Bubble height

A Cross-sectional area C Average tracer concentration in the liquid leaving the column C Initial concentration of tracer D Internal diameter of the tube D Axial dispersion coefficient f Frequency of slug formation g Gravitional acceleration H Height of liquid in the column in the absence of gas bubbles Height of the column i Wake length... 

For a scale-up of this process, we need data on the the stable bubble height /i, and on the "catchment areas" of the distribitor plates of the bench scale and... 

Rate of Mass Transfer in Bubble Plates. The Murphree vapor efficiency, much like the height of a transfer unit in packed absorbers, characterizes the rate of mass transfer in the equipment. The value of the efficiency depends on a large number of parameters not normally known, and its prediction is therefore difficult and involved. Correlations have led to widely used empirical relationships, which can be used for rough estimates (109,110). The most fundamental approach for tray efficiency estimation, however, summarizing intensive research on this topic, may be found in reference 111. 

The actual flotation phenomenon occurs in flotation cells usually arranged in batteries (12) and in industrial plants and individual cells can be any size from a few to 30 m in volume. Column cells have become popular, particularly in the separation of very fine particles in the minerals industry and coUoidal precipitates in environmental appHcations. Such cells can vary from 3 to 9 m in height and have circular or rectangular cross sections of 0.3 to 1.5 m wide. They essentially simulate a number of conventional cells stacked up on top of one another (Fig. 3). Microbubble flotation is a variant of column flotation, where gas bubbles are consistently in the range of 10—50 p.m. 

As bubbles rise through the bed, they coalesce into larger bubbles. The actual bubble size at any height above the distributor, in the bed is a function of the initial bubble size as it emerges from the gas distributor and the gas flow rate (16) ... 

This equation predicts that the height of a theoretical diffusion stage increases, ie, mass-transfer resistance increases, both with bed height and bed diameter. The diffusion resistance for Group B particles where the maximum stable bubble size and the bed height are critical parameters may also be calculated (21). 

These design fundamentals result in the requirement that space velocity, effective space—time, fraction of bubble gas exchanged with the emulsion gas, bubble residence time, bed expansion relative to settled bed height, and length-to-diameter ratio be held constant. Effective space—time, the product of bubble residence time and fraction of bubble gas exchanged, accounts for the reduction in gas residence time because of the rapid ascent of bubbles, and thereby for the lower conversions compared with a fixed bed with equal gas flow rates and catalyst weights. 

There are many laboratory methods for testing the relative merits of one defoamer against another. It is a simple matter to measure foam height as a function of time to compare the performance of various foam surfactants and defoamers. Unfortunately, this simplicity has led to a wide variety of methods and conditions used with no standard procedure that would make the measurement of foaminess as characteristic of a solution as its surface tension or viscosity. It has been suggested that the time an average bubble remains entrapped ia the foam is such a quantity (49), but very few workers ia the defoamer iadustry have adopted this proposal. Ia practice, a wide variety of methods are used that geaerally fall iato oae of five maia categories ... 

Dynamic Methods. This is a subdivision of the pneumatic class foam heights or volumes are monitored while the gas continues to produce bubbles. 

For sieve or valve plates, h = h , outlet weir height. For bubble-cap plates, h = height of static seal. Tbe original references present vaH-dations against laboratoiy and small-commercial-column data. Modifications of tbe efficiency equation for absorption-stripping are also included. 

The size of a bubble as a func tion of height was given by Darton et... 

To illustrate, consider the hmiting case in which the feed stream and the two liquid takeoff streams of Fig. 22-45 are each zero, thus resulting in batch operation. At steady state the rate of adsorbed carty-up will equal the rate of downward dispersion, or afV = DAdC/dh. Here a is the surface area of a bubble,/is the frequency of bubble formation. D is the dispersion (effective diffusion) coefficient based on the column cross-sectional area A, and C is the concentration at height h within the column. 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

Equation 8 has not been rigorously tested on freely bubbling beds because of the difficulty of making precise independent measurements of Dg or Ug under such conditions. It has been verified for slugging beds, however, as is shown in Figure 3. In the case of slugging, the surface level of the bed oscillates considerably, and in this case, the maximum bed height is used for H in Equation 8. 

Measurements in large fluidized beds of fine particles indicate that bubble coalescence often ceases within a short distance above the gas distributor plate. Indications from density measurements or single bubble velocities are that bubble velocity Ug and diameter often reach maximum stable values, which are invariant with height or fluidizing gas velocity. 

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