  The recently discovered exoplanets in binary or higher-order multiple stellar
systems sparked a new interest in the study of proto-planetary discs in stellar
aggregations. Here we focus on disc solids, as they make up the reservoir out
of which exoplanets are assembled and dominate (sub-)millimetre disc
observations. These observations suggest that discs in binary systems are
fainter and smaller than in isolated systems. In addition, disc dust sizes are
consistent with tidal truncation only if they orbit very eccentric binaries. In
a previous study we showed that the presence of a stellar companion hastens the
radial migration of solids, shortening disc lifetime and challenging planet
formation. In this paper we confront our theoretical and numerical results with
observations: disc dust fluxes and sizes from our models are computed at ALMA
wavelengths and compared with Taurus and $\rho$ Ophiuchus data. A general
agreement between theory and observations is found. In particular, we show that
the dust disc sizes are generally smaller than the binary truncation radius due
to the combined effect of grain growth and radial drift: therefore, small disc
sizes do not require implausibly high eccentricities to be explained.
Furthermore, the observed binary discs are compatible within $1\sigma$ with a
quadratic flux-radius correlation similar to that found for single-star discs
and show a close match with the models. However, the observational sample of
resolved binary discs is still small and additional data are required to draw
more robust conclusions on the flux-radius correlation and how it depends on
the binary properties.
