Bubble boundary layer

J6. Jiji, L. M Incipient boiling and the bubble boundary layer formation over a heated plate for forced convection flow in a pressurized rectangular channel, Ph.D. Thesis, Univ. of Michigan, Ann Arbor, 1962. 

In the bulk boiling section, which appears when the bubble boundary layers have developed so as to fill the core and all of the liquid has reached saturation, there are two important flow patterns bubbly flow and annular flow. In bubbly flow, the bubbles are evenly distributed in the saturated liquid. The superheated... 

Figure 3.18 A typical photograph defining the bubble boundary layer (pi - 500 psia, Vi - 1 ft/sec. 7 a, - 7] = 200°F, q/A = 0.804 x 10f) Btu/hr ft2). (From Jiji and Clark, 1964. Copyright 1964 by American Society of Mechanical Engineers, New York. Reprinted with permission.)...

Brown (1967) noted that a vapor bubble in a temperature gradient is subjected to a variation of surface tension which tends to move the interfacial liquid film. This motion, in turn, drags with it adjacent warm liquid so as to produce a net flow around the bubble from the hot to the cold region, which is released as a jet in the wake of the bubble (Fig. 4.10). Brown suggested that this mechanism, called thermocapillarity, can transfer a considerable fraction of the heat flux, and it appears to explain a number of observations about the bubble boundary layer, including the fact that the mean temperature in the boundary layer is lower than saturation (Jiji and Clark, 1964). 

Jiji, L. M.,andJ. A. Clark, 1964, Bubble Boundary Layer and Temperature Profiles for Forced Convection Boiling in Channel Flow, Trans. ASME, J. Heat Transfer 56 50 58. (4)... 

Studying the steady motion of a single medium-size bubble rising in a liquid medium under the influence of gravity, Levich (L3, L4) solved the continuity equation simultaneously with the equations of motion by introducing the concept of a boundary layer for the case of a bubble. This boundary layer accounts for the zero, or extremely low, shear stress at the interface. Despite some errors in deriving the equations, his result was later confirmed with minor improvements (A4, M3, M10). 

Assuming that the velocity distribution for flow past a gas bubble differs relatively little from the velocity distribution in an ideal liquid, and neglecting the curvature of the boundary layer, Levich finds that... 

The value of E is insensitive to small changes in ocean temperature but is quite sensitive to wind speed over the sea surface (boundary layer thickness, wave action, and bubble formation are functions of wind speed). Therefore changes in surface wind speed accompanying a climate change could affect rates of air-sea CO2 exchange. 

The main part of the report describes the results of systematic investigations into the hydrodynamic stress on particles in stirred tanks, reactors with dominating boundary-layer flow, shake flasks, viscosimeters, bubble columns and gas-operated loop reactors. These results for model and biological particle systems permit fundamental conclusions on particle stress and the dimensions and selection of suitable bioreactors according to the criterion of particle stress. 

Much higher shear forces than in stirred vessels can arise if the particles move into the gas-liquid boundary layer. For the roughly estimation of stress in bubble columns the Eq. (29) with the compression power, Eq. (10), can be used. The constant G is dependent on the particle system. The comparison of results of bubble columns with those from stirred vessel leads to G = > 1.35 for the floccular particle systems (see Sect. 6.3.6, Fig. 17) and for a water/kerosene emulsion (see Yoshida and Yamada [73]) to G =2.3. The value for the floe system was found mainly for hole gas distributors with hole diameters of dL = 0.2-2 mm, opening area AJA = dJ DY = (0.9... 80) 10 and filled heights of H = 0.4-2.1 m (see Fig. 15). 

On the other hand animal cells are especially sensitive as regards sparging. Obviously the cells are adsorbed at the gas liquid boundary layer and subjected to the most stress in the region of bubble formation at the sparger and bubble bursting at the liquid surface. 

For reactors with free turbulent flow without dominant boundary layer flows or gas/hquid interfaces (due to rising gas bubbles) such as stirred reactors with bafQes, all used model particle systems and also many biological systems produce similar results, and it may therefore be assumed that these results are also applicable to other particle systems. For stirred tanks in particular, the stress produced by impellers of various types can be predicted with the aid of a geometrical function (Eq. (20)) derived from the results of the measurements. Impellers with a large blade area in relation to the tank dimensions produce less shear, because of their uniform power input, in contrast to small and especially axial-flow impellers, such as propellers, and all kinds of inclined-blade impellers. 

As stated in Section 2.1, there is a waiting period between the time of release of one bubble and the time of nucleation of the next at a given nucleation site. This is the period when the thermal boundary layer is reestablished and when the surface temperature of the heater is reheated to that required for nucleation of the next bubble. To predict the waiting period, Hsu and Graham (1961) proposed a model using an active nucleus cavity of radius rc which has just produced a bubble that eventually departs from the surface and has trapped some residual vapor or gas that serves as a nucleus for a new bubble. When heating the liquid, the temperature of the gas in the nucleus also increases. Thus the bubble embryo is not activated until the surrounding liquid is hotter than the bubble interior, which is at... 

The thermal boundary-layer thicknesses in the liquid before bubble nucleation are much greater. 

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... 

For diabatic flow, that is, one-component flow with subcooled and saturated nucleate boiling, bubbles may exist at the wall of the tube and in the liquid boundary layer. In an investigation of steam-water flow characteristics at high pressures, Kirillov et al. (1978) showed the effects of mass flux and heat flux on the dependence of wave crest amplitude, 8f, on the steam quality, X (Fig. 3.46). The effects of mass and heat fluxes on the relative frictional pressure losses are shown in Figure 3.47. These experimental data agree quite satisfactorily with Tarasova s recommendation (Sec. 3.5.3). 

Heat transfer by liquid-vapor exchange caused by bubble agitation of the boundary layer, q Bl. (microconvection)... 

Kanai, A., and Mtyata, H. Numerical simulation of bubbles in a boundary layer by Maker-Density-Function . Proceedings of the 3rd International Conference on Multiphase Flow, Lion, France (1998). 

In a number of refining reactions where bubbles are formed by passing an inert gas through a liquid metal, the removal of impurities from the metal is accomplished by transfer across a boundary layer in the metal to the rising gas bubbles. The mass transfer coefficient can be calculated in this case by the use of the Calderbank equation (1968)... 

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