Relationship between bubble size

As shown in Section 2.2.5.1, a value of C d of 1.5 X 10-4 is recommended for sodium and a value of 4.65 X 10-4 for potassium (because of their respective modified Jakob numbers). Suffice it to say that the relationship between bubble size and detachment frequency in nucleate boiling of liquid metals is not yet well established, even though it is fundamental to a good understanding of such boiling process. 

Studies concerning bubbles characteristics in three-phase fluidized beds can be grouped into three categories. The first category includes the analysis of the relationship between bubble size and the velocity of single bubbles. The second group considers the characteristics of bubbles in freely bubbling beds. 

The pressure required to force water to enter the pore is called the breakthrough pressure. Bubble point as measured and reported in the literature is the air pressure needed to push out liquid imbibed in the pore of the membrane. The procedure for a bubble point test is described in ASTM Method F-316. The relationship between pore size and bubble point pressure is based on the application of the Young-Laplace equation. The smaller the... 

Interfacial area measurement. Knowledge of the interfacial area is indispensable in modeling two-phase flow (Dejesus and Kawaji, 1990), which determines the interphase transfer of mass, momentum, and energy in steady and transient flow. Ultrasonic techniques are used for such measurements. Since there is no direct relationship between the measurement of ultrasonic transmission and the volumetric interfacial area in bubbly flow, some estimate of the average bubble size is necessary to permit access to the volumetric interfacial area (Delhaye, 1986). In bubbly flows with bubbles several millimeters in diameter and with high void fractions, Stravs and von Stocker (1985) were apparently the first, in 1981, to propose the use of pulsed, 1- to 10-MHz ultrasound for measuring interfacial area. Independently, Amblard et al. (1983) used the same technique but at frequencies lower than 1 MHz. The volumetric interfacial area, T, is defined by (Delhaye, 1986)... 

Figure 11. Relationship between local mean bubble size and local mean bubble rise velocity in beds of different diameters (u0 = 9 cm/sec). (From Werther, 1974.)...

Bubble Point Constancy. Although the exact relationship between the bubble point and the "pore size" of a microfiltration membrane is a matter of dispute (11, 12, 13, 14), nevertheless, it remains the quickest and most convenient means for demonstrating the continuing integrity of a membrane filtration system. It is consequently important that the bubble point be both reproducible (within a given range) and constant. It was, therefore, of considerable interest to discover that the bubble points of both conventional and poly(vinylidene fluoride) membranes increased with immersion time in deionized water whereas those of Tyrann-M/E and polyamide remained essentially constant (Figure 6). 

A relationship exists between the size of bubbles that can be accommodated in a system containing fine particles of 300-600 pm diameter varies from about 30 to 100 pm. Since a large proportion of the bubbles in air-entrained concrete are less than 100 pm diameter, it is clear that this particle size is of considerable importance in determining the amount of air entrained. Therefore, even at constant sand content, an increase in the properties of particles of this size will lead to an increase in air content. This effect is shown for a number of sand contents in Fig. 3.21 [24]. 

A number of assumptions are involved in the derivation of the mathematical expressions for nucleation. First, the change of one phase into another is really a nonequilibrium process. There is no guarantee that equations derived for thermodynamic equilibrium will be valid when applied to nonequilibrium. For example, the relationship between surface tension and radius applies for a static bubble, but does it apply to a bubble which is changing in size Second, it is imagined that any cluster which grows to a nucleus is bodily removed from the liquid. Thus nuclei cannot accumulate. This idea leads to a chopped distri-... 

The effect of the operation conditions on PSD in each state is different. Although the bubble size distribution in the operation has been expressed by various PSD functions, the PSD function that is most utilized is the normal PSD function. However, there is no physical background for applying the normal PSD function to the bubble size distribution. Additionally, when the bubble distribution is expressed by various PSD functions, it becomes difficult to discuss the relationship between the parameters in PSD and operation condition. This is one of the obstacles in the development of particle technology. 

In subsequent metal oxide synthesis experiments, the relationship between cavitation numbers and Reynolds numbers to synthesis results, such as crystallographic strain, primary grain size, agglomerate size, or phase purity, was examined to develop an understanding of the effects of different bubble dynamics on crystal properties. 

The interpretation of local gas holdup, bubble chord length, and bubble velocity from the probe response has been discussed previously (13). As indicated earlier, the measured bubble length is not equal to the bubble diameter but rather is associated with the probability of a single bubble striking the probe over the projected area of the bubble and with the shape of the bubble. The relationship between measured chord length and bubble size has been discussed previously (1A, 15). The... 

Methods of objective measurement of cereal foam structures are reviewed, including image analysis, confocal microscopy and x-ray tomography. The analysis of foam structures and their relationship with mechanical and rheological properties is described, and also the relationships between these structures and sensory descriptors such as crispness, crunchiness and texture. The size, shape and anisotropy of bubbles and their cell walls in foams are seen as critical in determining their fracture properties and sensory perception of crispness. Techniques for measuring crispness using acoustic emission and force-deformation profiles are discussed. 

Chen8,9 studied the gas holdup of a 7-cm i.d. 244-cm long column randomly packed with open-end screen cylinders of various sizes (1.27 cm x 1.27 cm and 1.9 cm x 1.9 cm) and screen meshes (8-14 mesh). The results with an air-water system were obtained in the bubble-flow regime. The screen cylinders were found to reduce the gas holdup. The results showed that for t/0g < 4 cm s, the gas holdup was a linear function of gas velocity, a result similar to the one obtained in an unpacked bubble-column bul not in a column packed with Raschig rings or other conventional packings. He also showed that for low gas velocity, l/0G < 3.64 cm s 1 the parameter (hG - 1ig)//ig was a unique linear function of liquid velocity (independent of gas velocity). Here, /iG is the gas holdup at zero liquid velocity. He also obtained a relationship between the gas holdup and the slip velocity between gas and liquid. All the data were graphically illustrated, however, no analytical correlation was presented. 

This finding suggested, that the deviation between the chemical and the photographic (or other) determination of the interfacial area in plate columns (the chemical method generally provides lower values ) was not due to the material system. One possibility could be the depletion of the reaction component in the gas, which was dependent of the bubble size. Hofer and Mersmann [212] overcome this discrepancy with a relationship, which was related to the gas bubble and pressupposed knowledge of the bubble size distribution (d, was the characteristic diameter of the distribution) and the superficial velocity u ... 

FIGURE 47.5 A two-dimensional (2D) bubble plot used to examine the relationship between the exposure metric (Cmax) and safety biomarker response. Active treatment subjects from studies 1 and 2 are denoted by Is and 2s, respectively, and p s are placebo subjects from both studies. The bubbles (open circles) indicate the safety biomarker responses and the severity of the response is depicted by the size of the circles. 

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