Velocity measurement by coherent x-ray heterodyning.

We present a small-angle coherent x-ray scattering technique used for measuring flow velocities in slow moving materials. The technique is an extension of X-ray Photon Correlation Spectroscopy (XPCS): It involves mixing the scattering from moving tracer particles with a static reference that heterodynes the signal. This acts to elongate temporal effects caused by flow in homodyne measurements, allowing for a more robust measurement of flow properties. Using coherent x-ray heterodyning, velocities ranging from 0.1 to 10 μm/s were measured for a viscous fluid pushed through a rectangular channel. We describe experimental protocols and theory for making these Poiseuille flow profile measurements and also develop the relevant theory for using heterodyne XPCS to measure velocities in uniform and Couette flows.