The cell model developed since 1950s is a useful tool for exploring the behavior of particle assemblages, but it demands further careful development of the outer cell boundary conditions so that interaction in a particle swarm is better represented. In this paper, the cell model and its development were reviewed, and the modifications of outer cell boundary conditions were suggested. At the cell outer boundary, the restriction of uniform liquid flow was removed in our simulation conducted in the reference frame fixed with the particle. Zero shear stress condition was used to evaluate the outer boundary value of the stream function. Boundary vorticity was allowed to evolve to values compatible to existing stream function at the free shear outer boundary. The fore-aft symmetry of vorticity distribution at the outer boundary is thought critical to ensure the continuity of inflow and outflow between touching neighbor cells, and is also tested in the modified cell model. Numerical simulation in terms of stream function and vorticity based on the modified cell models was carried out to shed light on the interaction between liquid and particles. Lower predicted drag coefficient by the modified cell models was interpreted with the feature of flow structure. The drag coefficient from the simulation was also compared with correlations of drag coefficient reported in literature. It is found that the modified cell model with the uniformity of external flow relaxed and the fore-aft symmetry of boundary vorticity enforced was the most satisfactory on the overall performance of prediction.