Dust transport in protoplanetary discs with wind-driven accretion

It has recently been shown that the inner region of protoplanetary discs (PPDs) is governed by wind-driven accretion, and the resulting accretion flow showing complex vertical profiles. Such complex flow structures are further enhanced due to the Hall effect, especially when the background magnetic field is aligned with disc rotation. We investigate how such flow structures impact global dust transport via Monte Carlo simulations, focusing on two scenarios. In the first scenario, the toroidal magnetic field is maximized in the mid-plane, leading to accretion and decretion flows above and below. In the second scenario, the toroidal field changes sign across the mid-plane, leading to an accretion flow at the disc mid-plane, with decretion flows above and below. We find that in both cases, the contribution from additional gas flows can still be accurately incorporated into the advection-diffusion framework for vertically integrated dust transport, with enhanced dust radial (pseudo-)diffusion up to an effective alpha(eff) similar to 10(-2) for strongly coupled dust, even when background turbulence is weak alpha < 10(-4). Dust radial drift is also modestly enhanced in the second scenario. We provide a general analytical theory that accurately reproduces our simulation results, thus establishing a framework to model global dust transport that realistically incorporates vertical gas flow structures. We also note that the theory is equally applicable to the transport of chemical species.