  We use dust scaling relations to investigate the hypothesis that Virgo
cluster transition-type dwarfs are infalling star-forming field galaxies, which
is argued based on their optical features (e.g. disks, spiral arms, bars) and
kinematic properties similar to late-type galaxies. After their infall,
environmental effects gradually transform them into early-type galaxies through
the removal of their interstellar medium and quenching of all star formation
activity. In this paper, we aim to verify whether this hypothesis holds using
far-infrared diagnostics based on Herschel observations of the Virgo cluster
taken as part of the Herschel Virgo Cluster Survey (HeViCS). We select
transition-type objects in the nearest cluster, Virgo, based on spectral
diagnostics indicative for their residual or ongoing star formation. We detect
dust Md ~ 10^{5-6} Msun in 36% of the transition-type dwarfs located on the
high end of the stellar mass distribution. This suggests that the dust
reservoirs present in non-detections fall just below the Herschel detection
limit (< 1.1x10^5 Msun). Dust scaling relations support the hypothesis of a
transformation between infalling late-type galaxies to quiescent low-mass
spheroids governed by environmental effects, with dust-to-stellar mass
fractions for transition-type dwarfs in between values characteristic for
late-type objects and the lower dust fractions observed in early-type galaxies.
Several transition-type dwarfs demonstrate blue central cores, hinting at the
radially outside-in removal of gas and quenching of star formation activity.
The fact that dust is also confined to the inner regions suggests that metals
are stripped in the outer regions along with the gas. In the scenario of most
dust being stripped from the galaxy along with the gas, we argue that...
(abridged)
