Numerical Study of Mixing in Microchannels with Patterned Zeta Potential Surfaces

In a recent study, an effective means of mixing a low Reynolds number pressure-driven flow in a micro-channel was reported by Stroock et al.[10] using trenches on the lower wall that form a staggered herringbone pattern. In the present work numerical results are reported that indicate enhanced mixing using a similar herringbone pattern in the context of an electroosmotically driven flow in microchannels. Instead of trenches, all walls are flush, making microfabrication easier. The lower wall would have lithographically deposited polymer coatings that exhibit a zeta potential of a sign opposite to that at the other walls. These coatings are chosen to form a herringbone pattern. If mixing can be achieved using purely electro-osmotic flows, then it becomes easier to scale the channel dimensions to smaller values without the penalty of a dramatic increase in pressure drop. Moreover, the possibility of mixing with purely electro-osmotic flows that do not require time varying electric fields leads to a simpler system with fewer moving parts. With current micro-fabrication techniques, it is difficult to produce periodic patterned coatings on all four walls of a rectangular microchannel. For this reason, this study limits its scope to coatings applied only on the lower surface of the microchannel, with a rectangular cross-section. Numerical simulations are used in order to elucidate the dominant mechanism responsible for mixing, which is identified as the blinking-vortex [3]. The flow regime chosen to illustrate these effects is the same as that used by Stroock et al.[10], characterized by Reynolds numbers that are O(10) and Péclet numbers that are of O(10). The presence of patterned zeta potentials in a microchannel violates conditions of ideal electro-osmosis [4] and hence the flows are necessarily threedimensional. The efficiency of mixing is quantified by examining particle tracks at several downstream sections of the microchannel and averaging their concentration over boxes of finite size to model diffusion. It is found that the standard deviation of the concentration decays exponentially, and that the rate of decay is independent of the Péclet number when the latter is sufficiently large, indicating that chaotically-enhanced mixing is occurring. INTRODUCTION Mixing is difficult in many microfluidics applications because the flow regime is usually laminar, inertia effects are weak, and frequently the diffusion coefficients of the species of interest are low. In a laminar uniaxial flow, mixing is purely diffusive. The typical microchannel cross-section dimensions and average velocities are respectively of the order of 1 mm and 100 m/sec. The diffusion coefficient (DAB) for large molecules such as DNA and proteins in water is about 5 10 m/sec. The resulting Reynolds number is less than unity (Re 0.01–0.1), and the Péclet number (Pe = U w/DAB 20,000, where U is the average flow speed and w is the characteristic cross-section width) is very large, requiring long mixing time if driven only by diffusion. The characteristic axial distance for diffusive mixing (where the diffusion distance is roughly the channel width) is l w Pe 20 m. The resulting channel length for diffusive mixing in this regime can be prohibitively long. An enhanced mixing time can benefit applications such as DNA and protein analysis, cytometric analysis, flow injection, and chemical synthesis reactors. Researchers have proposed a variety of mixing mechanisms for low Reynolds numbers laminar flows, with those utilizing chaotic phenomena being relatively easy to fabricate. Active chaotic mixers require an external power