  We show, using differential dynamic microscopy, that the diffusivity of
non-motile cells in a three-dimensional (3D) population of motile E. coli is
enhanced by an amount proportional to the active cell flux. While non-motile
mutants without flagella and mutants with paralysed flagella have quite
different thermal diffusivities and therefore hydrodynamic radii, their
diffusivities are enhanced to the same extent by swimmers in the regime of cell
densities explored here. Integrating the advective motion of non-swimmers
caused by swimmers with finite persistence-length trajectories predicts our
observations to within 2%, indicating that fluid entrainment is not relevant
for diffusion enhancement in 3D.
