Photophoresis is a physical process based on momentum exchange between an illuminated dust particle and its gaseous environment. Its net effect in protoplanetary discs (PPD) is the outward transport of solid bodies from hot to cold regions. This process naturally leads to the formation of ring-shaped features where dust piles up. In this work, we study the dynamical effects of photophoresis in PPD by including the photophoretic force in the two-fluid (gas+dust) smoothed particle hydrodynamics (SPH) code developed by Barrière-Fouchet et al. (2005). We find that the conditions of pressure and temperature encountered in the inner regions of PPD result in important photophoretic forces, which dramatically affect the radial motion of solid bodies. Moreover, dust particles have different equilibrium locations in the disc depending on their size and their intrinsic density. The radial transport towards the outer parts of the disc is more efficient for silicates than for iron particles, which has important implications for meteoritic composition. Our results indicate that photophoresis must be taken into account in the inner regions of PPD to fully understand the dynamics and the evolution of the dust composition.