Chains of Particles or Drops at High Peclet Numbers

Chains of Particles or Drops at High Peclet Numbers 

Such a situation occurs in practice, say, in the process of extraction of substances from drops and dissolution of gases from bubbles. In particular, it takes place in the extraction process when the drops are introduced into the extraction column at the same points with equal time intervals and in the case of barbotage, for a constant flow rate of the barbotage gas. 

In the following, assume that the main resistance to mass exchange is in the continuous phase. 

The diffusion boundary layer of any given drop in chain interacts with the diffusion wake of the previous drop (located upstream). The concentration field in it is substantially nonuniform and is depleted because of the absorption of the solute at the surfaces of all preceding drops. By virtue of such interaction, the inner mass exchange will be appreciably retarded (the shielding phenomenon) compared with the case of isolated drops. 

It follows from this expression that the total diffusion flux to the second drop is less than half that for the first drop, and we have h/h — 0 as /c — oo. The total diffusion flux for all drops of the chain is equal to 

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