Bubble growth rate

Table 6.6 also demonstrates extraordinarily high bubble growth rates of 94.63, 72.8 and 95.3pm/ms. For these three cases, the growth rates are two orders of magnitude higher than the other cases. The authors noted that it is unclear why the bubble growth rate for such cases is much higher than the other cases. 

Cole R, Shulman HL (1966) Bubble growth rates at high Jacob numbers Int J Heat Mass Transfer 9 1377-1390... 

Note that high superheats, large liquid thermal conductivities, low pressures, and low bubble frequencies, all of which are more typical of liquid metals, tend to give bubble dynamics that approach the inertia-controlled case as the bubble growth rates are high. On the other hand, low superheats, low conductivities, high... 

The method of Theofanous et al. (1969) should be the most accurate for predicting bubble growth rates in large volumes of liquid metals at uniform superheats, although there has been no experimental data against which to test it directly. 

Hsu and Graham (1961) took into consideration the bubble shape and incorporated the thermal boundary-layer thickness, 8, into their equation, thus making the bubble growth rate a function of 8. Han and Griffith (1965b) took an approach similar to that of Hsu and Graham with more elaboration, and dealt with the constant-wall-temperature case. Their equation is... 

Staniszewski (1959) conducted experiments on bubble departure sites for boiling water and alcohol under various pressures and found the bubble departure diameter to be linearly proportional to the bubble growth rate at the last stage. 

BankofT, S. G., and R. D. Mikesell, 1959, Bubble Growth Rates in Highly Subcooled Nucleate Boiling, Chem. Eng. Prog. Symp. Ser. 55(29) 95—102. (2)... 

Griffith, P., 1958, Bubble Growth Rates in Boiling, in Trans. ASME, J. Heat Transfer, 80, 721-727. (2) Griffith, P., 1964, Two-Phase Flow in Pipes, in Developments in Heat Transfer, MIT Press, Cambridge, MA. (3)... 

In reality, Eqs. (13) and (14) should be solved simultaneously with Eqs. (8) and (9), but no analytical solution is available. However, we can examine the asymptotic solutions to Eqs. (13) and (14) to determine the bubble growth rate when heat transfer limits the growth, i.e., when P r) — Pq and r Tb so no inertial effects are present. For this extreme,... 

Mass balance condition at the bubble-melt interface (to determine bubble growth rate da/df) ... 

Figure 4-29 Comparison of calculated bubble rise and growth in C02-based and N2-based beer. The saturation pressure is 2 bars for both cases. Due to low solubility of N2, its concentration is small compared to that of CO2 at the same pressure, leading to much smaller bubble growth rate and rising velocity. From Zhang and Xu (2008).

The relationship between v in Eq. (13.21) and the bubble growth rate in Eq. (13.22) can be obtained on the basis of continuity equation for spherical coordinates ... 

The particle velocity at the bubble interface r = R(t) is, which is he bubble growth rate. Using this boundary condition, from Eq. (13.27), we have... 

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]. 

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