Bubble size factors

Ozone is only slightly soluble in water. Thus, factors that affect the mass transfer between the gas and Hquid phases are important and include temperature, pressure, contact time, contact surface area (bubble size), and pH. 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

The primary factor controlling how much gas is in the form of discontinuous bubbles is the lamellae stability. As lamellae rupture, the bubble size or texture increases. Indeed, if bubble coalescence is very rapid, then most all of the gas phase will be continuous and the effectiveness of foam as a mobility-control fluid will be lost. This paper addresses the fundamental mechanisms underlying foam stability in oil-free porous media. 

Bubble Dynamics. To adequately describe the jet, the bubble size generated by the jet needs to be studied. A substantial amount of gas leaks from the bubble, to the emulsion phase during bubble formation stage, particularly when the bed is less than minimally fluidized. A model developed on the basis of this mechanism predicted the experimental bubble diameter well when the experimental bubble frequency was used as an input. The experimentally observed bubble frequency is smaller by a factor of 3 to 5 than that calculated from the Davidson and Harrison model (1963), which assumed no net gas interchange between the bubble and the emulsion phase. This discrepancy is due primarily to the extensive bubble coalescence above the jet nozzle and the assumption that no gas leaks from the bubble phase. 

The value of Am strongly depends on the size distribution of the bubble diameter in the system and the volume fraction of the bubbles. These factors are strongly dependent not only on the liquid properties, but also on the gas/liquid flow ration and the energy dissipation. Opposite to the situation with respect to kiiq it is not possible to calculate Am with theoretical equations. This is the reason that in practise almost always the product of kuq and Am is considered. This product can easily be determined experimentally. 

III. Influence of Various Factors on Bubble Size A. Experimental Set-up... 

The measuring devices like rotameters, orifice meters, etc. can also be introduced into the equipment prior to the bubble forming device. Keeping the above general set-up in mind, we can now proceed to examine the factors which influence the bubble size. 

Normally, the various factors do not influence the bubble size to the same extent over the entire range of the other variables. Thus surface tension, which is one of the most important factors determining the bubble size at vanishingly small flow rates, assumes much less importance at higher flow rates. Similarly, the viscosity of the liquid is much more important at higher flow rates than at the lower ones. 

A considerable amount of contradiction exists regarding the influence of this variable. Schurmann (S6), while studying bubble formation in various liquids from porous earthenware, concluded that viscosity is the principal factor which determines the bubble volume. Similar conclusions have been drawn by Davidson and Schuler (D8), who find that an increase in viscosity causes a marked increase in the bubble size. 

In some multiphase reactors, stirring with an impeller or the flow pattern caused by gravity will control the interfacial area. By suitably designing and positioning propellers and reactant injection orifices or by using static mixers, it is possible to provide very efficient breakup of hquids into drops and bubbles. A factor of two decrease in drop or bubble size means a factor of four increase in interfacial area. 

Gas-liquid mass transfer in fermentors is discussed in detail in Section 12.4. In dealing with in gas-sparged stirred tanks, it is more rational to separate and a, because both are affected by different factors. It is possible to measure a by using either a light scattering technique [9] or a chemical method [4]. Ihe average bubble size can be estimated by Equation 7.26 from measured values of a and the gas holdup e. Correlations for have been obtained in this way [10, 11], but in order to use them it is necessary that a and d are known. 

Fermentation broths are suspensions of microbial cells in a culture media. Although we need not consider the enhancement factor E for respiration reactions (as noted above), the physical presence per se of microbial cells in the broth will affect the k a values in bubbling-type fermentors. The rates of oxygen absorption into aqueous suspensions of sterilized yeast cells were measured in (i) an unaerated stirred tank with a known free gas-liquid interfacial area (ii) a bubble column and (iii) an aerated stirred tank [6]. Data acquired with scheme (i) showed that the A l values were only minimally affected by the presence of cells, whereas for schemes (ii) and (iii), the gas holdup and k a values were decreased somewhat with increasing cell concentrations, because of smaller a due to increased bubble sizes. 

In salt solutions or mixtures of miscible liquids, the coalescence of tiny primary gas bubbles is suppressed significantly the higher the concentration of the solution, the better the size of the primary gas bubbles is preserved. The stable bubble size in this case is 0.2-0.5 mm, an order of magnitude smaller than in pure liquids. As a result of coalescence suppression, the enhancement factor of physical sorption m = (kLa)sol/(kLa)soly rises to 7 or 8, which has been confirmed by measurements of kLaL as a function of the concentration of various inorganic salts (both strong and weak electrolytes) as well as normal aliphatic alcohols (methanol to octanol) (Zlokarnik, 1980,1985). 

In the preceeding sections, development of the measurement technique and analysis of gas-phase characteristics in a slurry bubble column have been made along with some comparison of the experimental data with other correlations from the literature. Up to this point, analysis of gas-phase characteristics has included only single or binary liquid components. Recently, a large effect on gas holdup and bubble size has been observed for multicomponent liquid mixtures that contain small concentrations of surface-active species (24). In their study, mixtures of alcohols and water at alcohol concentrations less than 0.1 percent caused a dramatic increase in gas holdup (up to a factor of 2) and a decrease in bubble size (up to a factor of 4) compared to those observed for the water system. The authors think the effect is the result of- interaction between molecules of different species, leading to an enrichment of one species in the interface. Therefore, in multicomponent liquid mixtures, it is necessary to have knowledge of the presence of surface-active species as well as the physical properties of the fluid. 

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