Bubbles diameter

If the bed is slugging, bubble motion is retarded by the bed wall, and the bed or tube diameter, Z9, rather than the actual bubble diameter, determines the bubble rise velocity, ie... 

Flotation. Flotation (qv) is used alone or in combination with washing and cleaning to deink office paper and mixtures of old newsprint and old magazines (26). An effective flotation process must fulfill four functions. (/) The process must efficiently entrain air. Air bubble diameter is about 1000 p.m. Typically air bubbles occupy 25—60% of the flotation cell volume. Increa sing the airRquid ratio in the flotation cell is said to improve ink removal efficiency (27). (2) Ink must attach to air bubbles. This is primarily a function of surfactant chemistry. Air bubbles must have sufficient residence time in the cell for ink attachment to occur. (3) There must be minimal trapping of cellulose fibers in the froth layer. This depends on both cell design and surfactant chemistry. (4) The froth layer must be separated from the pulp slurry before too many air bubbles coUapse and return ink particles to the pulp slurry. 

In hen of careful independent checks of predictive accuracy, the results of the comprehensive theoretical work will not be presented here. Simpler, more easily understood predictive methods, for certain important limiting cases, will be presented. As a check on the accuracy of these simpler methods, it will perhaps be prudent to calculate the bubble diameter from the graphical representation by Mersmann (loc. cit.) of the resiJts of Kumar et al. (loc. cit.). 

Cf, C y, and Cq are the concentrations of the substance in question (which may be a colligend or a surfactant) in the feed stream, bottoms stream, and foamate (collapsed foam) respectively. G, F, and Q are the volumetric flow rates of gas, feed, and foamate respectively, is the surface excess in equilibrium with C y. S is the surface-to-volume ratio for a bubble. For a spherical bubble, S = 6/d, where d is the bubble diameter. For variation in bubble sizes, d should be taken as YLnid fLnidj, where n is the number of bubbles with diameter dj in a representative region of foam. 

Bubble sizes at formation generally increase with surface tension and orifice diameter. Prediction of sizes in swarms from multiple orifices is difficult. In aqueous solutions of low surface tension, Bubble diameters of the order of 1 mm are common. Bubbles produced by the more complicated techniques of pressure flotation or vacuum flotation are usually smaller, with diameters of the order of 0.1 mm or less. 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

In the tubular process a thin tube is extruded (usually in a vertically upward direction) and by blowing air through the die head the tube is inflated into a thin bubble. This is cooled, flattened out and wound up. The ratio of bubble diameter to die diameter is known as the blow-up ratio, the ratio of the haul-off rate to the natural extrusion rate is referred to as the draw-down ratio and the distance between the die and the frost line (when the extrudate becomes solidified and which can often be seen by the appearance of haziness), the freeze-line distance. 

The hold-up and bubble diameter in mechanically agitated vessels are given by the following empirical expressions ... 

When the bubble diameter approaches the diameter of the containing vessel, slug flow is said to exist. In such cases, the bubble rise velocity is given by... 

The flow pattern of gas within the emulsion phase surrounding a bubble depends on whether the bubble velocity Ug is less than or greater than minimum fluidization velocity U . For Ubflow lines. For Ub> U , the much different case of Figure 4(B) results. Here a gas element which leaves the bubble eap rises much more slowly than the bubble, and as the bubble passes, it remms to the base of the bubble. Thus, a cloud of captive gas surrounds a bubble as it rises. The ratio of eloud diameter to bubble diameter may be written... 

Bubble column, 69, 149-150, 293-298 Bubble diameter, 28, 42 Butyric acid, 4, 5... 

Houghton et al. (HI3) have reported data on the size, number, and size-distribution of bubbles. Distinction is made between bubble beds, in which bubble diameter and gas holdup tend to become constant as the gas velocity is increased (these observations being in agreement with those of other workers previously referred to), and foam beds, in which bubble diameter increases and bubble number per unit volume decreases for increasing gas velocity. Pore characteristics of the gas distributor affect the properties of foam beds, but not of bubble beds. Whether a bubble bed or a foam bed is formed depends on the properties of the liquid, in particular on the stability of bubbles at the liquid surface, foam beds being more likely to form in solutions than in pure liquids. 

Gal-Or and Resnick (Gl) have developed a simplified theoretical model for the calculation of mass-transfer rates for a sparingly soluble gas in an agtitated gas-liquid contactor. The model is based on the average gas residencetime, and its use requires, among other things, knowledge of bubble diameter. In a related study (G2) a photographic technique for the determination of bubble flow patterns and of the relative velocity between bubbles and liquid is described. 

These results are, however, only valid for the particle sizes referred to. Lee (L3) has reported measurements of average bubble diameter and gas-liquid interfacial area for gas-liquid fluidized beds of glass beads of 6-mm... 

C. Average Bubble Diameter and Bubble-Size Distribution. 307... 

Increase in interfacial area. The total surface area for diffusion is increased because the bubble diameter is smaller than for the free-bubbling case at the same gas flow rate hence there is a resultant increase in the overall absorption rate. The overall absorption rate will also increase when the diffusion is accompanied by simultaneous chemical reaction in the liquid phase, but the increase in surface area only has an appreciable effect when the chemical reaction rate is high the absorption rate for this case is then controlled by physical diffusion rather than by the chemical reaction rate (G6). 

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