Here we report the results of non-equilibrium molecular dynamics simulations of the flow of colloidal and polymer particles in a thin channel with explicit inclusion of the background fluid. The simulations used atomic channel walls which were thermostated and an external field was imposed to produce planar Poiseuille flow at low Reynolds number. Results are presented which show the effect of channel width and flow rate on the velocity profiles. For wide channels at low flow rates these profiles are in agreement with the results of macroscopic fluid dynamics simulations, but discrepancies start to appear when the flow rate is increased and/or the channel widths become smaller until finally the profiles are dominated by wall effects such as particle layering and then macroscopic theory is not even qualitatively correct. Importantly it is observed that colloidal particles tend to migrate to the walls, but the polymer solutions simulated here tend to migrate to the centre of the channel.