It was shown that the rationalization of the Fick I law proposed by Howe generally could not be proved from a detailed atomistic (kinetic) approach, and it could be valid only in very trivial limit (very dilute solution), for which the usual and proposed forms of Fick's first law were equivalent.
On the “Rationalisation” of Fick’s First Law. Z.Erdélyi, D.L.Beke: Scripta Materialia, 2003, 49[6], 613-7