It is very well known from the most fundamental considerations that on the microscale mixing is driven by diffusion, and that diffusion processes are inherently slow. This is particularly true in the applications of interest where binary mass diffusion coefficients are significantly low on the order of D12 = 1010–1011 m2/s or less. On a macroscale, mixing can be made more effective through turbulent transport, which reduces transport timescales by orders of magnitude relative to diffusive ones, and is commonplace in many systems of everyday and industrial use (e.g., internal combustion engines, gas turbine
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Micromixers 179 combustion systems, chemical reactors, etc.). Turbulent flows are character- ized by large Reynolds numbers, Re = UD/ν, where, U, is a velocity scale representative of the process, D is a length scale and, ν is the kinematic viscosity (or momentum diffusion coefficient) of the fluid. In microfluidic systems the length scales are of micron order (e.g., ranging from 1 mm to 500 mm), and because in bioanalytical applications the fluids are predomi- nantly aqueous solutions, the kinematic viscosity is on the order of 106 m2/s.
The transition Reynolds number from laminar to turbulent flow is approxi- mately 2300 for ducts and channels, so in order to have the benefit of fully developed turbulent flow, the Reynolds number ought to be higher than that. The critical Reynolds numbers for other flows, such as jets and free shear layers, are also on the order of several hundreds. If one wishes to generate turbulent flow (e.g., Re = 5000) in a microchannel 100 µm by 100 µm in cross-section, one requires a velocity of approximately 48m/s. At this velocity the pressure drop in the channel is more than 4 atmospheres per millimeter of length, which is prohibitive. Other than examining the feasi- bility of turbulent microflow, the example brings forth the fact that in addi- tion to the requirement of rapid and effective mixing, one has to be vigilant with respect to the required pressure to drive the microfluidic chip. High pressure requirements are undesirable because they require on-chip, micro- pumping devices able of sustaining them, which at present do not exist. In addition they impose higher loads on microfluidic chip components and make it more prone to leakage if not breakage and/or debonding of bonded surfaces. Increasing the microchannel cross-section alleviates the high pres- sure requirement, but increases the volume of the device. Nevertheless, in the above example, if one uses a 500 µm by 500 µm channel, the pressure drop per unit length of channel for the same Reynolds number is reduced by two orders of magnitude, but the volume of the channel is increased by a factor of 25. Larger chip volume translates into larger amounts of samples and reagents and to some extent negates part of the advantage of reducing bioanalytical processes to the microscale. The example highlights the fact that chip volume is yet another parameter one needs to be vigilant about.
In conclusion, turbulent flow on the microscale for the benefit of achieving effective mixing is not out of the question, but its usefulness is limited because of pressure drop and chip-volume constraints. It is perhaps not surprising that to the extent of the author’s awareness, the highest Reynolds number reported for the operation of a micromixer in the micromixing literature is laminar (500),4 well below the transition to turbulence value, with still a rather high pressure drop of approximately 0.47 atmospheres per millimeter of length. This mixer was a simple T-junction type fabricated in silicon and covered by Pyrex glass. It should be noted that in Wong et al.,4 very fast mixing was demonstrated at this value of the Reynolds number caused by instability in the shear layer formed at the interface of the mixed streams in a low-aspect-ratio channel (0.5) with a hydraulic diameter of 67 µm, but required a pressure of almost 5.5 atmospheres, which is its major operational drawback.
180 Bio-MEMS: Technologies and Applications In the absence of turbulent transport, the only recourse to achieving effec- tive mixing is the reduction of the molecular diffusion length. This follows from basic dimensional considerations because the time required to achieve full mixing is the diffusive time, tD = δD2/D12, necessary for the concentration signal to traverse a length, δD. When the mass diffusion coefficient is very small (<O [10–10 m2/s]) the only way to cut down on the mixing time is to reduce this diffusion length. Almost all efforts to improve mixing perfor- mance on the microscale strive to achieve this by employing a wide variety of means. For example, the so-called lamination micromixers5 pursue the creation of several alternating narrow layers of the compounds to be mixed, so as to cut down on the diffusion length; micromixers based on chaotic advection (chaotic stirring)6,7,8 pursue the same goal by kinematically folding the interfaces between the compounds multiple times; a broad variety of micromixers achieve the same through the use of time-varying external perturbations or exploiting instability mechanisms.
Much like other devices, micromixers are traditionally classified as active or passive depending on whether or not an external energy source is used other than that driving the flow through the device. Although active mixers may effectively provide rapid mixing, it cannot be denied that the additional mechanical and electronic devices, both on- and off- chip, often add undesirable complexity. These additional devices need extra energy, space, and if on-chip, may also be difficult to fabricate and integrate to form a cost-effective and compact lab-on-a-chip. Additionally, electrical fields and heat sometimes generated by active control may dam- age biological samples.9 Different methods and substrates have been used to fabricate both active and passive micromixers, but it is generally agreed that passive mixers are most often easier to fabricate and simpler in design than active mixers. This is more so for pressure-driven devices than elec- trically driven ones.
Several reviews of micromixers have appeared, especially during recent years, and we will mention a few. A brief review of passive and active micromixers can be found in Campbell and Grzybowski10 who also provide a tabulated assessment of performance and manufacturing complexity of a few mixers, but focus their discussion on self-assembled magnetic micromix- ers. Passive micromixers were recently reviewed in Hardt et al.11 A more comprehensive and nicely illustrated review of a broad variety of both pas- sive and active mixers available in the literature is presented in Nguyen and Wu5 and will not be duplicated herein. However, an overview with repre- sentative examples of micromixers from each class will be given here for the benefit of the reader. An overview will be given for passive, active and multiphase flow mixers, the former organized in terms of the driving force used to generate the main flow through the device, as appropriate. The last category (multiphase) is discussed separately, although it contains micro- mixers from both of the other categories, in order to emphasize that the related devices involve an auxiliary passive fluid and moving interfaces.
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Micromixers 181