Abstract
We study numerically and experimentally the stability of the transonic flow focusing used in serial femtosecond crystallography (SFX) to place complex biochemical species into the beam focus. Both the numerical and experimental results indicate that the minimum flow rate for steady jetting increases slightly with the gas stagnation pressure. There is a remarkable agreement between the stability limit predicted by the global stability analysis and that obtained experimentally. Our simulations show that the steady jetting interruption at the critical flow rate is caused by the growth of a perturbation with a constant phase shift. This result is consistent with the experimental observations, which indicate that both the meniscus tip and the emitted jet collapse almost simultaneously at the stability limit. We derive a scaling law for the jet diameter as a function of the liquid flow rate and gas density/pressure from more than one hundred simulations. The scaling law provides accurate predictions for the jet diameter within the range of values [0.549,10.9] μm analyzed in this work.
Highlights
In the original gaseous flow focusing configuration (Gañán Calvo, 1998), the liquid is injected at a constant flow rate Ql across a feeding capillary placed in front of a discharge orifice whose diameter is commensurate with that of the capillary
We study numerically and experimentally the transonic flow focusing used in SFX
The minimum values of liquid flow rate Ql obtained in the experiments are practically the same as those calculated from the global stability analysis (Fig. 6)
Summary
In the original gaseous flow focusing configuration (Gañán Calvo, 1998), the liquid is injected at a constant flow rate Ql across a feeding capillary placed in front of a discharge orifice whose diameter is commensurate with that of the capillary. Once a numerical solution of the hydrodynamic equations has been found, the values of the governing parameters can be swept to produce systematically new numerical flow focusing realizations with relatively short computing time In this way, one can determine the optimal conditions that maximize the energy transfer from the gas to the liquid. For this reason, the stability analysis is expected to be accurate for the present fluid configuration. We derive a scaling law to estimate the jet diameter for the geometrical configuration and physical properties considered in our analysis
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