Longitudinal dispersion mechanisms in packed beds

A theoretical study has been made of longitudinal dispersion mechanisms during steady flow of a fluid through unconsolidated spherical beads. The mathematical model utilizes a step function input of thermal energy and presents the solution for the transient behvior of the system. The longitudinal dispersion of the step input is considered the result of eddy mixing of the fluid, molecular conduction within the fluid, and a finite time lag for heat transfer to occur between fluid and particle. The latter mechanism is characterized by both a fluid film resistance and an intraparticle resistance. The exact solution, involving an infinite integral, is approximated to an error function form. The character of the contribution of each mechanism is apparent from the form of the approximate solution, and furthermore, the contributions are shown to be additive to yield the total dispersion. The conditions for convergence to the aproximate solution are indicated. The equations are presented such that the analysis is applicable to both heat and mass transfer processes.