In soft matter structure couples to flow and vice versa. Complementary to structural investigations, we here are interested in the determination of particle velocities of charged colloidal suspensions of different structure under flow. In a combined effort of theory and experiment we determine the Fourier transform of the super-heterodyne field auto-correlation function (power spectrum) which in frequency space is found to be well separated from homodyne contributions and low frequency noise. Under certain conditions the power spectrum is dominated by incoherently scattered light, originating from the unavoidable size polydispersity of colloidal particles. A simple approximate form for the low-wavenumber self-intermediate scattering function is proposed, reminiscent to the case of non-interacting particles. We experimentally scrutinize the range of applicability of these simplified calculations on employing a parabolic electro-osmotic flow profile. Both for non-interacting and strongly interacting fluid particle systems, the spectra are well described as diffusion-broadened velocity distributions comprising an osmotic flow-averaged superposition of Lorentzians at distinct locations. We discuss the performance and scope of this approach with particular focus on moderately strong interactions and on multiphase flow. In addition, we point to some remaining theoretical challenges in connection to the observed linear increase of the effective diffusion constant and the integrated spectral power with increasing electric field strength.
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