Probe-induced concentration distortions in molecular-beam mass-spectrometer sampling

Abstract

Undistorted one-dimensional concentration profiles in a binary one-dimensional stream (no sampling probe present) are generated, in a numerical analysis, using a source, a sink, and differing combinations of massdiffusion coefficient and chemical-relaxation time. Corresponding to each of these undistorted concentration profiles, several distorted concentration distributions are generated using the same combination of massdiffusion coefficient and chemical-relaxation time but inserting an infinitely long conical sampling probe at differing axial locations. The velocity and concentration distributions are calculated numerically taking into account axial symmetry, compressibility, and the nonzero sampling-orifice diameter d. A large radial concentration gradient is found at the orifice. Each distorted concentration profile is compared with the corresponding undistorted profile in order to determine the apparent axial shift of the centerline concentration due to the sampling. (The centerline concentration is the important concentration when analyzing the composition using a molecular-beam mass spectrometer system.) If, at the sampling orifice, the chemical relaxation time is much larger than the characteristic flow time and Re Sc ⪢ 1, then the apparent axial shift δ of the sampling location is found to be δ d=0.19 ( Re Sc) 1 2 where Re Sc ≡ flow velocity times orifice diameter divided by mass-diffusion coefficient at the orifice. The results are relevant to molecular-beam sampling from flames.