Analysis of the electroosmotic flow in a microchannel packed with homogeneous microspheres under electrokinetic wall effect

Abstract

Microfluidic systems based the electroosmotic flow in porous media has become a powerful pumping technology for biomedical diagnosis and chemical analysis. A mathematical model is developed to quantitatively describe the electroosmotic flow in a charged microcapillary densely packed with charged homogeneous microspheres. The model is based on the Carman–Kozeny theory, which assumes the porous medium to be equivalent to a series of parallel tortuous tubules. The interstitial tubular velocity is obtained by solving the Navier–Stokes equation and the Poisson–Boltzmann equation. The modified Brinkman’s macroscopic momentum equation is used for describing an electroosmotic flow in porous media with consideration of the electrokinetic wall effect. Such an equation is solved using three different methods: (i) the numerical method, (ii) the analytical solution, and (iii) the slip velocity approximation. Parametric studies are carried out for the electroosmotic flow in a charged microcapillary densely packed with charged microparticles under the influences of the working fluid property, the channel and particle size, and the zeta potential of charged surfaces. Specifically, the electrokinetic wall effects are discussed for several typical cases. In addition, the calculated results of the flow rate and pressure generated are compared with those reported in a published experimental work, and a good agreement between the present model and the published experiment is found. The physical insight provided by this study can be useful for the design and optimization of electrokinetic micropumps used for BioMEMS.