Hydrodynamic dispersion due to a variety of flow velocity profiles in a porous-walled microfluidic channel

Abstract

A reduced-order model for the advective-dispersive mass transfer due to a variety of flow velocity profiles in a porous-walled microfluidic channel is developed in this study. The fluid flow in the microfluidic channel is described by a generalized class of the Poiseuille equation proposed by Amatore et al. (2009), which includes the bluntness parameter for exhibiting the level of bluntness of the velocity profile. This flow formulation represents all the traditional velocity profiles for the purely pressure-driven (Poiseuille) flow, the combined pressure-driven and electro-osmotic flows, and the purely electro-osmotic flow (EOF) in the microfluidic channel. The resulting reduced-order model delivers the mass transfer coefficients, including the hydrodynamic dispersion and the effective advection coefficients, which are functions of the Peclet number and the bluntness parameter. The results reveal that the hydrodynamic dispersion decreases when the flow varies from the pressure-driven to the electro-osmotic. In other words, the smaller the bluntness parameter the smaller the hydrodynamic dispersion. The diffusive, transient, and advective mass transfer regimes can be identified from the ratio of the hydrodynamic dispersion coefficient in the porous-walled microfluidic channel to the one in the nonporous-walled microfluidic channel. It is found that the mass transfer between the microfluidic channel and the porous medium should be included in determination of the hydrodynamic dispersion coefficient due to a variety of flow velocity profiles in a porous-walled microfluidic channel for the transient and the advective regimes. The results also show that the smaller the bluntness parameter the slower the mass transfer. Furthermore, the mass transfer in a porous-walled microfluidic channel is slower than the mass transfer in a nonporous-walled microfluidic channel.