Characteristics of advection-diffusion-Langmuir adsorption processes in two-dimensional plane Poiseuille flows

The advection-diffusion-Langmuir adsorption processes of a liquid solution, colloid, or suspension occur in many biomedical and chemical engineering fields. The dynamics of the system can be described by the so-called advection-diffusion-reaction (ADR) equations and are greatly influenced by five nondimensional numbers. Up to now, cases over a wider range of parameters have not been thoroughly studied, and the quantitative dependence of the system dynamics on the parameters remains unclear. In this study, we systematically solve the ADR equations in two-dimensional plane Poiseuille flows for cases with selected values of parameters by the finite difference method. We identify two different regimes in terms of the distribution of the maximum adsorption flux and discuss the dominant mechanism of mass transfer and the influences of the nondimensional parameters in each regime. We then propose analytical models to describe the influences of specific parameters on the adsorption equilibrium time. The results of this research may provide a convenient method to identify the dominant processes in the advection-diffusion-Langmuir adsorption system in future studies.