Generation of high-intensity ultrasound through shock propagation in liquid jets

We investigated the generation and propagation of ultrasonic pressure waves produced by focused x-ray free-electron laser pulses in 14 to $30\mu \mathrm{m}$ diameter liquid water microjets. The pressure waves formed through reflections, at the surface of the microjets, of the initial shock launched in the liquid by the x-ray pulse. These waves developed a characteristic geometric pattern which is related to, but different from, the shock structures of supersonic gas jets. Fully developed waves had initial peak pressures ranging from less than –24 MPa to approximately 100 MPa, which exceed the compressive and tensile strengths of many materials, and correspond to extreme sound intensities on the order of $1\mathrm{GW}/\mathrm{m}{}^2$ and sound pressure levels above 270 dB (re: $1\mu \mathrm{Pa}$). The amplitudes and intensities were limited by the wave destroying its own propagation medium though cavitation, and therefore these ultrasonic waves in jets are one of the most intense propagating sounds that can be generated in liquid water. The pressure of the initial shock decayed exponentially, more rapidly in thinner jets, and the decay length was proportional to the jet diameter within the accuracy of measurements. Extrapolating our results to thinner jets, we find that the pressure waves may damage protein crystals carried by liquid jets in x-ray laser crystallography experiments conducted at megahertz repetition rates.

Figure 1

Experiment schematic. A water microjet is intercepted by a focused x-ray laser pulse that launches an initially cylindrical shock wave in the liquid. To observe the propagation of shock and pressure waves, the jet is imaged orthogonal to the jet and the x-ray pulse.

Figure 2

Generation and propagation of the pressure wave. The images show how after the generation of an initial shock by the XFEL pulse (1.7 mJ at source) in a 20.2-$\mu \mathrm{m}$ water jet, additional shocks and pressure oscillations develop. Two types of cavitation occurred: a cavitation cloud and single-cavitation bubbles.

Figure 3

Qualitative description of the phenomena induced by the initial shock. (a) Reflection of the initial shock at the surface of the jet generates negative pressure reflections that overlap and generate sufficiently large tensions to form a cavitation cloud. (b) Huygens-Fresnel construction of reflections from a linear plane pressure pulse propagating in a jet, showing that the closest place where all the reflections overlap trails the shock at one half of the jet diameter. (c) A nonlinear high-pressure pulse generates a rarefaction wave that catches up with the shock and weakens it, leading to a curved shock interface. The amplitude dispersion of the reflected wave's velocity generates a delayed pressure jump that becomes visible in the images.

Figure 4

The kinematics and pressure of the first shock wave. (a) Raw shock position data for one data set and corresponding smoothed data. (b) Smoothed shock position for all data sets. (c) Velocities of the first shock. (d) Pressures of the first shock. The data sets have the same line color and type in panels (b)–(d).

Figure 5

Attenuation of the first shock with the propagation distance scaled by the jet diameter. The shock initially decays with approximately the same exponential decay law for all data sets. When the shocks arrive at the maximum extent of the cavitation cloud, they have a pressure around 100 MPa for all conditions investigated.