Theory of Diffusion near Walls

A model previously proposed for momentum transport in fluids, in which momentum and energy are carried by dipole density waves centered on the molecule of interest, is here applied to a calculation of the hindering effect of a wall on diffusion. Consideration is given to both specular and diffuse reflection of the density waves by the wall. The ratio γ of the diffusion constant at a distance l from the wall to the bulk fluid diffusion constant is calculated for diffusion parallel to the wall (γ_x), and perpendicular to the wall (γ_z). For the diffuse reflection case ${\gamma }_x{\text{=(1+l}}_0^2{\text{/8l}}^2{\mathrm{)/N,\gamma }}_z{\text{=1/N,N=1+(l}}_0^2{\text{/4l}}^2{\text{)+(3l}}_0^4{\text{/288l}}^4)$ and l₀ is estimated as ${\text{9η(m}}_0{\mathrm{/kT)}}^{\frac{1}{2}}\text{/2ν}$ where η is the shear viscosity, m₀ the molecular mass, and ν the mass density of solvent; l₀ may be as large as several hundred angstroms for simple liquids at room temperature.