Fluid mixing enhancement through chaotic advection in mini micro channel 4

Chapter Conclusions and Recommendations Chapter Conclusions and Recommendations 8.1 Conclusions In this dissertation, we have investigated passive chaotic mixing in 3D microchannel, including the effectiveness of various configurations, the analysis and characterization methods, and influencing factors. Relevant information provides some reference for the design and optimization of chaotic micromixers. (1) New chaotic micromixer design, fabrication and experimental test A novel configuration, i.e. the two-layer-crossing-channel structure has been developed for passive chaotic mixing. It provides an efficient way for fluid manipulations, and hence to achieve chaotic advection in microchannels. Two chaotic mixers were proposed that not rely on fluid inertial effects. Rapid chaotic mixing can be achieved even at extremely low Reynolds numbers. The two-layer structure of the design can be easily realized using commonly accessible 3D micro-fabrication techniques. Numerical methods were first applied to examine the potential design, including the CFD analysis, the particle-tracing simulation and the quantification of mixing. Then the mixer was fabricated and experimentally tested. We have demonstrated the laser fabrication of PMMA mixer. This method is very flexible to allow design changes and is useful for rapid prototyping. Soft lithography was used for making miniature PDMS mixer. An optical method was introduced to examine the mixing quality. The applied fluid is highly viscous glycerol solution containing dye or — 167 — Chapter Conclusions and Recommendations chemical indicators, which guarantees a stringent test. The experimental observations agree well with the simulation results, further confirming the high mixing efficiency of the current design. (2) Dynamical analysis of chaotic mixing in spatial-periodic 3D flow For a mixer consisting of periodic structures, the flow in each mixer unit remains the same and can be projected onto a 3D torus. Thus relevant dynamical tools can be employed to analyze the flow and mixing. We first discussed a characterization method which combines (i) the dispersion rate of the fluids; and (ii) the Poincaré mapping information. The combination of the two allows us to reveal the dynamical properties of a chaotic mixer, such as being totally chaotic, partially chaotic or stable. Second, the Poincaré mapping approach was studied. For a practical flow, the specific description of the mapping function is usually not available. However, the mapping relationship can still be established using some approximation methods. In this study, the triangular weighted interpolation, Shepard’s method, and the least-square polynomial fitting were analyzed. The predicted mixing results using the mapping approach agree well with the data obtained from CFD studies. It provides an alternative way to examine the micromxier with spatial-periodic structures, and the enormous resources involved in CFD simulation can be greatly reduced. We also investigated the mechanism to produce chaotic flow in 3D microchannel. Many analyses have shown that chaos can be generated through applying perturbations on rotating flow. A detailed analysis of the flow in a partial chaotic mixer and TLCCM-B suggests that it follows a quasi-periodic route to chaos. As has been discussed, the periodic flow in the mixer can be projected into a 3D torus. — 168 — Chapter Conclusions and Recommendations The movement around the torus and the rotation in the Poincaré section introduce two interacting frequencies, resulting in either periodic or quasi-periodic behaviors. When perturbations are applied, the flow becomes unstable and transits to chaos. To further explain the linkage between the physical chaotic flow and dynamical systems, a prototype mathematical model is studied to imitate the cross-sectional flow in TLCCM-B. The numerical experiments allow us to further explore the different phenomena observed in the flow, such as periodic and chaotic behaviors. The findings can be used for practical chaotic micromixer design. (3) Influence of Re and geometrical effects For the same mixer, its mixing capability may exhibit much difference depending on the applied Reynolds number. It reflects the influences of fluid inertial effects. As an example, the mixing in a 3D serpentine channel was studied at different Re. When Re is small enough that fluid inertial forces can be neglected, the flow approaches the linear Stokes flow. Correspondingly, the mixing (without diffusion) becomes reversible. This phenomenon was demonstrated with a co-joined serpentine channel. With increase of Re, the fluid inertial forces begin to play a more important role. Stirring of the fluids becomes easier. In this Re range, the Dean instability and the self-rotation effects can be employed for micromixer design. The geometrical effects on passive chaotic mixing were also analyzed. Generally, the geometrical structure of a passive mixer should be complex enough to cause effective perturbations. Otherwise, simple structures may result in partial chaos and invariant flow structures. Our studies showed that it could be avoided through a proper reorientation of the channel. Even a slight change of the channel geometry may alter the flow pattern and remove the invariant flow structures. The mixing in — 169 — Chapter Conclusions and Recommendations microchannel with patterned grooves was also discussed. Changing the groove length can enhance the fluid mixing. For the SHM mixer, using deeper grooves can accelerate the rotation of flow. The number of grooves included per mixer unit can be reduced to obtain a shorter mixing length. 8.2 Recommendations In the current study, we have concentrated on the design and analysis of passive chaotic micromixers. In the future, investigations may be carried out on the following aspects. (1) Influence of chaotic flow on diffusive mixing For the inert-particle-tracing method as applied in current study, the fluid uniformity as represented by the tracing particles is obtained solely through advection process. For practical fluid mixing, it also includes the diffusive mixing besides that through advection process. It will accelerate and may also change the profile of mixing. For example, non-diffusive tracers cannot penetrate the closed KAM surface. In contrast, the invariant flow structures can be eliminated in the long run through molecular diffusion (Jones, 1994). The chaotic flow favors the diffusive mixing in the following two aspects. First, the stretching and folding of the fluids always increase the area of the material interface. It allows the diffusion to occur over a larger area. Second, in the direction perpendicular to the stretching direction, the fluid striation thickness is reduced. In the meantime, the concentration gradient is increased. It will further promote the mixing as the diffusion flux is proportional to the concentration gradient. These issues can be examined in future studies. — 170 — Chapter Conclusions and Recommendations (2) Potential applications of current chaotic mixer The micromixer is an important component in many microfluidic systems. In recent years, there have been increasing reports on its applications. For the current TLCCM mixer, it exhibits rapid mixing at Re[...]... The Kinematics of Mixing: Stretching, Chaos, and Transport New York: Cambridge University Press Ottino JM 1990 Mixing, chaotic advection and turbulence Annu Rev Fluid Mech 22:207-253 Ottino JM, Leong CW, Rising H, Swanson PD 1988 Morphological structures produced by mixing in chaotic flows Nature 333 :41 9 -42 5 — 185 — References Ottino JM, Wiggins S 20 04 Designing optimal micromixers Science 305 :48 5 -48 6... 23: 346 1- 347 3 Nguyen NT, Wu ZG 2005 Micro- mixers - a review J Micromech Microeng 15:R1-R16 Nishijima Y, Oster G 1960 Diffusion in glycerol-water mixture Bulletin of the Chemical Society of Japan 33(12): 1 649 -1651 Niu X, Lee TK 2003 Efficient spatial-temporal chaotic mixing in microchannels J Micromech Microeng 13 :45 4 -46 2 Oldshue JY 1983 Fluid mixing technology New York: Chemical Engineering McGraw-Hill Ottino... mixing using bubbles in branched microfluidic channels Appl Phys Lett 86: 244 108 (1-3) Glasgow I, Aubry N 2003 Enhancement of microfluidic mixing using time pulsing Lab Chip 3:1 14- 120 Grumann M, Geipel A, Riegger L, Zengerle R, Ducrée J 2005 Batch-mode mixing on centrifugal microfluidic platforms Lab Chip 5:560-565 Guer YL, Schall É 20 04 A mapping tool using anisotropic unstructured meshes to study mixing. .. References Micromech Microeng 15:935- 943 Liu M, Muzzio FJ, Peskin RL 19 94 Quantification of mixing in aperiodic chaotic flows Chaos, Solitons & Fractals 4: 869-893 Liu RH, Grodzinski P 2003 Development of integrated microfluidic system for genetic analysis J Microlith Microfab Microsyst 2 (4) : 340 -355 Liu RH, Lenigk R, Druyor-Sanchez RL, Yang J, Grodzinski P 2003 Hybridization enhancement using cavitation microstreaming... using micromixing Selective friedelcrafts aminoalkylation J Am Chem Soc 127:11666-11675 Nagata S 1975 Mixing: Principles and Applications New York: Wiley Neils C, Tyree Z, Finlayson B, Folch A 20 04 Combinatorial mixing of microfluidic streams Lab Chip 4: 342 -350 Ng JMK, Gitlin I, Stroock AD, Whitesides GM 2002 Components for integrated poly(dimethylsiloxane) microfluidic systems Electrophoresis 23: 346 1- 347 3... 2005 A serpentine laminating micromixer combing splitting/recombination and advection Lab chip 5:739- 747 Kim DS, Lee SW, Kwon TH, Lee SS 20 04 A barrier embedded chaotic micromixer J Micromech Microeng 14: 798-805 Kim J, Xu X 2003 Excimer laser fabrication of polymer microfluidic devices J Laser Appl 15 (4) :255-260 Klank H, Kutter JP, Geschke O 2002 CO2-laser micromachining and back-end processing for rapid... Woolley AT 2003 Thermal bonding of polymeric capillary electrophoresis microdevices in water Anal.Chem.75:1 941 -1 945 — 180 — References Khakhar DV, Rising H, Ottino JM 1988 Analysis of chaotic mixing in two model systems J Fluid Mech 172 :41 9 -45 1 Khakhar DV, Franjione JG, Ottino JM 1987 A case study of chaotic mixing in deterministic flows: the partitioned-pipe mixer Chem Eng Sci 42 :2909-2926 Kim DS, Lee... Chem 76:18 24- 1831 Liu RH, Yang J, Pindera MZ, Athavale M, Grodzinski P 2002 Bubble-induced acoustic micromixing Lab Chip 2:151-157 Liu YH, Zumbrunnen DA 1999 Toughness enhancement in polymer blends due to the in- situ formation by chaotic mixing of fine-scale extended structures J Mater Sci 34: 1921-1931 Lu LH, Ryu KS, Liu C 2002 A magnetic microstirrer and array for microfluidic mixing J Microelectromech... transfer enhancement by pulsatile laminar flow in an axisymmetric wavy channel Int J Heat Mass Transfer 42 : 2571-2581 Lee CY, Lee GB, Fu LM, Lee KH, Yang RJ 20 04 Electrokinetically driven active micro- mixers utilizing zeta potential variation induced by field effect J Micromech Microeng 4: 1390-1398 Lee CY, Lee GB, Lin JL, Huang FC, Liao CS 2005 Integrated microfluidic systems for cell lysis, mixing/ pumping... 1997 Microchannel electrophoretic separations of DNA in injection-molded plastic substrates Anal Chem 69:2626-2630 McDonald JC, Chabinyc ML, Metallo SJ, Anderson JR, Stroock AD, Whitesides GM 2002 Prototyping of microfluidic devices in poly(dimethylsiloxane) using solid-object printing Anal Chem. 74: 1537-1 545 Mengeaud V, Josserand J, Girault HH 2002 Mixing processes in a zigzag microchannel: finite . Meiners JC. 20 04. Topologic mixing on a microfluidic chip. Appl. Phys. Lett. 84: 2193-2195 Chien W-L, Rising H, Ottino JM. 1986. Laminar and chaotic mixing in several cavity flows. J. Fluid. Mech Fractals 4: 929- 940 Jones SW, Aref H. 1988. Chaotic advection in pulsed source-sink systems. Phys. Fluids 31(3) :46 9 -48 5 Jones SW, Thomas OM, Aref H. 1989. Chaotic advection by laminar flow in a. microfluidic components. Lab Chip 6: 540 - 549 Muzzio FJ, Meneveau C, Swanson PD, Ottino JM. 1992. Scaling and multifractal properties of mixing in chaotic flows. Phys. Fluids A 4: 143 9- 145 6 References