The dynamics of dust and gas can be quite different from each other when the dust is poorly coupled to the gas. In protoplanetary discs, it is well known that this decoupling of the dust and gas can lead to diverse spatial structures and dust-to-gas ratios. In this paper, we study the dynamics of dust and gas during the earlier phase of protostellar collapse, before a protoplanetary disc is formed. We find that for dust grains with sizes < 10 micron, the dust is well coupled during the collapse of a rotating, pre-stellar core and there is little variation of the dust-to-gas ratio during the collapse. However, if larger grains are present, they may have trajectories that are very different from the gas during the collapse, leading to mid-plane settling and/or oscillations of the dust grains through the mid-plane. This may produce variations in the dust-to-gas ratio and very different distributions of large and small dust grains at the very earliest stages of star formation, if large grains are present in pre-stellar cores.
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