Fluid mixing enhancement through chaotic advection in mini micro channel 1

FLUID MIXING ENHANCEMENT THROUGH CHAOTIC ADVECTION IN MINI/MICROCHANNEL XIA HUANMING (M. Eng., National University of Singapore) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2009 Acknowledgements First, I would like to express my sincere gratitude to my supervisors, Professor Shu Chang and Professor Chew Yong Tian, for their invaluable guidance, close concern, patience and encouragement. Their warm support throughout this work is deeply appreciated. In addition, I wish to thank Dr Stephen Wan from Singapore Institute of Manufacturing Technology (SIMTech), who willingly shares his invaluable experience in experiments and simulation. Assistance from Miss Tan Joo Lett, Mr. Teh Kim Ming in laser processing work is also appreciated. Special thanks to Dr Wang Zhenfeng and Mr Ricky Theodore TJEUNG for their kind help for fabrication of PDMS microfluidic mixer. I would like to acknowledge the National University of Singapore for awarding me the research scholarship and providing me an opportunity to conduct this research at Mechanical Engineering Department. I would also thank all the staff members in the Fluid Division for their valuable assistance. Finally, I am very grateful to my family for their love and support. Thanks also go to all my friends for their help during my study in NUS. — i — Table of Contents Acknowledgements i Table of Contents ii Summary vii Nomenclature ix List of Figures xi List of Tables xix Chapter Introduction 1.1 A brief retrospect on fluid mixing study 1.1.1 Mixing and its applications 1.1.2 Fluid mixing mechanisms and traditional mixing devices 1.2 New issue — fluid mixing at micro scales 1.2.1 Microfluidics and the need of micro fluid mixing 1.2.2 The difficulty of micro fluid mixing 1.2.3 Micromixers and their classification 10 1.3 Fluid mixing enhancement through chaotic advection 15 1.3.1 Development of chaotic advection 15 1.3.2 Chaotic mixing and its applications 17 1.3.3 Chaotic microfluidic mixer 18 1.4 Objectives of the present study 22 1.5 Organization of the dissertation 24 — ii — Chapter Numerical and Experimental Methods 2.1 Numerical approach 26 2.1.1 Relevant numerical set-ups for CFD simulation 27 2.1.2 Convection-diffusion model 28 2.1.3 Inert-particle-tracing method 31 2.2 Quantification of mixing 33 2.2.1 Stretching of the material interface 34 2.2.2 Standard deviation based on the particle-tracing method 35 2.3 Error analysis and validation of simulation results 37 2.4 Experimental mixing test 39 Chapter Rapid Chaotic Micromixer 3.1 Novel design of passive chaotic micromixer 41 3.1.1 New configuration for efficient passive chaotic mixing 41 3.1.2 Geometrical structure of TLCCM mixer 44 3.2 Flow pattern analysis 46 3.2.1 Flow in TLCCM-A 46 3.2.2 Flow in TLCCM-B 48 3.3 Results of the convection-diffusion model 49 3.4 Results of inert-particle-tracing simulation 53 3.4.1 Examples of particle trajectories 53 3.4.2 Cross-sectional mixing results 55 3.4.3 Stretching of the material interface 59 3.5 Pressure loss 61 3.6 Conclusions 62 — iii — Chapter Fabrication and Experimental Testing 4.1 Introduction on fabrication of microfluidic devices 64 4.2 Meso-scale mixer devices for preliminary testing 66 4.2.1 Fabrication processes 66 4.2.2 Experimental mixing results 67 4.3 Miniature PMMA mixer for further confirmation 70 4.3.1 Direct laser cutting of microchannel 70 4.3.2 Thermal bonding of PMMA substrates 72 4.3.3 Experimental mixing results 76 4.4 Miniature PDMS mixer 78 4.5 Mixing test using chemical method 81 4.5.1 Testing method 81 4.5.2 Mixing results 82 4.6 Conclusions 83 Chapter Analysis of Three-dimensional and Spatial-periodic Chaotic Mixer 5.1 Projection of a spatial-periodic mixer into a 3D torus 89 5.2 A characterization method with one single mixer unit 90 5.2.1 Lyapunov exponent 90 5.2.2 Averaged dispersion rate of the mixer 93 5.2.3 The mechanism to analyze local mixing properties 96 5.2.4 Results and discussions 98 5.3 The mapping approach 102 — iv — 5.3.1 Methods to approximate the Poincaré map 104 5.3.2 Application to TLCCM-A 110 5.4 Conclusions 118 Chapter Perturbed Rotating Flow and Chaotic Mixing 6.1 Analysis of the partial chaotic mixer 119 6.1.1 A rotating flow with intermittent perturbation 119 6.1.2 Observation of periodic and chaotic flow behaviors 122 6.1.3 The transition to chaotic flow 126 6.2 TLCCM-B — two interacting rotating flows 128 6.3 Numerical experiments on two-coupled rotating flows 130 6.3.1 Definition of the flow system 130 6.3.2 Numerical experiments 131 6.4 Some discussion on 3D steady and 2D unsteady chaotic flow 137 6.5 Conclusions 140 Chapter Reynolds Number and Geometrical Effects on Passive Chaotic Mixing 7.1 Influence of the fluid inertial effects on chaotic mixing 141 7.1.1 Performance of a 3D serpentine mixer at different Re 141 7.1.2 Reversible mixing in a co-joined 3D serpentine channel 146 7.2 Geometrical influences on passive chaotic mixing 149 7.2.1 Elimination of isolated regions through reorientation of fluids 149 7.2.2 Improved mixing in microchannel with grooved surface 154 7.2.3 Optimization of SHM mixer 160 — v — 7.3 Conclusions Chapter 164 Conclusions and Recommendations 8.1 Conclusions 167 8.2 Recommendations 170 References 173 Appendix A Experimental Apparatus 191 Appendix B CO2 Laser Processing of PMMA 192 Appendix C A Compact TLCCM Mixer 196 — vi — Summary Microfluidics technology has received intensive attention in recent years due to its wide applications in biological and chemical systems. One major issue is to mix fluids at microscopic scales. In micro-geometries, the fluid viscous effect becomes dominant, and micro flow typically falls in the laminar regime. In the absence of turbulence, the fluid mixing becomes purely dependent on diffusion, which is a slow molecular process. On the other hand, in many biological and chemical processes, fast and complete mixing of relevant fluids is of crucial importance. The mixing quality may determine the performance of the whole microfluidic system. In order to meet the mixing requirements, various micromixers have been reported. Active mixers can provide efficient mixing, but involve moving parts and external resources. For passive mixers, many previous designs exhibit dependence on the fluid inertial effects and only work well at relatively higher Reynolds number range. Up to date, micro fluid mixing remains one of the most challenging problems and needs further exploration. In this work, we have studied new passive micromixer design using the chaotic advection mechanism. Novel designs have been developed. The models consist of two branch microchannels that intermittently overlap and interlink across each other. While the fluids are driven through the channel, rapid chaotic mixing can be achieved through the repeated stretching and folding, splitting and recombination process. One apparent advantage of the design is its independence of the fluid inertial effects. Rapid mixing can be achieved even at extremely low Reynolds numbers (Re[...]... created by tracing point (0.5r0, -300) (point 0 in Fig.6.9 (b)) with respect to o1 within in t =10 000 (a) a = 1. 0π , T =1 (b) a = 1. 5π , T =1 135 Fig 6 .11 Exponential divergence between trajectory pair Φ(−0.0 01, 0) and Φ(0.0 01, 0) at a= 1. 5π , T =1, r0 =0.5 13 5 Fig 6 .12 Mixing in the coupled rotation flow system at a = 1. 5π , T =1 The initial material blobs are 0.2 × 0.2 and centered at o1 (0.25, 0), and... applied for continuous operation 1. 2 New issue — fluid mixing at micro scales 1. 2 .1 Microfluidics and the need of micro fluid mixing 1. 2 .1. 1 Development of the microfluidics technology The advent of microfluidics has benefited from the progress in the microanalytical methods and microfabrication technology (Whitesides, 2006) One — 4 — Chapter 1 Introduction motivation is the development of the micro- total-analytical... number of passes on channel geometry 19 4 — xix — Chapter 1 Introduction Chapter 1 Introduction 1. 1 A brief retrospect on fluid mixing study 1. 1 .1 Mixing and its applications Mixing is present in many fields, from the food, pharmaceutical, chemical and environmental industries to our daily life Roughly speaking, mixing means the stirring of initially separated substances to increase the homogeneity It may... released at the centre of inlet 1 and inlet 2 15 7 Fig 7 .18 Mixing results in the microchannel with grooved surface at Re=0.3 (a) Model A, α = 0.33 (b) Model B, α = 0.33 The cross sections are as indicated in Fig 7 .14 (b) (c) Quantified mixing results 15 8 Fig 7 .19 Experimental mixing pictures in grooved channel at Re=0. 01 The applied fluid is 98% glycerol-2% food dye solution 15 9 Fig 7.20 Schematic structure... reconstruction 12 4 Fig 6.3 Reconstructed phase-portraits using [ x( z ), y ( z ), x( z + dz )] They correspond to: (a) Period -1 point ( 41. 5, 14 8) (b) Period3 point (90.6, 16 5.9) (c) Point (24, 13 0) near the edge of the stable region (d) Point (17 , 12 3) in the chaotic area 12 5 Fig 6.4 Divergence of neighboring particle trajectories in the partial chaotic mixer 12 6 Fig 6.5 Evolution of examined fluid particles in. .. rotation flows 13 1 — xv — Fig 6.8 Influence of time interval T on chaotic mixing, r0 =0.5, a = 1. 0π The Poincaré sections are created by tracing 10 particles distributed along the x-axis at x= ± 0.0 01 , ± 0.05 , ± 0 .1 , ± 0 .15 and ± 0.2 13 2 Fig 6.9 Particle trajectories at (a) point (0.5r0, 00) and (b) point (0.5r0, -300) with respect to o1 Parameters are: a = 1. 0π , T =1 134 Fig 6 .10 Poincaré section... scientific discipline only from around the 19 50s (Paul et al., 2003) Due to its diversity in applications, early studies on mixing were mainly on a case-by-case basis Relevant discussions can be found in Uhl & Gray (19 66), Nagata (19 75), Oldshue (19 83), and Ottino (19 89) In the current study, we have mainly investigated the fluid mixing problem Basically, fluid mixing involves the reduction in the length... (a) Re=0.2 (b) Re=60 10 2 Fig 5 .12 Triangular weighted interpolation scheme 10 5 Fig 5 .13 Local Shepard method 10 6 Fig 5 .14 Point distribution for mapping approach (Mesh 1, 11 222 points) 11 0 Fig 5 .15 Weighted least-square polynomial fitting (a) before and (b) after improvement (о): supporting points (●): interpolating point, and its exact position on the next plane (□): the mapping position Data are... are indicated by the dashed lines in figure (a) (c) Standard deviation versus the mixer length 16 2 Fig 7.22 Experimental mixing pictures in SHM at Re~0. 01 164 Fig A .1 Experimental apparatus for mixing test of PDMS microfluidic mixer 19 1 Fig B .1 The CO2 Laser system used to fabricate the PMMA mixers 19 2 Fig B.2 Cross-section profile of a microchannel cut by CO2 laser 19 3 Fig B.3 Width/ depth of the channel. .. the top-layer channel The distance between neighboring knot positions is defined as 1( ≈ 636 µm ) Other parameters are consistent with TLCCM-B 15 2 Fig 7 .11 Projection results of the trajectories Φ (- 81. 6, 88.8) and Φ ( 61. 5, 15 2) ( µm ) in the x-y plane M1, Re=0.2 15 2 Fig 7 .12 Distribution of the fluid elements in successive mixer planes in M1 at Re=0.2 15 2 Fig 7 .13 Comparison of the mixing results between . Introduction 1. 1 A brief retrospect on fluid mixing study 1 1. 1 .1 Mixing and its applications 1 1. 1.2 Fluid mixing mechanisms and traditional mixing devices 2 1. 2 New issue — fluid mixing at micro. Chaotic Mixing 7 .1 Influence of the fluid inertial effects on chaotic mixing 14 1 7 .1. 1 Performance of a 3D serpentine mixer at different Re 14 1 7 .1. 2 Reversible mixing in a co-joined 3D serpentine. 1. 2 .1 Microfluidics and the need of micro fluid mixing 4 1. 2.2 The difficulty of micro fluid mixing 8 1. 2.3 Micromixers and their classification 10 1. 3 Fluid mixing enhancement through chaotic