Sub-grid Modeling of Electrokinetic Effects in Micro Flows

Dr. C.P. Chen

Department of Chemical and Materials Engineering
University of Alabama in Huntsville

October 29, 2004
202 Madison Hall
3:00 PM (Coffee and Cookies at 2:30)

Abstract

Advances in micro-fabrication processes have generated tremendous interests in miniaturizing chemical and biomedical analyses into integrated micro-systems (Lab-on-Chip devices). To successfully design and operate the micro fluidics system, it is essential to understand the fundamental fluid flow phenomena when channel sizes are shrink to micron or even nano dimensions. One important phenomenon is the electro kinetic effect in micro/nano channels due to the existence of the electrical double layer (EDL) near a solid-liquid interface. Not only EDL is responsible for electro-osmosis pumping when an electric field parallel to the surface is imposed, EDL also causes extra flow resistance (the electro-viscous effect) and flow anomaly (such as early transition from laminar to turbulent flow) observed in pressure-driven micro-channel flows. Modeling and simulation of electro-kinetic effects on micro flows poses significant numerical challenge due to the fact that the sizes of the double layer (10 nm up to microns) are very "thin" compared to channel width (can be up to 100's of μm). To fully resolve the double layer, tremendous computational cells are required in a typical finite volume method. It is impractical for designing purpose on typical lab-on-chip platform, in which the length of the micro channel can be orders of magnitude larger than the width and the flow geometries are three dimensional and complicated. In this study, a novel sub-grid integration method to properly account for the physics of EDL is developed. This integration approach can be used on simple or complicated flow geometries. Resolution of the double layer is not needed in this approach, and the effects of the double layer are accurately accounted for at the same time. With this approach, the numeric grid size can be much larger than the thickness of double layer. Presented in this report are a description of the approach, model development, implementation, and validation studies of a straight rectangular micro channel flow and a T-junction Lab-on-Chip micro fluidics flow performed in LOCAD (Lab-on-Chip Application Development) of NASA-Marshall Space Flight Center. The results show significant extra flow resistance (up to 40% reduction of flow velocity in T-junction flow), due to the electro-viscous effect, when compared to the classical laminar flow theory.