During the last decades, much effort has been devoted to explain the
discrepancy between the amount of intracluster medium (ICM) estimated from
stellar evolution theories and that emerging from observations in globular
clusters (GCs). One possible scenario is the accretion of this medium by an
intermediate-mass black hole (IMBH) at the centre of the cluster. In this work,
we aim at modelling the cluster colour-excess profile as a tracer of the ICM
density, both with and without an IMBH. Comparing the profiles with
observations allows us to test the existence of IMBHs and their possible role
in the cleansing of the ICM. We derive the intracluster density profiles from
hydrodynamical models of accretion onto a central IMBH in a GC and we determine
the corresponding dust density. This model is applied to a list of 25 Galactic
GCs. We find that central IMBHs decrease the ICM by several orders of
magnitude. In a subset of 9 clusters, the absence of the black hole combined
with a low intracluster medium temperature would be at odds with present gas
mass content estimations. As a result, we conclude that IMBHs are an effective
cleansing mechanism of the ICM of GCs. We construct synthetic extinction maps
for M 62 and {\omega} Cen, two clusters in the small subset of 9 with observed
2D extinction maps. We find that under reasonable assumptions regarding the
model parameters, if the gas temperature in M 62 is close to 8000 K, an IMBH
needs to be invoked. Further ICM observations regarding both the gas and dust
in GCs could help to settle this issue.Comment: Accepted for publication in MNRAS.11 pages, 7 figure