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The Earth is strongly depleted in carbon compared to the dust in the ISM,implying efficient removal of refractory carbon before parent body formation.It has been argued that grains get rid of their carbon through oxidation andphotolysis in the exposed upper disk layers. We assess the efficacy of theseC-removal mechanisms accounting for the vertical and radial transport ofgrains. We obtain the carbon and carbon free mass budget of solids by solvingtwo 1D advection-diffusion equations, accounting for the dust grain sizedistribution and radial transport. The carbon removal acts on the fraction ofthe grains that are in the exposed layer and requires efficient verticaltransport. In models without radial transport, oxidation and photolysis candestroy most of the refractory carbon in terrestrial planet formation region.But it only reaches the observed depletion levels for extreme parametercombinations and requires that parent body formation was delayed by 1 Myr.Adding radial transport of solids prevents the depletion entirely, leavingrefractory carbon equally distributed throughout the disk. It is unlikely thatthe observed carbon depletion can ultimately be attributed to mechanismsoperating on small grains in the disk surface layers. Other mechanisms need tobe studied, for example flash heating events or FU Ori outbursts in order toremove carbon quickly and deeply. However, a sustained drift barrier orstrongly reduced radial grain mobility are necessary to prevent replenishmentof carbon from the outer disk.

Radial and vertical dust transport inhibit refractory carbon depletion in protoplanetary disks