Adsorption phenomenon of neutral particles and a kinetic equation at the interface

The adsorption phenomenon of neutral particles in a sample having the shape of a slab is theoretically investigated by using a particular form for the kinetic equation at the limiting surfaces. The time evolution of the bulk and surface densities is determined in a closed form by means of a simple expression. A discussion on the characteristic times entering in the problem is reported. Finally, a microscopic model giving rise to a kinetic equation similar to the one used in the analysis is proposed, and the phenomenological parameters determined. The analysis is suitable for the description of the adsorption phenomena of dyes in nematic liquid crystals.

Figure 1

Behavior of $\rho (Z,t^{*})∕{\rho }_0$ vs $Z$, as predicted by Eq. (21) for $t^{*}=4t∕{\tau }_D=0.01$. The curves are depicted for a representative set of the parameters $r_1$ and $r_2$. Solid line corresponds to $r_1=10.0$ and $r_2=1.0$, dotted line to $r_1=1.0$ and $r_2=1.0$, dashed line to $r_1=1.0$ and $r_2=5.0$, and dashed dotted line to $r_1=1.0$ and $r_2=10.0$.

Figure 2

Behavior of $2\sigma (t*)∕{\rho }_{0}d$ vs $t^{*}=4t∕{\tau }_D$. Solid line was depicted for $r_1=10.0$ and $r_2=1.0$, dotted line for $r_1=1.0$ and $r_2=1.0$, and dashed line for $r_1=1.0$ and $r_2=5.0$.