  Particle size is a key variable in understanding the behaviour of the
particulate products that underpin much of our modern lives. Typically obtained
from suspensions at rest, measuring the particle size under flowing conditions
would enable advances for in-line testing during manufacture and
high-throughput testing during development. However, samples are often turbid,
multiply scattering light and preventing the direct use of common sizing
techniques. Differential dynamic microscopy (DDM) is a powerful technique for
analysing video microscopy of such samples, measuring diffusion and hence
particle size without the need to resolve individual particles while free of
substantial user input. However, when applying DDM to a flowing sample,
diffusive dynamics are rapidly dominated by flow effects, preventing particle
sizing. Here, we develop "flow-DDM", a novel analysis scheme that combines
optimised imaging conditions, a drift-velocity correction and modelling of the
impact of flow. Flow-DDM allows a decoupling of flow from diffusive motion that
facilitates successful particle size measurements at flow speeds an order of
magnitude higher than for DDM. We demonstrate the generality of the technique
by applying flow-DDM to two separate microscopy methods and flow geometries.
