7.3 Passive Micromixers
7.3.1 Pressure-Driven Passive Micromixers
Micromixers 181
182 Bio-MEMS: Technologies and Applications of which is specific to their mixer configuration, and reduced dead time by a factor of approximately eight relative to the previously mentioned capil- lary-based mixers, by optimizing focusing. The hydrodynamic focusing con- cept was used with equal success by Pabit and Hagen,17 who employed coaxial, UV-transparent, fused silica capillaries (20 µm ID in 100 mm ID) to achieve off-chip rapid mixing for fast kinetic studies using UV-excited fluo- rescence probes. The hydrodynamic focusing effect also contributed to effi- cient solvent extraction by Hibara et al.,18 who generated a multilayer flow of miscible and immiscible fluids in 70 µm–wide channels of low aspect ratio (0.43) using a focusing Ψ-junction configuration in combination with a down- stream Ψ-junction one. Although achieving rapid mixing was not their objec- tive, their simple, single-manufacturing-layer, glass device, could be operated as a micromixer.A Ψ-junction mixer realized in silicon and featuring a contraction upstream and an expansion downstream of the mixing channel was developed by Veenstra et al.19 With a modest aspect ratio (2), they achieved improved mixing at a low Reynolds number (0.23) and essentially provided an indication of how an increased aspect ratio can reduce mixing time or reduce pressure drop. Y-junction micromixers have been successfully employed by Wu et al.20 to study nonlinear diffusive mixing in microchan- nels. Interested in gas mixing, Gobby et al.21 performed numerical simula- tions at low Reynolds numbers studying the characteristics of Ψ- and T- junction micromixers with and without throttling downstream of the mixing point. They concluded that mixing in gases is improved with throttling and with modest increases in mixing channel aspect ratio (3). A two-wafer, mul- tistream (10) mixer with a contraction into a high-aspect-ratio (8) mixing channel was developed by Floyd et al.22 on a silicon chip through the use of deep reactive ion etching (DRIE). This mixer, which was integrated with a heat exchanger and a probing region to perform infrared transmission kinet- ics studies of liquid reactions, yielded fully mixed product in a few tens of milliseconds at a modestly high Reynolds number (97). Considering that the estimated pressure drop is very modest, this type of mixer is promising for bio-analytical applications, although the two-wafer alignment and costly DRIE requirement in its manufacture cannot be overlooked. Various two- and three-stream high-aspect-ratio (6) micromixers were evaluated through numerical simulations by Maha et al.23 in terms of pressure drop and mixing performance for batch operation. It was shown that a combination of high- aspect-ratio narrow channels combined with hydrodynamic focusing and an optimization design scheme for batch mixture production can reduce mixture production time by an order of magnitude for a fixed pressure drop requirement, or reduce pressure drop by several orders of magnitude for a fixed mixture production time relative to unitary aspect ratio counterpart mixers. This was demonstrated experimentally by Maha24 for such micro- mixers hot embossed on polymethylmethacrylate (PMMA) and polycarbon- ate (PC) polymers using micromilled brass mold inserts. The simple manufacturing process, capacity for inexpensive mass production and inte- grability of such polymer mixers make them very good candidates for
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Micromixers 183 integration into disposable polymer microchips to perform a variety of bio- assays. A very low aspect ratio (0.012), Ψ-junction glass micromixer was developed by Holden et al.25 to simultaneously produce mixtures of quasi- continuously varying concentrations. This was elegantly achieved by an array of exit channels connected with their entrances arranged diagonally over the span of the mixing channel. Up to eleven discretely different con- centrations were produced simultaneously. A tilted UV lithography tech- nique was used by Yang et al.26 to fabricate a micromixer on SU-8 incorpo- rating opposing arrays of staggered spatially distributed impinging microjets in a T-junction mixer channel. This novel and rare three-dimensional mixer on a single layer is readily integrable on SU-8 chips.
A number of micromixers have been designed and realized incorporating passive elements, which can generate secondary flows, to fold the fluid interfaces and improve local diffusional mixing by cutting down the diffu- sion length. Introduction of such elements also results in a pressure drop overhead because of increased dissipation. So it is useful to put the relevant designs in this perspective when evaluating their performance, if pressure drop information is available, which is rarely the case. Most of the micro- mixers incorporating secondary flow–generating elements can be viewed as stirring devices often involving chaotic advection mechanisms.
It is well known that bends in channels generate secondary flows at mod- estly high, to high Reynolds numbers in the laminar regime. This has been employed by several investigators and mixers with bends have been used in integrated chips.27 The same principle, augmented by elastic-fluid insta- bilities, was also demonstrated to be effective in improving mixing on the microscale by Pathak et al.28 for non-Newtonian fluids in low-aspect-ratio serpentine microchannels. Arrays of modest-aspect-ratio (2) single-level, ser- pentine (zigzag) microchannels combined with simple Ψ-junction mixers were introduced and used by Kamidate et al.,29 and more recently by Lin et al.,30 to successfully generate, in a predictable manner, dynamically con- trolled spatial and temporal concentration gradients on glass-covered poly- dimethylsiloxane (PDMS) microchips embossed using silicon mold inserts.
A numerical study by Mengeaud et al.31 indicates that successive bends in serpentine (zigzag) channels improve mixing at high Reynolds numbers (O[102]), and that increasing the number of bends per unit length of channel while holding its width constant, can be detrimental to the mixing enhance- ment. Their results should be put in perspective of the fact that their simu- lations were two-dimensional, while in such flows 3-dimensional effects could be substantial. A passive, single-layer micromixer incorporating com- plex Tesla structures has been demonstrated by Hong et al.32 in a cyclo-olefin- copolymer (COC), low-aspect-ratio (0.45) microchannel fed by a T-junction.
The structures are essentially a combination of a serpentine channel with curved walls and wedgelike obstacles. Improved mixing was realized with this device and attributed to Coanda effects in the curved parts of the channel requiring a modest Reynolds number (6), which is the lowest among the single-layer passive microchannel mixers with bends.
184 Bio-MEMS: Technologies and Applications Three-dimensional (two-level), serpentine, microchannels of low aspect ratio (0.5) fed by a T-junction were introduced by Liu et al.,33 who demon- strated faster and more complete mixing at modestly high Reynolds numbers (up to 75) compared to single-level serpentine and straight channel counter- parts. Standard silicon manufacturing technology was used to realize the 3- dimensional design, which required a two-wafer process and resulted in channels of trapezoidal cross-sections. A similar 3-dimensional two-layer design, realized in PDMS by Park et al.,34 also incorporated rounded channel walls to induce rotation in addition to the bend-induced secondary flows and a splitting and recombination scheme similar to that of Schwesinger et al.14 This design realized improved mixing performance for Reynolds num- bers in the 1 to 50 range. A multilevel 3-dimensional micromixing device of vascular tortuosity was developed and demonstrated by Therriault et al.35 incorporated the effects of bends and flow splitting and recombination on numerous levels, and displayed significant mixing effectiveness improve- ment over a broad Reynolds number range (greater than 1). This improve- ment was shown to increase almost exponentially with the Reynolds number.
Putting the added complexity of a multiple layer process aside and the potentially increased dead volume, the two- and multilayer designs men- tioned in this paragraph could be good candidates for batch production micromixers.
Improved mixing has also been realized through the use of grooved chan- nels as generators of secondary flows. In one of the earliest works, Stroock et al.36 took advantage of chaotic advection generated by secondary flows in low-aspect-ratio (0.35) microchannels bearing angled or herringbone-pat- terned grooves on the bottom surface and demonstrated significant mixing improvement relative to the ungrooved channel baseline. Their glass-cov- ered, Y-junction mixer microchannels were embossed in PDMS using a mold insert fabricated by a two-layer photolithography process on SU-8. About the same time, Johnson et al.37 also demonstrated mixing improvements in low-aspect-ratio (0.43) T-junction mixer microchannels stamped in polycar- bonate (PC) with laser-ablated angled grooves on their bottom surface. A computational parametric study was conducted by Wang et al.38 on the performance of grooved mixing channels; they concluded that the minimum length to generate a single recirculation in the channel depends exponentially on the groove aspect ratio and is relative independent of velocity. In an other numerical study, Liu et al.39 revealed that at low Reynolds numbers (1), both the 3-dimensional serpentine channel mixer (e.g., as in Liu et al.33) and the one employing a herringbone groove pattern on the channel wall (e.g., as in Stroock et al.36) perform comparably, while at a higher Reynolds number (10) the serpentine design maintains its performance while the one with the herringbone grooves does not. Nevertheless, added manufacturing complex- ity and added dead volume notwithstanding, grooved channels have been proven to be effective means for enhancing mixing on the microscale in low- aspect-ratio microchannels at low to modest Reynolds numbers. They could
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Micromixers 185 be promising for integration into multifunction biochips especially if man- ufactured successfully on various biocompatible materials.
The potential of attaining improved mixing by placing obstacles in micro- channels has also been explored. While it is well known that at very low Reynolds numbers obstacles cannot generate secondary flows such as recir- culations, it is possible to achieve this at higher Reynolds numbers. This was also shown in a numerical study by Wang et al.,40 who investigated the effect on mixing due to various arrangements of cylindrical obstacles in a micro- channel. An effective micromixer incorporating staggered cylindrical obsta- cles in a mixing chamber was demonstrated by Lin et al.41 on a silicon chip generating fluid streams of high Reynolds numbers (approximately 380). A ceramic cross-junction microchannel mixer with sidewall obstacles was dem- onstrated also at high Reynolds numbers (greater than 100) by Wong et al.42 This configuration produces essentially a serpentine channel and the benefits are predominantly due to the successive bends. Micromixers employing obstacles can be realized with relative ease using single-layer or wafer man- ufacturing processes, yet the high Reynolds number requirements imply high operating pressures, which is the major drawback of this approach.
Swirl chambers have also been employed on the microscale to achieve effective mixing. The multi-inlet design of Böhm et al,43 realized in a glass- covered silicon chip using two wafers and DRIE is an early example of this type. It was a very effective mixing device, but required very high pressures (15 atmospheres) and a costly manufacturing process. Recently Lin et al.44 simulated and demonstrated a multi-inlet swirl-chamber micromixer with performance at low Reynolds numbers (less than 20) realized in a multilayer silicon chip. Swirl-chamber mixers can be effective micromixing devices, but in general they require multilayer manufacturing, high pressures, and increased volume.
A combination of a microvalve and chamber design was realized by Vold- man et al.45 to provide both mixing and valving action on a glass-covered silicone chip. This was micromanufactured in two silicon wafers, one of which incorporated a cantilevered flap-valve element, and required DRIE.
This dual-function device, which performed reasonably well in terms of mixing time for batch applications, could also be used as an active mixer with improved performance by pulsing the supply of the valved fluid.