On Fick's first law and the equations of quasi-static motion governing the molecular diffusion

TL;DR

This paper examines molecular diffusion in biphasic fluids through continuum mechanics and thermodynamics, establishing the link between diffusive drag force and relative velocity, and deriving Fick's first law as a condition for positive dissipated power.

Contribution

It provides a novel derivation of Fick's first law from continuum mechanics and thermodynamics, emphasizing the role of diffusive drag force and energy dissipation.

Findings

Diffusive drag force is linked to relative diffusion velocity.

Fick's first law ensures positive dissipated power.

The approach differs from Truesdell's in continuum mechanics.

Abstract

The problem of the molecular diffusion in a biphasic fluid mixture is studied here from the two complementary points of view of Continuum Mechanics - in a somewhat different manner from Truesdell in "Mechanical basis of diffusion" (J. Chem. Physics (U.S.), 37 (1962) 2336-2344) - and that of Thermodynamics. It is established that the force involved in the 'diffusive drag', i.e. in the inter-constituent viscous friction, is necessarily linked to the relative diffusion velocity of one constituent with respect to the other. We also end up with Fick's first law, which appears to be a sufficient condition for the dissipated power associated with the diffusive motions to be positive.