Bubble function

Planar imaging techniques like conventional photography and high-speed video imaging HSVI (Takahashi et al. 1992) have been used to visualise multiphase flows in mixed tanks. The observations about the mechanisms of bubble breakage, coalescence and wake effects can be used for the development of mechanistic bubble functions (Takahashi and Nienow 1993). HSVI requires plenty of well-directed light. 

For bubble and dew-point calculations we have, respectively, the objective functions... 

The Newton-Raphson approach, being essentially a point-slope method, converges most rapidly for near linear objective functions. Thus it is helpful to note that tends to vary as 1/P and as exp(l/T). For bubble-point-temperature calculation, we can define an objective function... 

Bubble-point temperature or dew-point temperatures are calculated iteratively by applying the Newton-Raphson iteration to the objective functions given by Equations (7-23) or (7-24) respectively. 

The value of the compresjiibility of oil is a function of the amount of dissolved gas, but is in the order of 10 x 10" psi" By comparison, typical water and gas compressibilities are 4x10" psi" and 500 x 10" psi" respectively. Above the bubble point in an oil reservoir the compressibility of the oil is a major determinant of how the pressure declines for a given change in volume (brought about by a withdrawal of reservoir fluid during production). 

The linear speed of sound in the Hquid is yi, B, and n are constants that should be set to the appropriate values for water. Any acoustic forcing function is included in the pressure at infinity term, (0- The pressure at the bubble wall, P(R), is given by... 

The function of aeration in a wastewater treatment system is to maintain an aerobic condition. Water, upon exposure to air, tends to estabUsh an equihbrium concentration of dissolved oxygen (DO). Oxygen absorption is controlled by gas solubiUty and diffusion at the gas—hquid interface. Mechanical or artificial aeration may be utilised to speed up this process. Agitating the water, creating drops or a thin layer, or bubbling air through water speeds up absorption because each increases the surface area at the interface. 

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) ... 

Because bubbles occupy space in a bubbling fluid bed, the expansion of the bed becomes a function of both the bubble velocity and the volume of the gas entering the bed ... 

Fig. 17. TDH above vigorously bubbling or turbulent fluidized beds as a function of bed diameter from 0.025 to 7.5 m (27).

Defoamers. Foam is a common problem in papermaking systems (27). It is caused by surface-active agents which are present in the pulp slurry or in the chemical additives. In addition, partially hydrophobic soHd materials can function as foam stabilizers. Foam can exist as surface foam or as a combination of surface foam and entrained air bubbles. Surface foam usually can be removed by water or steam showers and causes few problems. Entrained air bubbles, however, can slow drainage of the stock and hence reduce machine speed. Another serious effect is the formation of translucent circular spots in the finished sheet caused by permanently entrained air. 

Oxidation of cumene to cumene hydroperoxide is usually achieved in three to four oxidizers in series, where the fractional conversion is about the same for each reactor. Fresh cumene and recycled cumene are fed to the first reactor. Air is bubbled in at the bottom of the reactor and leaves at the top of each reactor. The oxidizers are operated at low to moderate pressure. Due to the exothermic nature of the oxidation reaction, heat is generated and must be removed by external cooling. A portion of cumene reacts to form dimethylbenzyl alcohol and acetophenone. Methanol is formed in the acetophenone reaction and is further oxidized to formaldehyde and formic acid. A small amount of water is also formed by the various reactions. The selectivity of the oxidation reaction is a function of oxidation conditions temperature, conversion level, residence time, and oxygen partial pressure. Typical commercial yield of cumene hydroperoxide is about 95 mol % in the oxidizers. The reaction effluent is stripped off unreacted cumene which is then recycled as feedstock. Spent air from the oxidizers is treated to recover 99.99% of the cumene and other volatile organic compounds. 

Fig. 17. Cavitation phenomenon in pumps showing cavitation bubble distribution and rate of weight loss as a function of cavitation coefficient at constant...

Flow Regimes in Multiphase Reactors. Reactant contacting, product separations, rates of mass and heat transport, and ultimately reaction conversion and product yields are strong functions of the gas and Hquid flow patterns within the reactors. The nomenclature of commonly observed flow patterns or flow regimes reflects observed flow characteristics, ie, armular, bubbly, plug, slug, spray, stratified, and wavy. 

Fig. 9. Bubble-wake interactions in a gas—Hquid-soHd reactor (a) soHds concentration profile within bubble-wake domain, where A—A and B—B represent planes through the bubble, vortex, and wake (b) projected impact of interactions on reaction rate as function of particle si2e and Hquid velocity, where (—)...

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. 

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 ... 

For bubble-cap plates, hydraulic-gradient must be given serious consideration. It is a function of cap size, shape, and density on the plate. Methods for analyzing bubble-cap gradient may be found in the chapter by BoUes (Smith, De.sign of Equilibrium Stage Proce.s.se.s, Chap. 14, McGraw-Hill, New York, 1963) or in previous edition of this handbook. 

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