Diffusion in Bubbles, Drops, and Jets

These values are within 5% of the values calculated with the penetration theory correction factor matrix and support our earlier suggestion that it is sufficient to use the simpler film model correction factor matrix in multicomponent mass transfer calculations at high mass transfer rates.  

One very important restriction in the development of the surface renewal models is the assumption that the penetrating, or diffusing, component does not see the bulk fluid, which, to all intents and purposes, is located at an infinite distance from the interface. This assumption is implicit in the boundary condition (Eq. 9.1.6) and is strictly true only for short Fourier times 

For long contact times and/or short distances between the interface and the core 5, the solution given above for the zero-flux coefficient does not apply. This situation may arise for mass transfer inside liquid droplets that stay sufficiently long in contact with the surrounding gas or liquid. For long contact times, the diffusing species will penetrate deep into the heart of the bubble (or drop), and it is important in such cases to define the mass transfer coefficient in terms of the driving forces Ax, = — x, , where represents 

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Figure 9.6. Idealized view of (a) spherical gas bubbles in a liquid, (h) liquid droplets in a gas, and (c) cylindrical gas jets in a liquid. Diffusion in bubbles, drops, and jets may be modeled by solving the diffusion equations for cylindrical and spherical coordinates.

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