Mathematical model for predicting the molecular intensity of a solenoid-actuated pulsed beam source

Abstract

A mathematical model for evaluating the molecular intensity produced by a solenoid-actuated pulsed beam source is described. The particular source studied here is used to introduce reactant gas pulses at various user-specified intervals into a fixed-bed microreactor system for transient catalysis studies where quantification of the inlet pulse intensity is required for data analysis. The model equations which describe the beam source performance utilize relationships from one-dimensional isentropic gas expansion, gas effusion through a small hole, and macroscopic mass balances around the valve orifice from which a closed-form algebraic expression for the pulse intensity is obtained. The parameters in this expression represent observables which include the ideal gas specific heat capacity ratio, the stagnation properties of the gas in the supply chamber of the beam source, and the beam valve driver settings. Comparisons between experimental and predicted values for the pulse intensities, where the latter are of the order 1017 molecules per pulse, show excellent agreement.