Coupled heat and multicomponent mass transfer in particulate systems with residence time and size distributions

Abstract

A theory is presented for the general case of coupled heat and multicomponent mass transfer in dispersions and suspensions with residence time and particle size distributions. The general formulations describe the behavior of industrial or biological particulate systems in terms of equations familiar from non-equilibrium thermodynamics and transport phenomena. Using matrix notation and appropriate transformations the resulting partial differential equations are first decoupled and then transformed into ordinary differential equations by employing an integral operator whose kernel takes into account the particle size and residence time distributions. Moment equations of the size distribution are formulated and used to evaluate general interrelationships among average sizes, interfacial surface area, dispersed-phase holdup fraction, and total average rates of transfer from the particle population. The total average heat- and mass-transfer rates in multiphase particulate systems are evaluated in terms of a general normalized size distribution and the expected values of the various fluxes involved. The properties of a proposed general normalized size distribution are discussed and compared with experimental results of bubble size distributions in a gas-liquid dispersion.