Average diffusion-to-the-wall times for laser-tagged molecules in a long cylinder

Abstract.

An approximate closed-form expression is derived for the average wall-reaching rate k_W or time τ_W=k_W ^-1 of laser-tagged molecules diluted in an inert carrier gas migrating to the wall of a long cylinder where they are removed with sticking coefficient η_W. The exact equation for the sticky wall problem requires a trial-and-error solution of a transcendental relation with Bessel–functions. With the aid of the Fermi–Amaldi albedo theory, an explicit “compromise” relation is derived which approximates the exact diffusion curve of k_W versus η_W rather well. The result is applied to obtain curves of k_W versus η_W at different gas mix pressures for UF₆ diluted in N₂.