The Energy -Minimized Multi - Scale (EMMS) model was extended to analyze both local heterogeneity and overall heterogeneity in vertical cocurrent - up particle - fluid two - phase flow. This analysis elucidates the transition from the dense fluidization regime to the dilute transport regime in relation to the so -called saturatuin carrying capacity

and also explains the coexistence of two different regions

dilute at the top and dense in the bottom

in a unit

which causes axial heterogeneity. It is indicated that the stability condition for dilute transport is different from that for dense fluidization

resulting

therefore

in different flow structures. Both local and overall heterogeneity can be attributed to energy minimization. Wall effect plays a positive role in minimizing energy

and therefore causes radial heterogeneity. Experiments showed that radial heterogeneity could be suppressed by alternate contraction and expansion of the cross - sectional area of a unit.