Nonuniform Flow Dynamics Probed by Nanosecond X-Ray Speckle Visibility Spectroscopy

We report observations of nanosecond nonuniform colloidal dynamics in a free flowing liquid jet using ultrafast x-ray speckle visibility spectroscopy. Utilizing a nanosecond double-bunch mode, the Linac Coherent Light Source free electron laser produced pairs of femtosecond coherent hard x-ray pulses. By exploring anisotropy in the visibility of summed speckle patterns which relates to the correlation functions, we evaluate not only the average particle flow rate in a colloidal nanoparticle jet, but also the nonuniform flow field within. The methodology presented here establishes the foundation for the study of nano- and atomic-scale inhomogeneous fluctuations in complex matter using x-ray free electron laser sources.

Figure 1

Schematic of the two-pulse XPCS experiments. Two x-ray pulses with a time separation of $\tau$ were generated using the nanosecond double-bunch mode and delivered to the sample. A high-speed intensity monitor upstream of the sample measured the relative intensities of the two pulses within each pulse pair. A 2D detector 8 meters downstream of the sample recorded the sum of the scattering from each pulse pair. Enlarged views are shown of the region of interest outlined by the yellow rectangle of the simulated speckle pattern sum for $\tau =0$ and $\tau \to \infty$, illustrating the loss of contrast when $\tau$ exceeds the timescale of the dynamics.

Figure 2

Calibrated contrasts for $r=0$, 0.5, 1 as a function of flow rate. The curves show the calculated contrast decay assuming a uniform jet with different beam sizes. The two dashed gray lines indicate the range for $\beta (0.5)$. The high limit is smaller than ${\beta }_{1(2)}$ due to the nonideal spatial overlap between the two pulses.

Figure 3

Simulation of the anisotropic jet dynamics. (a) Simulated speckle pattern sum from a parabolic-flow jet at an averaged speed of $\overline{v}=0.5\mathrm{m}/\mathrm{s}$. (b) and (c) Enlarged views of the two ROIs outlined in yellow centered at $0.015{\AA }^{-1}$ for $\varphi \sim 0$ and $\varphi \sim \pi /2$. (d) For fixed $Q=0.0055{\AA }^{-1}$, $\gamma =0$ (parabolic flow), and $\overline{v}=5\mathrm{m}/\mathrm{s}$, calculated $|f{|}^2$ as a function of time for ${\varphi }_{1-5}=0,\pi /8,\pi /4,3\pi /8$, and $\pi /2$. (e) For fixed $Q=0.0055{\AA }^{-1}$, $\overline{v}=7.5\mathrm{m}/\mathrm{s}$ and $\tau =49\mathrm{ns}$, calculated $|f{|}^2$ as a function of azimuthal angle $\varphi$ for ${\gamma }_{1-5}=0.95$, 0.9, 0.85, 0.8, and 0. (f) For fixed $\overline{v}=0.5\mathrm{m}/\mathrm{s}$, $\gamma =0$ (parabolic flow), and $\tau =49\mathrm{ns}$, calculated $|f{|}^2$ as a function of azimuthal angle $\varphi$ for $Q_{1-4}=0.0055$, 0.011, 0.015, and $0.024{\AA }^{-1}$.

Figure 4

(a) Dependence of $|f{|}^2$ on azimuthal angle $\varphi$ for six flow rates from 1 to $8\mathrm{mL}/\min$, revealing anisotropic dynamics. The curves are fits giving the $\gamma$ values displayed in (b). The dashed line is a guide to the eye.