Binary Mass Transfer in Spherical and Cylindrical Geometries

1 Binary Mass Transfer in Spherical and Cylindrical Geometries 

For a binary system, under conditions of small mass transfer fluxes, the unsteady-state diffusion equations may be solved to give the fractional approach to equilibrium F defined by (see Clift et al., 1978) 

The time averaged mass transfer coefficient Tc may be extracted from Eq. 9.4.4 as 

We see from Eqs. 9.4.2 and 9.4.6 that when t oo equilibrium is attained, and the average composition (xj) will equal the surface composition Xjy. The time averaged Sherwood number and mass transfer coefficients for a rigid spherical particle may be obtained directly from Eqs. 9.4.4 and 9.4.5 with F given by Eq. 9.4.6 above. The Sherwood number at time t may be found using Eqs. 9.4.3 and 9.4.6 as 

When the size of the bubble (or droplet) exceeds a certain limit the dispersed phase may begin to circulate or oscillate. The Kronig-Brink model for circulation within the dispersed phase gives the following expression for the fractional approach to equilibrium 

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