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Electrokinetic Mixing in Microfluidic
Systems Chih-Chang Chang and Ruey-Jen Yang* Department of Engineering Science, College of
Engineering, National Cheng Kung University Email address: rjyang@mail.ncku.edu.tw Microfluidics and Nanofluidics, Vol. 3, No. 5, pp.501-525, 2007 |
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 The applications of
electrokinetics in the development of microfluidic devices
have been widely attractive in the past decade. Electrokinetic
devices generally require no external mechanical moving parts and
can be made portable by replacing the power supply by small battery.
Therefore, electrokinetic-based microfluidic systems can serve as a
viable tool in creating a lab-on-a-chip (LOC) or micro-total
analysis system (μTAS) for use in biological and chemical assays.
Mixing of analytes and reagents is a critical step in realizing
lab-on-a-chip. This step is difficult due to the flow in microscale
devices which are typically limited to low Reynolds numbers,
turbulence does not readily occur. The mixing of two or more fluid
streams in a simple microchannel is dominated by the molecular
diffusion effect. The diffusive mixing time is given by tm ~
w2/D and the mixing length (lm) along the
downstream channel increases linearly with the Péclet number (i.e.
lm ~
Pe×w), where w and D are the channel width and
molecular diffusivity. However, the rate of diffusive mixing in
microscale channels is very slow compared to the convection of the
fluid along the channel since the Péclet number of typical
microchannel flows is very high due to biomolecules (e.g. DNA and
protein) with relatively low molecular diffusivities. To reduce the
mixing time and length, various schemes to enhance micro-mixing have
been proposed in the past years. This review reports recent
developments in the micro-mixing schemes based on DC and AC
electrokinetics. The overview given in this article provides a
potential user or researcher of electrokinetic-based technology to
select the most favorable mixing scheme for applications in the
field of micro-total analysis systems.Mixing principle and chaotic mixing Although it is difficult to induce turbulence (so-called Eulerian chaos) in microchannels, an effective mixing in low Reynolds number flow regimes can be obtained by the chaotic advection mechanism (or so-called Lagrangian chaos or laminar chaos), which provides an effective increase in the interfacial contact area and concentration gradient due to reduction of the striation thickness (i.e. diffusion length). In this way, mixing time and length can be considerably reduced. If an exponential reduction of striation thickness should occur, the mixing time and mixing length can be reduced down to tm ~ ln(Pe) and lm ~ ln(Pe), respectively, for chaotic flows in the limit of large Pe. An effective mixing always requires repeated stretching and folding of fluid elements, e.g blanking vortex models. Blinking vortex models are similar to the link twist map (LTM) strategy which is based on a dynamic system theory described in the literature [1]. An LTM is often obtained when the dynamic system has a structure such that the motion can be described by the repeated application of two twist maps. Over the past few years, many effective micromixers have been designed according to the LTM strategy. Micro-mixing based on electrokinetics In this review, electrokinetic mixing is categorized as either active or passive mixing, as shown in Fig.1. Passive mixing refers to the mixing effect in electrokinetically-driven systems and is enhanced by virtue of their particular geometry topologies, surface properties, or instability phenomenon which occurs naturally under a static (DC) electric field. Active mixing refers to the enhancement of mixing in electrokinetically-driven microfluidic systems using a time-dependent electric field or in pressure-driven flow systems by means of an externally time-dependent or -indepentent electrical force. Chaotic mixing can be achieved by means of the following schemes: dielectrophoreric (DEP) force perturbation, the shaking of electrowetting-based droplet, DC/AC EKI (or EHD) instability, field-induced electroosmosis, and surface charges or grooved surface patterning.  
FIG.2 (a) Heterogeneous surface charge patterning
configuration in a T-shape microchannel. (b) Experimental image of
species mixing in the homogeneous and heterogeneous charged
microchannel. [2]
FIG. 1 Classification scheme for microfluidic mixing
based on electrokinetics. In general, electrokinetic passive mixing can be categorized as either lamination or chaotic mixing. In the case of lamination mixing, mixing mainly relies on the molecular diffusion effect between two or more parallel streams, while chaotic mixing usually refers to the interfacial contact area between two mixing streams. Heterogeneous surface charge (or zeta potential) patterning is one passive method to create chaotic electroosmotic flow mixing. Biddiss et al. [2] used a polybrene-coated method to create a non-uniform zeta potential distribution on the bottom of a PDMS microchannel, as shown in Fig.2(a). The zeta potential of native-oxidized PDMS and polybrene-coated surfaces are -83mV and 32mV, respectively. In this mixing channel, the channel wall with negative zeta potential drives the flow along the net flow direction, while the heterogeneous surface with a positive zeta potential tends to stop the flow. To satisfy continuity, transverse flow components must be induced in the heterogeneous regions (i.e. transverse pressure gradients are induced), resulting in secondary flows within the mixing channel. In Fig.2(b), it can be seen that the transverse flow was induced and the mixing was greatly enhanced in the heterogeneous microchannel. In addition, Chang and Yang [3] also employed a particle tracking method to visualize the fluid mixing process from a cross-section perspective in heterogeneous microchannels, as shown in Fig.3. The mixing channels considered in their study were characterized by a periodically repeating mixing protocol. Figure 3(a) shows that clockwise transversely rotational flows with an elliptic region (i.e. an unmixed island) are generated in the microchannel. According to Kolmogorov -Arnold-Moser (KAM) theorem in the dynamic system, the fluid in this region cannot mix with their surroundings (without a molecular diffusion effect). Thus, the mixing is locally chaotic in the mixing channel with patterned straight diagonal heterogeneous strips. In contrast, the unmixed island vanishes in Fig. 3 (b) and the global chaotic mixing is induced. It is seen that two unequal counter-rotating vortex flows (i.e. a blinking vortex) exist in this mixing system. The blinking vortex provides the main transport mechanism of the two different colored particles from left to right and right to left in a periodic manner. The concept of this design fits within the LTM framework [1].  
FIG.4 (a) Schematic of AC electroosmosis induced a
secondary flow in a microchannel with a pair of coplanar electrodes.
(b) Fluorescence images of mixing between two streams with or
without an applied sinusoidal voltage. [5]
FIG.3 Visualization of mixing at different periods in
microchannels with (a) straight diagonal heterogeneous strips and
(b) staggered asymmetric herringbone heterogeneous strips. The zeta
potential ratio of the heterogeneous strip (ζ2) to channel wall (ζ1) is -0.5. [3] The choice of driving amplitudes and frequencies, and optimization of operation conditions usually is a challenge in designing an active micro-mixer. Under appropriate operation conditions, the major portion of electrokinetic active mixing schemes in the literature is able to induce chaotic mixing. Field-induced electroosmosis has been widely applied to the active control of electroosmotic flows and liquid pumping in microchannels [4], with a lesser application in micro-mixing. Sasaki et al. [5] proposed a rapid micro-mixing scheme for a pressure-driven flow system combined with AC electroosmosis. AC electroosmosis can be induced by an AC field without electrochemical reactions on electrodes like electrolysis and bubble generation, so long as the frequency is higher than the inverse electrode reaction time (>1 kHz). The double layer polarization is induced by a capacitive charging mechanism. The time-averaged slip velocity on the electrode surface is proportional to the square of the applied voltage on electrode [4]. Therefore, a higher electroosmotic flow velocity can be produced with a lower applied voltage at an optimal frequency. Figure 4 (a) shows a schematic of an AC electroosmosis induced flow pattern in a microchannel with a semi-elliptic cross section. By designing a twisted electrode patterning configuration as shown in Fig.4 (b), a blinking vortex flow can be produced in the downstream channel which results in a chaotic mixing. This mixer also fits within the LTM framework [2]. There remain opportunities for new developments in electrokinetic micromixers based on field-induced electroosmosis. Future directions In general, the performance of chaotic advection mixers is not largely dependent on the Péclet number. Accordingly, the development of future micromixers should focus particularly on passive or active chaotic mixing schemes. In DC electrokinetically-driven microfluidic systems, high flow rates usually require high electric field strengths, and even then a high power supply is required. This is a great disadvantage in trying to realize a portable microfluidic system. Accordingly, low-voltage, AC electrokinetic techniques are expected to receive increasing attention in the coming years. Finally, it is known that the high flow rates required to achieve species mixing can be produced through various field-induced electrokinetic phenomena [4]. Therefore, the application of field-induced electrokinetic techniques to realize active mixers and portable microfluidic systems is likely to emerge as a major research topic in the microfluidics community in the near future. References
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