Note on Murray's paper on bubbles in fluidized beds

Abstract

Murray's equation (53) for the velocity of rise of a three-dimensional (spherical) bubble of diameter d_B can be written $U_B = K[gd_B|6c]^{\frac{1}{2}}$ where the unassigned coefficient c enters Murray's analysis in the linearization of the convective momentum term in the momentum equation for the solids (17). (Equations (53) and (17) are as numbered in Murray 1965b.) This compares with the expression $U_B = K[\frac{1}{2}gd_B]^{\frac{1}{2}}$ used by Rowe & Partridge (1965), who determined the velocity coefficient, K, for several fluidized systems by measuring bubble diameter and velocity from X-ray ciné photographs. Values of c calculated from the measured values of K are listed in table 1, from which it is seen that the coefficients are not truly constant. The observed values of Murray's c are also appreciably less than c = 1 or c = ⅗, the two values tentatively suggested by mathematical reasoning, and Murray's figure 13, based on earlier velocity measurements over a limited range of particle sizes, is not a critical test of the value of the constancy of c.