Fick's Insights on Liquid Diffusion

In 1855, Adolph Fick published ''On Liquid Diffusion'', mathematically treating salt movements in liquids as a diffusion process, analogous to heat diffusion. Less recognized is the fact that Fick also provided a detailed account of the implications of salt diffusion to transport through membranes. A careful look at Fick (1855) shows that his conceptualization of molecular diffusion was more comprehensive than could be captured with the mathematical methods available to him, and therefore his expression, referred to as Fick's Law, dealt only with salt flux. He viewed salt diffusion in liquids as a binary process, with salt moving in one way and water moving in the other. Fick's analysis of the consequences of such a binary process operating in a hydrophilic pore in a membrane offers insights that are relevant to earth systems. This paper draws attention to Fick's rationale, and its implications to hydrogeological systems. Fick (1829-1901; Figure 1), a gifted scientist, published the first book on medical physics (Fick, 1858), discussing the application of optics, solid mechanics, gas diffusion, and heat budget to biological systems. Fick's paper is divisible into two parts. The first describes his experimental verification of the applicability of Fourier's equation to liquid diffusion. The second is a detailed discussion of diffusion through a membrane. Although Fick's Law specifically quantifies solute flux, Fick visualized a simultaneous movement of water and stated, ''It is evident that a volume of water equal to that of the salt passes simultaneously out of the upper stratum into the lower.'' (Fick, 1855, p.30). Fick drew upon Fourier's model purely by analogy. He assumed that concentration gradient impelled salt movement, without inquiring why concentration gradient should constitute a driving force. As for water movement, he stated intuitively, ''a force of suction comes into play on each side of the membrane, proportional to the difference of concentration, consequently a stronger force at the upper side corresponding to the saturated solution'' (Fick, 1855, p.38)