Bubble transport coefficient

The K-L model, because of its greater simplicity, thus seems to be the model of choice for systems with smaller bubbles. In this paper we shall show how the K-L model can be used to predict the experimental results obtained by Massimilla and Johnstone (1961) on the catalytic oxidation of ammonia. It will be seen that the performance of their system was largely controlled by reaction limitations within the bed s phases. The effects of various parameters on bed performance are examined for such a reaction-limited system, and then the effects of these parameters for a transport-limited system are also discussed. Finally, we consider the effect of using average values of the bubble diameter and transport coefficients on model predictions. 

Evaluation of the Average Transport Coefficient and Bubble Size. A constant bubble size is used when evaluating the properties of the fluidized bed, and since bubbles in real beds vary in size, it is important to ask what bubble size should be used. 

The dependence of the transport coefficient between the bubble and the cloud on the bubble diameter. 

One notes the greatest disparity between the two transport coefficients for large ratios of the maximum to minimum bubble diameter and for columns with h/D ratios in the range of 2 to 20 (.6<3<6). 

Figure 4. Ratio of the average bubble-cloud transport coefficient to the transport coefficient evaluated at h/2 as a function of the aspect ratio for various ratios the maximum to minimum bubble diameter, r...

Above Re s vD/v = 2 x 10 the turbulent inertial forces prevailed over the gravitational forces in the flow, in that approximately the same transport coefficient was found for both bubble movements ... 

Gas Bubble to Bulk Liquid(kj) A persistent problem in measuring transport coefficients from bubbles is the evaluation of the interfacial area. Calder-bank. solved this problem by using a light-transmission method. His data and other results in the literature were reasonably well correlated" by the equation... 

Many heterogeneous reactions are accelerated by the enhanced micromixing properties of cavitating sound fields. Oscillating and transient bubbles create intense microstreaming in the vicinity of suspended solids. Macromixing is induced by acoustic streaming and the oscillation of bubbles in the sound field. In most cases, a locally different mass-transport coefficient is observed. A tenfold increase in mass-transfer coefficients compared with silent reactions was measured [18]. 

In contrast to the strong effect of gas properties, it has been found that the thermal properties of the solid particles have relatively small effect on the heat transfer coefficient in bubbling fluidized beds. This appears to be counter-intuitive since much of the thermal transport process at the submerged heat transfer surface is presumed to be associated with contact between solid particles and the heat transfer surface. Nevertheless, experimental measurements such as those of Ziegler et al. (1964) indicate that the heat transfer coefficient was essentially independent of particle thermal conductivity and varied only mildly with particle heat capacity. These investigators measured heat transfer coefficients in bubbling fluidized beds of different metallic particles which had essentially the same solid density but varied in thermal conductivity by a factor of nine and in heat capacity by a factor of two. 

With the carrier stream unsegmented by air bubbles, dispersion results from two processes, convective transport and diffusional transport. The former leads to the formation of a parabolic velocity profile in the direction of the flow. In the latter, radial diffusion is most significant which provides for mixing in directions perpendicular to the flow. The extent of dispersion is characterized by the dispersion coefficient/). 

For gas-liquid combinations with relatively small uptake coefficients ( 10 4-10-7), longer interaction times between the gas and liquid are needed than can be obtained with the falling-droplet apparatus. These are provided in a bubble apparatus, a typical example of which is shown in Fig. 5.24. The gas of interest as a mixture with an inert carrier gas is introduced as a stream of bubbles into the liquid of interest. The interaction time is varied by moving the gas injector relative to the surface. The composition of the gas exiting the top of the liquid is measured as a function of the interaction time (typically 0.1-1 s), e.g., by mass spectrometry. The interaction time is limited by the depth in the liquid at which the bubbles are injected and their buoyancy. Longer interaction times and better control over them have been achieved using a modified apparatus in which the bubbles are generated and transported horizontally (Swartz et a.l., 1997). 

First, consider the diffusion of an organic compound across the boundary between two environmental systems, A and B. Imagine that at time 1 = 0, the surface of system A (e.g., an air bubble, a silt particle, etc.) is suddenly juxtaposed to a (very large) system B (e.g., the water of a lake, Fig. 18.5a). Mixing in system B is sufficient that the concentration of the selected compound at the boundary of the injected medium is kept at the constant value, Cg. This concentration is different from the initial concentration in A, CA. In system A, transport occurs by diffusion only. We want to calculate the concentration in system A as it evolves in space and time, CA(x,t). For the time being, we will assume that the equilibrium distribution coefficient between A and B is 1. Hence, the concentration of A seeks to change to be equal to that of system B. 

A useful description of mixing in bubble columns is provided by the dispersion model. The global mixing effects are generally characterized by the dispersion coefficients El and Eq of the two phases which are defined in analogy to Fick s law for diffusive transport. Dispersion in bubble columns has been the subject of many investigations which have recently been reviewed by Shah et al. (45). Particularly, plenty of data are available for liquid-phase dispersion. 

Studies on the ciearance (pi/h) of modei hydrophilic solutes such as calcein (MW 623) and dextrans FD-4 (MW 4400) and FD-40 (MW 38000) in tritiated water across the skin under the influence of US have revealed a good flux correlation with H20. Unexpectedly, the slopes obtained by linear regression of the plots were consistent for all solutes examined [116]. In other words, the permeability coefficients of the solutes were comparable with those of tritiated water and independent of molecular size up to 40 kDa under the effect of US. This can be ascribed to the above-described asymmetric collapse of transient cavitation bubbles at the liquid-solid interface, which can produce transport routes for hydrophilic solutes in the stratium corneum. 

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