Cluster Formation in Expanding Supersonic Jets: Effect of Pressure, Temperature, Nozzle Size, and Test Gas

To study homogeneous condensation in an expanding nozzle flow, cluster beams were sampled from the core of the flow field and transferred into a vacuum chamber for further analysis. Sonic and hypersonic nozzles with throat diameters 0.015 cm ≤ d ≤ 0.15 cm were used. Source temperature was varied between 120 ≤ T0 ≤ 450° K, source pressure between 100 ≤ p0 ≤ 12 000 torr. Test gases were the rare gases (except He), N2, and CO2. The size of the clusters (=microdroplets or -crystals) and the intensity of the cluster beam was measured with a through-flow ionization detector with retarding potential system to get the mass-to-charge distribution of the cluster ions. The mean cluster size N̄ varied between 102 and 104 atoms/cluster. The mean cluster size remained almost constant with increasing T0 if p0 was increased simultaneously according to the isentropic relation p0T0γ /(1−γ)=const. Considering the various types of cluster-growth reactions one expects to get cluster beams with the same size, if p0 and T0 fall within the narrow range between the isentrope p0T0γ /(1−γ)=const and the line for equal bimolecular processes, p0T0(1.5γ −1)/(1−γ)=const. The experiments confirm this result. The same model predicts that a decrease of nozzle throat diameter d can be compensated by an increase of source pressure p0 such that p0dq=const with 0q1. The experimental scaling law for constant cluster size gives q=0.8 for argon and q=0.6 for CO2. Comparing different gases, the same cluster size N̄ was obtained for the rare gases if they were in corresponding states prior to expansion and if the reduced nozzle scale was the same. This confirms the model of ``corresponding jets'' which extends the thermodynamic principle of corresponding states to real gas effects in a time-dependent system like a nozzle flow, and which applies equally to condensation in slow and fast expansions, including the transition to molecular flow.