Bubbles average diameter

In experiments with bubble-columns containing suspended sand particles with average diameter 0.12 mm, an increase in heat-transfer coefficient was observed with increasing sand concentration, maximum values of 6000 kcal/m2-hr-°C being measured for suspensions containing 50% sand (based on the liquid volume). 

Cumo et al. (1969) reported that the pressure effect on the bubble diameter is linear in a Freon-114 flow, as shown in Figure 5.43. They tested the two-phase Freon-114 flow in a vertical rectangular test section at a mass flux of 100 g/cm2 s (0.737 x 106 lb/ft2 hr). The average bubble diameters at various system pressures were obtained from high-speed photographic recordings. The effect of reduced pressure, p pci, on the average diameter of Freon bubbles is correlated as... 

This relationship was verified at small heat fluxes only. Also a correlation for the average diameter of a bubble at the instant of break-off is available (F8) from experimental evidence for bubbles of steam and of hydrogen. 

Microballoons are bubbles with an average diameter of 40 pm (range 10-100 pm). They were originally used as a filler to control the density of plastic products. They are available as glass or bakelite material. 

Cova (3 ) measured the solid concentration profiles of a Raney nickel catalyst with an average diameter of 15.7 ym in a h.6 cm id reactor, using water and acetone as the liquids. He developed a sedimentation diffusion model, assuming solid and liquid dispersion coefficients were equal, and slurry settling velocities were independent of solid concentration. The model was then applied to data for Raney nickel in 6.35 and kk.J cm id bubble columns, in both cocurrent and countercurrent flow. 

The average bubble radius (as well as the biggest and smallest size), the maximum distance between the opposite walls of the bubble (relative diameter) [8] and the specific liquid/air interface are involved in the estimation of dispersity. However, the distribution of bubbles by size, for example by radius of equivalent spheres, reveals completely the foam dispersity. Additional information about dispersity which takes into account the difference in polyhedral shapes is gathered from the number and shape of polyhedron faces (see Section 1.2). 

A three-phase reaction involves a solid, C, which is slurried in an inert solvent in which it is soluble and a gas, A, which is bubbled through the slurry. The reaction is A + C -> Products, and is assumed to be instantaneous. There is no gas-side resistance to mass transfer. The average diameter of the solids can be considered to be much less than the thickness of the liquid film. The following data are available for the system under consideration ... 

Example 9.11 An aerator in an activated sludge reactor is located 3.5 m below the surface. The temperature inside the reactor is 30°C. What are the rise velocity of the bubbles, contact time for aeration. Re, Gi and G2 The approximate average diameter of the bubbles at mid-depth is 0.25 cm. 

Surfactant Surf. cone. (gm/liter) Flow rates (cm min) Average Foam bubble density, diameter, Pf 6 (gm/liter) (cm) ... 

Steady bubble diameter in turbulent bubble flow Diameter of particle Number-averaged mean bubble diameter Volume-surface mean bubble diameter... 

Figure 19 shows the dependence of average diameters of craters or holes, D, formed due to the attachment of hydrogen bubbles on electrolysis time, from which the increase in average diameters of holes with the electrolysis time can be clearly seen. The dependences of the number of craters or holes formed due to the attachment... 

To estimate the average turbulent fluid particle velocity, the second-order structure function (9.14) is interpreted as an absolute particle velocity squared and defined for two points in the fluid separated by a distance equal to the bubble diameter d. The structure function is then given as 5v [d) = uz z + d) — Vz(z)]. If the magnitude of the diameter d lies within the inertial subrange of turbulence, the structure function can be calculated as 5v d) = C(ed) / . The discrete absolute mean velocity of bubbles with diameter di is thus approximated as ... 

The interphase forces considered were steady drag, added (virtual) mass and lift. The steady drag force on a collection of dispersed bubbles with a given average diameter was described by (5.48) and (5.34). The transversal lift force was determined by the conventional model (5.65), whereas the added mass force was approximated by (5.112). 

Actually, of course, the drops or bubbles differ in size and are not spherical. However, for given values of and a an equivalent average diameter can be defined by an equation similar to Eq. (9.39) as follows ... 

However, flotation is more economical in concentrated pulps and a presence of bubbles with diameter <0.5 mm is completely unsuitable (Jain, 1987). The optimal flotation rate corresponds to particle size interval of 30-40pm. Apart from this average size the flotation rate decreases very rapidly. 

The average diameter of disperse phase in mixer rotation zone calculated for system "liquid-gas" by (5.5) and (5.8) was 1,2 mm. However outside the mixing zone the averaged diameter of bubbles is quickly increased due to the reduction of turbulence level and consequently of intensive bubbles coalescence. In peripheral part of tank apparatus the average diameter of disperse phase particles d2 in system "liquid-gas" can be calculated by empirical dependence [116] ... 

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