  Context. Despite the recent discovery of spiral-shaped features in
protoplanetary discs in the near-infrared and millimetric wavelengths, there is
still an active discussion to understand how they formed. In fact, the spiral
waves observed in discs around young stars can be due to different physical
mechanisms: planet/companion torques, gravitational perturbations or
illumination effects. Aims. We study the spirals formed in the gaseous phase
due to two diametrically opposed shadows cast at fixed disc locations. The
shadows are created by an inclined non-precessing disc inside the cavity, which
is assumed to be optically thick. In particular, we analyse the effect of these
spirals on the dynamics of the dust particles and discuss their detectability
in transition discs. Methods. We perform gaseous hydrodynamical simulations
with shadows, then we compute the dust evolution on top of the gaseous
distribution, and finally we produce synthetic ALMA observations of the dust
emission based on radiative transfer calculations. Results. Our main finding is
that mm- to cm-sized dust particles are efficiently trapped inside the
shadow-triggered spirals. We also observe that particles of various sizes
starting at different stellocentric distances are well mixed inside these
pressure maxima. This dynamical effect would favour grain growth and affect the
resulting composition of planetesimals in the disc. In addition, our radiative
transfer calculations show spiral patterns in the disc at 1.6 {\mu}m and 1.3
mm. Due to their faint thermal emission (compared to the bright inner regions
of the disc) the spirals cannot be detected with ALMA. Our synthetic
observations prove however that shadows are observable as dips in the thermal
emission.
