Limitations of the Chemical Potential

Abstract

It is often assumed that the negative gradient of chemical potential indicates the direction of transport by diffusion. Diffusion is the transport of a fluid constituent induced by a concentration gradient. The objective of this review paper is to explain the purpose and correct application of the chemical potential. Fick's law is derived here from Newton's second law of motion. Diffusion is a transport mechanism involving the motion of individual molecules, and does not induce a resistance associated with fluid viscosity. Consequently, unlike advection, the mean hydraulic radius of flow channels does not affect resistance to diffusion. A concentration gradient is not reflected in the pressure gradient acting externally on reference volumes of fluid. Both external driving force and a concentration gradient may result in motion of the center of mass of reference volumes of fluid. If a density gradient exists, the vector sum of external forces does not describe the resultant driving force. A concentration gradient induces constituent velocity relative to the fluid boundaries, not relative to the center of mass. Chemical potential includes pressure as a variable, and cannot predict the direction of diffusion because pressure is a driving force for advection, not diffusion. Chemical potential describes equilibrium conditions and is not useful for evaluating mass transport.