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.
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