  X-ray photon correlation spectroscopy was used to probe the diffusive
dynamics of colloidal particles in a shear flow. Combining X-ray techniques
with microfluidics is an experimental strategy that reduces the risk of x-ray
induced beam damage and also allows time-resolved studies of processes taking
place in flowcells. The experimental results and theoretical predictions
presented here, show that in the low shear limit, for a ``transverse flow''
scattering geometry (scattering wave vector q perpendicular to the direction of
flow) the measured relaxation times are independent of the flow rate and
determined only by the diffusive motion of the particles. This is not generally
valid and in particular, for a ``longitudinal flow'' (q || flow) scattering
geometry, the relaxation times are strongly affected by the flow-induced motion
of the particles. Our results show that the Brownian diffusion of colloidal
particles can be measured in a flowing sample and that, up to flux limitations,
the experimental conditions under which this is possible are easier to achieve
at higher values of q.
