Elsevier

Chemical Engineering Science

Volume 65, Issue 5, 1 March 2010, Pages 1865-1874
Chemical Engineering Science

Residence-time distribution as a measure of mixing in T-junction and multilaminated/elongational flow micromixers

https://doi.org/10.1016/j.ces.2009.11.038Get rights and content

Abstract

The ineffective mixing in microchannel mixers or reactors, primarily due to the laminar flow behavior in such microfluidic devices, has become an issue of significant interest to many researchers working in the field of microreaction engineering and related disciplines. The present study describes the numerical and experimental investigation of mixing performance in a proposed multilaminated/elongational flow micromixer (herein referred to as MEFM-4) and a standard T-junction micromixer (TjM). These two micromixers that employ different mixing enhancement strategies were fabricated from silicon using micro-electromechanical systems (MEMS) technology. Computational fluid dynamics (CFD) approach was first used to establish the experimental platform for the mixing study. Tracer experiment utilizing UV–vis absorption spectroscopy detection technique was used to obtain the required concentration data for residence-time distribution (RTD) analysis. The RTD and its coefficient of variation (CoV) were used for indirect characterization of flow and mixing behavior in the micromixers. Using this measure, the proposed MEFM-4, as expected, exhibits a better mixing performance (with its narrower RTD and lower CoV values) than the standard TjM. The comparison of results from the CFD simulation and the experiment shows very good agreement, especially in the low Reynolds number flow regime (Re<29). In combination with matching experiment and advanced microfabrication techniques, CFD simulation is a powerful tool for effective design and evaluation of simple to complex microfluidic devices for useful applications in chemical analysis and synthesis.

Introduction

The unique applications associated with microchemical systems and their components such as micromixers, microreactors, microheat exchangers, etc., have currently made microreaction technology one of the rapidly developing and innovative fields in chemical engineering and related disciplines. The recent rapid advances in micromachining technologies have extended the applications of some microfluidic components for analytical purposes, as in the micro-total analysis systems (μ-TAS) (van den Berg et al., 1994; West et al., 2008), to the design of miniaturized devices for synthetic applications (Burns and Ramshaw, 1999; Haswell et al., 2001). Microchemical systems as a new generation of miniature chemical processing systems would be most attractive where size, weight and safety are critical application issues. Such areas of potential or established applications include on-demand/on-site synthesis of specialty and toxic chemicals (Burns and Ramshaw, 1999; Voloshin et al., 2007); biological analysis in medicine, forensics, and environmental control; fuel cells for power applications; and high-performance, lightweight systems for space exploration needs (Wegeng et al., 1996).

Mixing in microchannels is one of the most important technical issues that are critical to the development and application of microchemical systems. For applications such as kinetic studies of fast reactions, effective and rapid mixing of fluids is very important. Despite the fact that microchannel fluidic devices possess very high surface-to-volume ratio that is beneficial for high mass and heat transfer rates (with shorter residence time), their small transverse dimensions along with low processing flow rate are a critical drawback to achieve good mixing. In essence, the microscale devices’ geometrical and/or operational parameters inherently lead to diffusion-dominated laminar flow (low Reynolds number, Re, typically between 0.1 and 100). In recognition of the fact that mixing is a challenge, quite a number of research papers along with extensive reviews on micromixers (Hessel et al., 2005; Nguyen and Wu, 2005) have been published. Different investigators have studied theoretically and/or experimentally various devices and methods to effect rapid mixing either passively or actively in micromixers. Active mixers rely on moving structure or a time-variant pressure and/or electric field (Nguyen and Wu, 2005), for instance, to enhance mixing. Issues such as cost and complexity of fabrication, heat generation, and non-compatibility with biological or delicate samples, have limited application of active micromixers. In contrast, passive mixers effect mixing using static or passive mixing structures and various mixing strategies have been widely studied. Apart from the standard T-junction or T-shaped micromixer (Adeosun and Lawal, 2009b; Bothe et al., 2006; Engler et al., 2004; Hoffmann et al., 2006), the staggered herringbone mixer (Stroock et al., 2002) is another passive micromixer that has been studied extensively.

Passive mixers are also of interest in this study, especially those utilizing the mechanisms of fluid lamination, split-and-recombine or elongational flow, and “geometric focusing” for mixing enhancement. Branebjerg et al. (1996) performed theoretical, numerical, and experimental investigation of flow and mixing behavior in a multi-stage multilaminated micromixer (made from Pyrex-glass and silicon) developed for μ-TAS application. By performing mixing experiments utilizing fast reaction of phenol red and acid, complete mixing was reported in 100–300 ms in this micromixer operating in the flow range of 1–10 μL/min. Bessoth et al. (1999) designed an efficient, silicon/glass-made microstructure mixer (with internal volume of ∼600 nL) based on the principle of flow lamination and split-and-recombine distributive mixing. The mixing quality of the mixer was assessed using flow visualization and fluorescence quenching experiments and found the mixer to attain 95% mixing within 15 ms. Veenstra et al. (1999) reported a simple characterization method of mixing phenolic solution into water for a diffusion micromixer, whose design is based on “geometric focusing” or simple narrowing of the mixer's single channel. This mixer that is applicable to flow injection analysis systems was found to exhibit complete mixing for flow rates <2 μL/min.

In the present study, the proposed MEFM-4 is designed for higher throughput than the above-reviewed micromixers and it combines the mechanisms of fluid multilamination, elongational flow, and geometric focusing for effective mixing enhancement. The MEFM-4 is evaluated along with the standard TjM for their mixing performance. Microchannel mixers can be turned into microreactors by coating or packing them with catalytically active material (Losey et al., 2002) or as in case of homogeneous catalytic microreactors where a catalyst is present in the solution with at least one of the reactants (Fogler, 1999). Silicon is chosen, from among other materials such as ceramics, glass, metals, and polydimethylsiloxane (PDMS), as the substrate material for the fabrication of our mixing devices. The reasons for choosing silicon include the existence of well-established and adaptable MEMS microfabrication technology (Madou, 2002); excellent physical and chemical properties; and the prospect of integrating silicon-based and glass-based flow and temperature micro-sensors with microsystems for analytical and synthesis purposes (Jensen, 2006).

In order to characterize theoretically and/or experimentally the extent of mixing behavior in microfluidic devices, investigators used measures/methods such as flow visualization of test solutions (containing a chemical indicator) and imaging (Liu et al., 2000; Stroock et al., 2002), test chemical reactions such as “Villermaux–Dushman” competing parallel reactions (Ehrfeld et al., 1999; Panic et al., 2004), and RTD (Adeosun and Lawal, 2005; Boskovic and Loebbecke, 2008; Cantu-Perez et al., 2008; Trachsel et al., 2005). Other measures for quantification of the degree of mixing include intensity of segregation (Wong et al., 2003), particle tracking method (Aubin et al., 2003), Poincare section analysis (Beebe et al., 2001), and Lyapunov exponent (Suzuki and Ho, 2002). The non-availability to-date of commercial on-chip micro mixing sensors makes the experimental quantitative evaluation of the degree of mixing in micromixers a formidable challenge. Flow visualization and imaging that has been used by many researchers is a generally fast, relatively simple, and optically desirable mixing characterization method. However in most cases, the accuracy of this method is dependent on a number of factors such as the sensitivity of test solutions, low local resolution of instrumentation, and slow response of the data/image acquisition system for the objective characterization of mixing quality. These concerns were confirmed by our preliminary flow visualization experiments using fluorescence microscopy. Therefore, using direct or indirect measures of mixing other than flow visualization/imaging is highly desirable. In this study, RTD is chosen as an indirect mixing characterization measure. In fact, from reaction engineering's perspective, RTD data obtained from tracer experiments can also be used to estimate conversion or “conversion bounds” (for reacting fluids) in non-ideal flow systems (Fogler, 1999) such as microreactors.

The objective of this work is to apply the concept of RTD to the numerical and experimental investigation of mixing in two MEMS-based micromixers—standard and proposed mixing-enhanced configurations. Firstly, the computational fluid dynamics (CFD) software package, FLUENT™ interfaced with preprocessor Gambit, was adaptively used for the numerical simulation of a tracer (or stimulus–response) experiment in the microscale flow systems. For the tracer experiment, the concentration data have to be obtained and analyzed in such a manner that the effects of the usual imperfect injection of tracer and connecting tubings are considerably reduced. Therefore, “convolution integral” theorem (Levenspiel, 1999) was used to obtain a model description of the RTD data for the mixing devices. This theorem and the semi-empirical model used are discussed in the experimental section of this study. Finally, the simulation and the experimental results are compared, while the performance of the micromixers is evaluated using RTD and one of its characteristics. This work is aimed at expanding the knowledge base essential to the establishment of rational and efficient procedure for the design and evaluation of effective microchannel mixers.

Section snippets

Microchannel configurations studied

The proposed MEFM-4 (shown in Fig. 1) was investigated along with a standard TjM (shown in Fig. 2) for their mixing performance. The design of the TjM is based on the simple mixing concept of contacting two substreams of fluids at the T-junction while the MEFM-4 was designed based on the concept of fluid multilamination and elongational flow. The fluid multilamination in MEFM-4 leads to the desired reduction in diffusion path of fluids in the flow transverse direction while the elongational

Fabrication of micromixers

The fabrication and packaging of both the standard TjM and our proposed MEFM-4 were successfully completed using the state-of-the-art facilities at Cornell Nanofabrication Facility (CNF) and Applied Microengineering Ltd. (AML). The micromixers were made from silicon and Pyrex™ using MEMS microfabrication technology and the associated microchannel fabrication and packaging methods (Madou, 2002; Verpoorte and De Rooij, 2003). Double-side polished silicon wafers (p-type 〈1 0 0〉 4-in diameter) 800-

Comparison of experimental results with numerical predictions

Experimental and numerical data were obtained at volumetric flow rates (Q) of 0.25, 0.40, 0.50, and 0.60 mL/min since a flow rate range of 0.25–0.60 mL/min was found to be highly suitable for our setup. The associated low Reynolds number range is 6.4–28.4. The Reynolds number (Re=uLc/υ) and fluid Peclet number (Pe=uLc/DAB) are shown in Table 1, Table 2. The calculations of Re and Pe are based on the outlet cross-sectional areas of the microchannel mixers (1000 μm by 300 μm for MEFM-4; 400 μm by 300 

Conclusions

The mixing performance in a multilaminated/elongational flow micromixer (MEFM-4) and T-junction micromixer (TjM) was investigated experimentally as well as numerically. The work involved the use of CFD simulations as a vital design, optimization and characterization tool; fabrication of the mixing units using silicon-MEMS technology; and performing experiments to validate the numerical predictions of the mixing characterization. RTDs and its CoV values, obtained by analyzing the concentration

Notation

A(t)absorbance as a function of time, dimensionless
C(t)tracer concentration in the outlet stream as a function of time, kg/m3
Cin(tt)measured inlet concentration of the tracer at a time (tt′), kg/m3 or dimensionless
Coutm(t)measured output concentration data at a time t, kg/m3 or dimensionless
Coutp(t)predicted outlet concentration of the tracer at a time t, kg/m3 or dimensionless
DABbinary diffusivity for system A–B, m2/s
E(t)residence-time distribution function obtained directly, s−1
E(t)

Acknowledgments

The authors gratefully acknowledge the grants provided by The Department of Energy-Industrial Technologies Program (DOE-ITP) and American Chemical Society Petroleum Research Fund (ACS PRF) in support of this research project. The silicon and glass microfabrications were performed in part at the Cornell NanoScale Facility (CNF), a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765). We would also like to thank

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