The existence of multiple regimes of distinctive flow structure is a remarkable characteristic of fluidization, which is far from being physically interpreted under a unified approach. The energy minimization multi-scale model (Particle-Fluid Two-Phase Flow, the Energy Minimization Multi-Scale Method, Metallurgical Industry Press, Beijing, 1994) is potentially such an approach in which the inclusion of stability criteria enables the prediction of heterogeneity and non-linear behaviors in fluidized beds. However, fully analytical solution of the model is impossible so far, and numerical solutions have resorted to general optimizing software. Therefore, the detailed characteristics of the solutions and their theoretical implications have not been fully explored. In this paper, we have achieved this by a rigorous numerical approach and by retrieving all missing roots, which leads to physical mapping of fluidization regimes. The model is also extended to unsteady conditions with acceleration and simplified by employing a single stability criterion, which identifies choking as a jump between two branches of the stable solution. Calculations based on this version are in reasonable agreement with measurements on bench, pilot and commercial scale circulating fluidized beds.