Bubble-Water Gas Transfer

Bubbles comphcate the mass transfer process because the concentration of gases in the bubble is not constant with time. Instead of being exposed to the atmosphere -which is assumed to be a large container such that ambient concentrations do not change in the time of interest - a bubble volume is more limited, and the concentration of the various compounds can change due to mass flux or due to a change in pressure. This means that, for a volatile compound (for a gas), the equilibrium concentration at the water surface is not constant. 

to keep the total at 100%, other gas concentrations need to be adjusted accordingly. 

We will conserve both nitrogen and oxygen gas. Often, argon is considered to be similar to nitrogen because both are nonreactive and have close to the same diffusion coefficient. Because both gases are volatile, there is no significant resistance on the gas side of the interface, and 

the change of concentration in the water phase is given by 

The concentration inside of the bubble must also be considered  

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Figure 8.16. Parameters important to the bubble-water gas transfer.

We can see that the equations and solution technique have an added degree of complexity for bubble-water gas transfer, primarily because of the variation of pressure and because the gas control volume cannot be considered large. These are, however, simply the mass conservation equations, which should not be considered difficult, only cumbersome. Any reduction of these equations is an assumption, which would need to be justified for the particular apphcation. If transfer of a trace gas is of interest, then similar equations for the trace gas would need to be added to those provided above. 

The two-film model of gas exchange Chemical enhancement The Schmidt number Surface renewal model Micrometeorological models Bubble-mediated gas transfer Laboratory Studies of Air-Water Gas Exchange... 

Broecker H. C. and Siems W. (1984) The role of bubbles for gas transfer from water to air at higher wind speeds. Experiments in the wind-wave facility in Hamburg. In Gas Transfer at Water Surfaces (eds. W. Brutsaert and G. H. Jirka). Reidel, Dordrecht, pp. 229-236. 

The transport of heat as is insensitive to bubble-mediated gas transfer, i.e., it measures the transfer rate of a gas with high solubility. In conjunction with measurement of other trace gases this feature might allow distinguishing between the different transport mechanisms governing air-water gas transfer. 

Thus, when deahng with gas transfer in aerobic fermentors, it is important to consider only the resistance at the gas-liquid interface, usually at the surface of gas bubbles. As the solubihty of oxygen in water is relatively low (cf. Section 6.2 and Table 6.1), we can neglect the gas-phase resistance when dealing with oxygen absorption into the aqueous media, and consider only the liquid film mass transfer coefficient Aj and the volumetric coefficient k a, which are practically equal to and K a, respectively. Although carbon dioxide is considerably more soluble in water than oxygen, we can also consider that the liquid film resistance will control the rate of carbon dioxide desorption from the aqueous media. 

Merlivat L. and Memery L. (1983) Gas exchange across an air-water interface experimental results and modehng of bubble contribution to transfer. J. Geophys. Res. 88, 707—724. 

An early example of a patent on membrane contactor for gas transfer is in Ref. [12]. Harvesting of oxygen dissolved in water and discharging of CO2 to the water is presented in Ref. [13]. A membrane device to separate gas bubbles from infusion fluids such as human-body fluids is claimed in Ref. [14]. A hollow fiber membrane device for removal of gas bubbles that dissolve gasses from fluids delivered into a patient during medical procedures is disclosed in Ref. [15]. Membrane contactors have also found application in dissolved gas control in bioreactors discussed in Refs. [16-17]. 

To account for the process of bubble-induced gas exchange we modify the gas transfer equation to include both the transfer at the air-water interface, Fawi (Eq. (10.1)), and the flux caused by bubbles, Fb. The total flux, Fj, is now... 

The fliox created by bubbles has been mathematically described in many ways, but all present theories are strongly dependent on assumptions regarding the nature of the bubble surface, the initial size spectra of the bubbles, and the distributions of bubbles with depth. A model that has been used to predict the effect of bubbles on gas saturation (Keeling, 1993, as modified from Fuchs et al, 1987) assumes that the full spectrum of bubble process can be described by a combination of two bubble transfer processes (Fig. 10.10). The first is the mechanism by which small bubbles, < 50 pim in diameter, completely collapse and inject their contents into the water. This mechanism has been called air injection or total trapping by bubbles. In this case flux of gas from the bubble depends only on the total volume of air transferred by these bubbles, which is described by an empirical transfer velocity, Vinj (mol m d atm ) and the mole fraction, X, of the gas in the air... 

The second mechanism, called exchange or partial trapping describes the process of bubble transfer caused by larger bubbles, 50-500 (xm in diameter, that do not collapse but exchange gases across the bubble-water interface and then rejoin the atmosphere. In this case the flux depends on a different empirical constant. Vex (mol m d atm ), the atmospheric gas mole fraction, X, and the degree of overpressure of the gas in the bubble, W, caused by hydrostatic pressure and surface tension compared with the atmospheric pressure, P. The entire bubble flux can now be written as... 

The more advanced model of Wu and Gidapow 19) is used to explore novel reactor designs optimum catalyst size and reactor configuration. The model included the effect of the mass transfer coefficient between the liquid phase and the gas phase and the water-gas shift reaction. With reaction, diis model was used to predict slurry height, gas hold-up and the rate of methanol production of the Air Products/DOE LaPorte slurry bubble column reactor. 

The kinetic theory model was extended to include the effect of the mass transfer coefficient between the liquid and the gas and the water gas shift reaction in the slurry bubble column reactor. The computed granular temperature was around 30 cm /sec and the computed catalyst viscosity was closed to 1.0 cp. The volumetric mass transfer coefficient estimated by the simulation has a good agreement with experimental values shown in the literature. The optimum particle size was determined for maximum methanol production in a SBCR. The size was about 60 - 70 microns, found for maximum granular temperature. This particle size is similar to FCC particle used in petroleum refining. 

Purge and trap (PAT), Chapter 33, involves bubbling a gas through a liquid which contains volatile or semivolatile compounds. These compounds transfer into the gas bubble based on the second law of thermodynamics systems tend to maximum disorder, or compounds go from high concentration to low concentration. In this case, the inside of the gas bubble is at zero concentration so volatile compounds in the liquid transfer into the bubble in the form of a vapor. The bubbles of gas rise to the surface, pass through an adsorption tube, and the contents trapped. This is not only a separation technique, but it is valuable in concentrating trace materials. The most common use of this technique is to separate EPA s priority pollutants from water supplies. 

Fig. 1. Processes that influence transfer of gases across the natural air-water interface. Some of these include wind shear, waves, Langmuir circulation, turbulent mixing, and bubbles injected by breaking waves. In addition, films of organic surface active materials reduce direct gas transfer through the air water interface and through bubble surfaces...

Variability in bubble populations and dynamics of formation and mass transfer must also contribute to variability in reported gas transfer velocities (for a recent review see [78]). At higher wind speeds, bubbles strongly mediate gas transfer [41, 45, 60, 61]. Bubble populations produced by breaking waves are substantially different in fresh water and seawater [79] and are also likely to vary depending on water temperature, atmospheric pressure, and the presence of surface active matter. Slauenwhite and Johnson [80] found that populations of bubbles produced by break-up of a 5 pi bubble in passage through a small orifice increased by a factor of 3-5 in number in seawater relative to fresh water. They also found that lower temperatures and the presence of natural surface active materials from a diatom bloom significantly enhanced bubble production. 

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