Transonic flow focusing: stability analysis and jet diameter

•We analyze the stability of transonic flow focusing.•We determine the minimum liquid flow rate for steady jetting.•We derive a scaling law for the jet diameter. 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.