Coalescer function

When describing oxygen concentration profiles measured during yeast fermentations in a bubble column Buchholz (7) also introduced a coalescence function which accounts for the decrease in kLa with increasing distance from the sparger. 

The reduction of kj a at the reactor entrance to its special independent value, k a is characterized by the coalescence function, ... 

Bubble breakage and coalescence functions can be fitted against the local, time-averaged BSDs. In this way, a generalised model for the mass transfer area that includes... 

Bapat et al. (1983) 1983 Interval of quiescence Monte Carlo method Direct Used breakage and coalescence functions to predict spatially varying drop size distribution and mass transfer rates. 

Oleophilic material can also be fabricated into loose media, and the media collected in a vessel. If the material is fabricated in a granular form and assembled into a deep bed gravity settler, the deep bed filter can also perform a coalescing function. 

The preceding treatment relates primarily to flocculation rates, while the irreversible aging of emulsions involves the coalescence of droplets, the prelude to which is the thinning of the liquid film separating the droplets. Similar theories were developed by Spielman [54] and by Honig and co-workers [55], which added hydrodynamic considerations to basic DLVO theory. A successful experimental test of these equations was made by Bernstein and co-workers [56] (see also Ref. 57). Coalescence leads eventually to separation of bulk oil phase, and a practical measure of emulsion stability is the rate of increase of the volume of this phase, V, as a function of time. A useful equation is... 

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) ... 

Drops coalesce because of coUisions and drainage of Hquid trapped between colliding drops. Therefore, coalescence frequency can be defined as the product of coUision frequency and efficiency per coUision. The coUision frequency depends on number of drops and flow parameters such as shear rate and fluid forces. The coUision efficiency is a function of Hquid drainage rate, surface forces, and attractive forces such as van der Waal s. Because dispersed phase drop size depends on physical properties which are sometimes difficult to measure, it becomes necessary to carry out laboratory experiments to define the process mixing requirements. A suitable mixing system can then be designed based on satisfying these requirements. 

In (8.35) Y is the flow stress in simple tension (and may itself be a function of the temperature and strain rate) and is the critical volumetric strain at void coalescence (calculated within the model to equal 0.15 independent of material). Note that the ductile fragmentation energy depends directly on the fragment size s. With (8.35), (8.30) through (8.32) become, for ideal ductile spall fragmentation,... 

Siemes and Weiss (SI4) investigated axial mixing of the liquid phase in a two-phase bubble-column with no net liquid flow. Column diameter was 42 mm and the height of the liquid layer 1400 mm at zero gas flow. Water and air were the fluid media. The experiments were carried out by the injection of a pulse of electrolyte solution at one position in the bed and measurement of the concentration as a function of time at another position. The mixing phenomenon was treated mathematically as a diffusion process. Diffusion coefficients increased markedly with increasing gas velocity, from about 2 cm2/sec at a superficial gas velocity of 1 cm/sec to from 30 to 70 cm2/sec at a velocity of 7 cm/sec. The diffusion coefficient also varied with bubble size, and thus, because of coalescence, with distance from the gas distributor. 

Equation (17) indicates that the entire distribution may be determined if one parameter, av, is known as a function of the physical properties of the system and the operating variables. It is constant for a particular system under constant operating conditions. This equation has been checked in a batch system of hydrosols coagulating in Brownian motion, where a changes with time due to coalescence and breakup of particles, and in a liquid-liquid dispersion, in which av is not a function of time (B4, G5). The agreement in both cases is good. The deviation in Fig. 2 probably results from the distortion of the bubbles from spherical shape and a departure from random collisions, coalescence, and breakup of bubbles. 

This constant was a function of particle size, agitation rate, and the surface properties of the particles, and its functional form suggested that the probability of coalescence was proportional to the surface area per unit volume of the... 

FIG. 36 Morphological changes of the sulfuric acid droplets as a function of time at about 94%. The three droplets (marked D) are the same as those shown in Fignre 35. After a period of time of abont 10 or more minntes, the droplets spread and coalesce (5). Spreading coincides with the corrosion reaction of the aluminnm snbstrate. Image size is 10 p,m X 10 p,m. (From Ref. 85.)... 

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