Context. Despite the recent discovery of spiral-shaped features in protoplanetary discs in the near-infrared and millimetre 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 by 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 performed gaseous hydrodynamical simulations with shadows, then we computed the dust evolution on top of the gaseous distribution, and finally we produced synthetic ALMA observations of the dust emission based on radiative transfer calculations. Results. Our main finding is that millimetre- to centimetre-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 μm 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. However, our synthetic observations prove that shadows are observable as dips in the thermal emission.