Low-Dimensional Modeling of Transport and Reactions in Two-Phase Stratified Flow

Abstract

In this work, we develop low-dimensional models to describe steady-state mass transfer and reactions in two-phase stratified flow in microchannels. The partial differential equations that consider the effect of axial convection, transverse diffusion, and reaction are averaged in the transverse direction using the Lyapunov–Schmidt method. The resulting reduced-order model describes the evolution of the cup-mixing average and cross-section average concentrations along the axial direction. Two different reduced models are obtained: a One-Equation-Averaged (OEA) model, in which we average across both fluids simultaneously, and a Two-Equation-Averaged (TEA) model, in which we average across each fluid separately by embedding in a family of cognate problems. The OEA model cannot capture the initial mass transfer between the phases when they first come into contact at the inlet of the channel. It can only be used when there is a deviation from equilibrium due to a reaction. The TEA model overcomes these limitati...