The Monte Carlo method has been used for simulating two-dimensional diffusive motion of hard disks as a Pearsonian random walk (in which each displacement is of equal length but in a random direction) and for analyzing the kinetics of a diffusion-controlled irreversible bimolecular reaction between the diffusing entities. The results are compared with predictions based on hydrodynamic theory (the diffusion equation), which was recently shown to be consistent with the experimental data on the self-quenching of 1-palmitoyl-2(1-pyrenedecanoyl)-sn-glycero-3 -phosphocholine (py(10)- PC) in 1-palmitoyl-2-oleoyl-sn-gycero-3-phosphocholine (POPC) fluid bilayers (Martins et al. J. Phys. Chem. 1996, 100, 1889). Regardless of the time range analyzed and of the physical characteristics (diffusion constants and radii) of the reactants, the agreement between the random walk picture and the hydrodynamic treatment improves as the magnitude of the step of the diffusive displacement becomes smaller and one approaches the continuum limit. The study confirms earlier deductions about the limits of validity of the hydrodynamic theory (for reactions in 2D space) and reveals the need for more comprehensive experimental data.