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

Abstract

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 $\text{≤ d ≤ 0.15\hspace{0.17em}}\mathrm{cm}$ were used. Source temperature was varied between ${\text{120 ≤ T}}_0\text{≤ 450°}\mathrm{K}$ , source pressure between ${\text{100 ≤ p}}_0\text{≤ 12\hspace{0.17em}000}$ 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 $\mathrm{N̄}$ 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 $p_0{T}_0^{\text{γ /(1−γ)}}=\mathrm{const}$ . 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 $p_0{T}_0^{\text{γ /(1−γ)}}=\mathrm{const}$ and the line for equal bimolecular processes, $p_0{T}_0^{\text{(1.5γ −1)/(1−γ)}}=\mathrm{const}$ . 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 $p_0{d}^q=\mathrm{const}$ with 0<q<1. 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 $\mathrm{N̄}$ 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.