Characteristic Time of Aqueous-Phase Diffusion in a Droplet

4 Characteristic Time of Aqueous-Phase Diffusion in a Droplet 

Consider unsteady-state diffusion of a dissolved species in a droplet, initially free of solute, when the surface concentration is raised to Cs at t = 0. The problem can then be stated mathematically as 

Note that the problem statement is very similar to that solved for interfacial transport with a different boundary condition at the droplet surface. A standard separation of variables solution of (12.72) and (12.73) gives 

The characteristic time for aqueous-phase diffusion x is obtained from the first term in the exponential in the solution  

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