Parabolic flow tube reactor for tandem DMA studies of cluster ion evaporation kinetics: Design, theoretical data inversion, and preliminary results for ionic liquid nanodrops

Abstract

We seek to infer single-molecule evaporation rates from airborne ionic liquid clusters mobility-selected on a first DMA, flowing through a heated tube, with the ratio of product to parent fluxes determined on a second DMA. We connect theoretically the measured flux ratio to the reaction rate k via separation of variables, by assuming parabolic flow at large Peclet number (Pe). To minimize the non-parabolic entry flow region, we operate at moderate Reynolds numbers (∼150), resulting in a limited Pe. We identify practical conditions with small entry length and negligible finite-Pe corrections for the full (elliptic) non-reactive problem, which is numerically manageable despite the non-orthogonal eigenfunctions. We argue that moderate Pe corrections for the reactive problem are also small. The parent species problem is analogous to the nonreactive Graetz problem, though including the dimensionless first order reaction rate K as a free parameter. The product species problem involves an extra diffusivity ratio γ and non-standard functions, efficiently calculated by the computer program Mathematica. All other calculations involve diagonal matrices, enabling covering all the relevant range of dimensionless parameters: 1≤K ≤ 100; 1≤γ ≤ 1.4; arbitrary tube length x. These numerical results are condensed into tables for interpolations, enabling the quick inference of reaction constants from experimental data. The procedure is used to invert experimental data yielding the volatility of clusters of the ionic liquid EMI-FAP having diameters smaller than 3 nm. The approach is limited to situations where only one or two reaction products form.