In the past decade, observational evidence that Globular Clusters (GCs) harbour multiple stellar populations has grown steadily. These observations are hard to reconcile with the classical picture of star formation in GCs, which approximates them as a single generation of stars. Bastian et al. recently suggested an evolutionary scenario in which a second, chemically distinct, population is formed by the accretion of chemically enriched material onto the protoplanetary disc of low-mass stars in the initial GC population. Using assumptions that represent the (dynamical) conditions in a typical GC, we investigate whether a low-mass star surrounded by a protoplanetary disc can accrete sufficient enriched material to account for the observed abundances in ‘second generation’ stars. We compare the outcome of two different smoothed particle hydrodynamics codes and focus on the lifetime and stability of the disc and on the gas accretion rate onto both the star and the disc.