall motion of a bubble in an ultrasonic field with an angular frequency of co = 2nf can be described by the Rayleigh-Plesset equation ... 

The term (dV(x, t)/Adt) is really (c R(x. t)jdt) the bubble growth rate at r = R, but it is also interesting to obtain an equation for the electrolyte rate of micro-convection, that is, at a distance x(t) r R(t). These expressions were originally used considering the continuity equation for the heat transfer in nucleate boiling [76]. 

On the other hand, the change in the dissolved gas concentration is directly the value of the gradient at r = R, and the radial convective-diffusion toward the bulk of the electrolyte because of the bubble growth [80] ... 

W. Chen, R. Mei, and J. F. Klausner, Vapour Bubble Growth in Highly Subcooled Heterogeneous Boiling, in Convective Flow Boiling, J. C. Chen ed., pp. 91-98, Taylor Francis, Washington, DC, 1996. 

Bruijn (B24) employs the quasi-stationary approximation, as discussed in Bankoif (B8), to the growth of vapor bubbles in superheated binary liquid mixtures. As noted previously, this neglect of the convective term in the diffusion equation is justified only when Aj< l, which is usually not the case in atmospheric boiling. On the other hand, this technique would be applicable to isothermal gas bubble growth in three-component systems, where two of the components are dissolved gases. 

Flatt (F3) computes bubble growth rates due to radiolytic gas formation in a power excursion in a homogeneous reactor. For very small bubbles the growth is assumed to be quasi-stationary so that the convective term can be dropped from the diffusion equation. A distributed exponential volume source is assumed. An integral equation for the radius is then obtained, from which upper and lower bounds for the radius of the bubble can be deduced. 

In this expression for h2st the Nusselt number Nu is the greater of a sphere forced convection Nusselt ntimber or one derived from the Plesset-Zwick bubble growth formula ... 

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