Micromixing described in terms of inertial-convective disintegration of large eddies and viscous-convective interactions among small eddies—I. General development and batch systems

Abstract

A model based on the spectral interpretation of the decay of concentration fluctuations in liquids ( Sc ⪢ 1) is developed. The content of the system is divided into a zone of completely segregated fluid and a partially segregated molecular mixing zone. Inertial-convective decay of large eddies forming the completely segregated zone results in the growth of the molecular mixing zone. Mixing in the latter zone proceeds as a result of viscous-convective engulfment of the surrounding fluid by growing vortices until the entire volume is homogeneous at the molecular scale. A population balance describes the distribution of entrance times among eddies in the molecular mixing zone. At any time, eddies originating from a given stream are uniquely identified by their entrance time to the molecular mixing zone. In Part I of this series, the model is developed and extended to batch systems. The decay of concentration fluctuations in an isotropic homogeneous mixer, the conversion of single instantaneous and fast reactions and the selectivity of complex reactions in batch and plug flow reactors are predicted, and are compared with available experimental data in the literature.