Penetration theory, boundary layer thickness

No Chemical Reaction in the Liquid Phase. This is the other limiting case where one calculates the time dependence of the radius of the spherical solid pellet when the Damkohler number approaches zero. Hence, species A dissolves into stagnant liquid B and the mass transfer boundary layer thickness grows with the square root of time according to the classic penetration theory. In other words,... 

The penetration theory is attributed to Higbie (1935). In this theory, the fluid in the diffusive boundary layer is periodically removed by eddies. The penetration theory also assumes that the viscous sublayer, for transport of momentum, is thick, relative to the concentration boundary layer, and that each renewal event is complete or extends right down to the interface. The diffusion process is then continually unsteady because of this periodic renewal. This process can be described by a generalization of equation (E8.5.6) ... 

We want to calculate this new coefficient, just as we calculated the dilute coefficient in earlier sections of this chapter. In general, we might expect to repeat the whole chapter, producing an entirely new series of equations for the film, penetration, and surface-renewal, and boundary-layer theories. However, these calculations not only would be difficult but also would retain the unknown parameters like film thickness and contact time. 

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