Solution of Diffusion Equation Near an Interface

consider the mass transport equation within roughly 28c of the interface, where there is no turbulent transport because Sc S  

The gradients in the x- and y-directions are probably small when compared with the large gradient in the z-direction. This will be sufficient to overcome the fact that u and V are greater than w. Thus, 

In addition, we know these relationships for mass flux  

Note that our recipe does not require measurement of any concentration - that is becausei L = Kl D, turbulence). Kl is not a function of concentration. It is thus logical that we do not have to measure concentration to measure Kl, as long as we know the fundamental relation between turbulence and mass transfer. Of course, there are difficulties with this four-step recipe. Primarily, item 1 Measure w(z,t) within 25c of the interface. In water, a fairly large concentration boundary layer would be 100 /u.m. How are we going to get a profile of velocity measurements to determine w(z,t) within 200 /xm of the interface, when the measuring volumes of most instruments are greater than 200 /um This is the problem that Thomas Hanratty and coworkers recognized and solved. 

Hanratty et al. s Solution to Recipe Item 1. Recipe item 1 will have a set of substeps that must be undertaken to find a solution to this measurement problem. They are  

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