  Transitional discs have central regions characterised by significant
depletion of both dust and gas compared to younger, optically-thick discs.
However, gas and dust are not depleted by equal amounts: gas surface densities
are typically reduced by factors of $\sim 100$, but small dust grains are
sometimes depleted by far larger factors, to the point of being undetectable.
While this extreme dust depletion is often attributed to planet formation, in
this paper we show that another physical mechanism is possible: expulsion of
grains from the disc by radiation pressure. We explore this mechanism using 2D
simulations of dust dynamics, simultaneously solving the equation of radiative
transfer with the evolution equations for dust diffusion and advection under
the combined effects of stellar radiation and hydrodynamic interaction with a
turbulent, accreting background gas disc. We show that, in transition discs
that are depleted in both gas and dust fraction by factors of $\sim 100-1000$
compared to minimum mass Solar nebular values, and where the ratio of accretion
rate to stellar luminosity is low ($\dot{M}/L \lesssim 10^{-10}$ $M_\odot$
yr$^{-1}$ $L_\odot^{-1}$), radiative clearing of any remaining $\sim 0.5$
$\mu$m and larger grains is both rapid and inevitable. The process is
size-dependent, with smaller grains removed fastest and larger ones persisting
for longer times. Our proposed mechanism thus naturally explains the extreme
depletion of small grains commonly-found in transition discs. We further
suggest that the dependence of this mechanism on grain size and optical
properties may explain some of the unusual grain properties recently discovered
in a number of transition discs. The simulation code we develop is freely
available.
