In the present paper, the performance of Lagrangian eddy interaction models in homogeneous isotropic stationary turbulence (HIST) is investigated. The relationships between the eddy time and length scales and certain integral scales in HIST are investigated in detail. One-dimensional dispersion of non-fluid particles is then analysed. The influence of the fluid velocity auto-correlation along the particle path, G(tau), is noted. An upper bound is determined for G(tau) and is used to investigate the performance of eddy interaction models in the prediction of dispersion of heavy, non-fluid particles. Numerical simulations are used to confirm the analysis for a wide range of particle ’relaxation times’.