Meso-scale structures lead to heterogeneity of gas-solid flows which cannot be properly modeled by homogeneous drag models. Heterogeneous drag models have been developed, but there are still some problems with these heterogeneous drag models. The present work identifies the key reasons why predictions of the QL-EMMS drag model do not match those of the experimentally based O-S model and then aims to improve the QL-EMMS model. Since the meso-scale structures are the key reason for the heterogeneities in the two-phase flows, the influence of the cluster characteristics on the drag force needs to be further understood. The present work investigates the effects of both the cluster size and the cluster density on the drag function by sensitivity analyses. Both influences are analyzed to show that the cluster density has a greater effect on the drag force. Thus, the inaccuracy of the drag model is due to the inaccuracy of the cluster density model with the essential reasons being the basic concepts in EMMS theory. Then the characteristics of cluster density are further investigated to show that the cluster density curve tends to coincide with the homogeneous 45 degrees line in the extreme dilute and dense extremes, and then tends to the heterogeneous state around a local solid volume fraction epsilon(s) = 0.1. A mathematical model was then developed to complement EMMS theory. (C) 2015 Elsevier B.V. All rights reserved.