Recently, Horio et al. (1989) have proposed a set of scaling laws for circulating fluidized beds based on the clustering annular flow model developed by Ishii et al. (1989). This model is a combination of the core-annulus model of Nakamura and Capes (1973) and the cluster flow model of Yerushalmi et al. (1978). The flow is described as clusters moving upward in the core and a downward annulus near the walls. Slip velocities in both regions are based on cluster diameter rather than particle diameter, and it is assumed that cluster distribution is homogenous [-the particulate fluidization equation of Richardson and Zaki (1973) is used]. Cluster diameters and voidages within clusters for the core and for the annulus are introduced in the model as dependent variables. The analysis is similar to that of Nakamura and Capes (1973). This model is also incomplete. Ishii et al. (1989) suggested that completeness could be achieved by assuming that the flow is configured such that the pressure drop across the bed is minimized. This is the same assumption made by Nakamura and Capes, although no theoretical or physical explanation was given by either Ishii et al. or Nakamura and Capes (1973) as to the validity of this assumption. Ishii et al. (1989) present an expression for the core-annulus diameter ratio based on this assumption, and this compares reasonably well with their data.