Sherwood’s Plot: Fundamental or Empirical?

There are several examples of heuristic rules first proposed from empirical observation, which eventually earned physicochemical validity after the fundamental derivation of a posteriori. This may be the case of Sherwood’s plot – for which a sound rationalization from first principles, entailing enthalpy and mass balances, is provided here; it applies to (fine) chemicals undergoing concentration followed by purification at large, where such costs override the whole processing.