Quantifying mixing using equilibrium reactions

Physics of Fluids

Volumn 21, Issue 3, 2009, Pages

  Wheat, Philip M ^a   Posner, Jonathan D ^a  

^a Arizona State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; CALCIUM CHLORIDE; DIFFUSION IN LIQUIDS; DISSOCIATION; FLUORESCENCE; MICROCHANNELS;

ADVECTION-DIFFUSION EQUATION; BACKGROUND CONCENTRATION; EQUILIBRIUM REACTIONS; PRODUCT CONCENTRATION; QUANTITATIVE MEASUREMENT; QUANTITATIVE MEASURES; REACTANT CONCENTRATIONS; THREE-DIMENSIONAL STRUCTURE;

MIXING;

EID: 64249095807     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3078247     Document Type: Article

References (33)

1. R. K. Thakur, C. Vial, K. D. P. Nigam, E. B. Nauman, and G. Djelveh, "Static mixers in the process industries - A review," Chem. Eng. Res. Des. CERDEE0263-876210.1205/026387603322302968 81, 787 (2003).
2. M. W. Thring, "Some recent developments in the physics of fuel combustion," Br. J. Appl. Phys. BJAPAJ0508-344310.1088/0508-3443/8/ 3/301 8, 89 (1957).
3. R. H. Liu, M. A. Stremler, K. V. Sharp, M. G. Olsen, J. G. Santiago, R. J. Adrian, H. Aref, and D. J. Beebe, "Passive mixing in a three-dimensional serpentine microchannel," J. Microelectromech. Syst. JMIYET1057-715710.1109/84.846699 9, 190 (2000).
4. H. Roder, K. Maki, and H. Cheng, "Early events in protein folding explored by rapid mixing methods," Chem. Rev. (Washington, D.C.) CHREAY0009-266510.1021/cr040430y 106, 1836 (2006).
5. D. E. Hertzog, X. Michalet, M. Jager, X. X. Kong, J. G. Santiago, S. Weiss, and O. Bakajin, "Femtomole mixer for microsecond kinetic studies of protein folding," Anal. Chem. ANCHAM0003-270010.1021/ ac048661s 76, 7169 (2004).
6. D. R. Reyes, D. Iossifidis, P. A. Auroux, and A. Manz, "Micro total analysis systems. 1. Introduction, theory, and technology," Anal. Chem. ANCHAM0003-270010.1021/ac0202435 74, 2623 (2002).
7. N. T. Nguyen and Z. G. Wu, "Micromixers - A review," J. Micromech. Microeng. JMMIEZ0960-131710.1088/0960-1317/15/2/R01 15, R1 (2005).
8. P. Gravesen, J. Branebjerg, and O. S. Jensen, "Microfluidics - A review," J. Micromech. Microeng. JMMIEZ0960-131710.1088/0960-1317/3/ 4/002 3, 168 (1993).
9. H. A. Stone, A. D. Stroock, and A. Ajdari, "Engineering flows in small devices: Microfluidics toward a lab-on-a-chip," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.36.050802.122124 36, 381 (2004).
10. V. Hessel, H. Lowe, and F. Schonfeld, "Micromixers - A review on passive and active mixing principles," Chem. Eng. Sci. CESCAC0009-250910.1016/j.ces.2004.11.033 60, 2479 (2005).
11. S. Allison, C. Y. Chen, and D. Stigter, "The length dependence of translational diffusion, free solution electrophoretic mobility, and electrophoretic tether force of rigid rod-like model duplex DNA," Biophys. J. BIOJAU0006-349510.1016/S0006-3495(01)75900-0 81, 2558 (2001).
12. J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, Cambridge, 1989).
13. J. G. Vandevusse, "Mixing by agitation of miscible liquids. 1.," Chem. Eng. Sci. CESCAC0009-250910.1016/0009-2509(55)85020-8 4, 178 (1955).
14. P. V. Danckwerts, "Continuous flow systems. Distribution of residence times," Chem. Eng. Sci. CESCAC0009-250910.1016/ 0009-2509(53)80001-1 2, 1 (1953).
15. A. D. Stroock, S. K. W. Dertinger, A. Ajdari, I. Mezic, H. A. Stone, and G. M. Whitesides, "Chaotic mixer for microchannels," Science SCIEAS0036-807510.1126/science.1066238 295, 647 (2002).
16. M. S. Munson and P. Yager, "Simple quantitative optical method for monitoring the extent of mixing applied to a novel microfluidic mixer," Anal. Chim. Acta ACACAM0003-267010.1016/j.aca.2003.11.064 507, 63 (2004).
17. S. Panic, S. Loebbecke, T. Tuercke, J. Antes, and D. Boskovic, "Experimental approaches to a better understanding of mixing performance of microfluidic devices," Chem. Eng. J. CMEJAJ0300-946710.1016/j.cej.2003.10.026 101, 409 (2004).
18. P. E. Arratia and J. P. Gollub, "Predicting the progress of diffusively limited chemical reactions in the presence of chaotic advection," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.96.024501 96, 024501 (2006).
19. H. J. Catrakis, R. C. Aguirre, and J. Ruiz-Plancarte, "Area-volume properties of fluid interfaces in turbulence: Scale-local self-similarity and cumulative scale dependence," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002008911 462, 245 (2002); J. Baldyga and J. R. Bourne, "Interpretation of turbulent mixing using, fractals and multifractals," Chem. Eng. Sci. CESCAC0009-250910.1016/ 0009-2509(94)00217-F 50, 381 (1995); P. E. Dimotakis, "Turbulent mixing," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/ annurev.fluid.36.050802.122015 37, 329 (2005); J. M. Ottino, "Mixing, chaotic advection, and turbulence," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.22.1.207 22, 207 (1990).
20. H. Song, J. D. Tice, and R. F. Ismagilov, "A microfluidic system for controlling reaction networks in time," Angew. Chem., Int. Ed. ACIEF51433-785110.1002/anie.200390203 42, 768 (2003).
21. J. Voldman, M. L. Gray, and M. A. Schmidt, "An integrated liquid mixer/valve," J. Microelectromech. Syst. JMIYET1057-715710.1109/ 84.870054 9, 295 (2000).
22. D. A. Walker, "A fluorescence technique for measurement of concentration in mixing liquids," J. Phys. E JPSIAE0022-373510.1088/ 0022-3735/20/2/019 20, 217 (1987).
23. J. D. Posner and J. G. Santiago, "Convective instability of electrokinetic flows in a cross-shaped microchannel," J. Fluid Mech. JFLSA70022-112010.1017/S0022112005008542 555, 1 (2006).
24. A. B. Harkins, N. Kurebayashi, and S. M. Baylor, "Resting myoplasmic free calcium in frog skeletal-muscle fibers estimated with Fluo-3," Biophys. J. BIOJAU0006-349510.1016/S0006-3495(93)81112-3 65, 865 (1993).
25. F. A. Lattanzio and D. K. Bartschat, "The effect of ph on rate constants, ion selectivity and thermodynamic properties of fluorescent calcium and magnesium indicators," Biochem. Biophys. Res. Commun. BBRCA90006-291X10.1016/0006-291X(91)91966-G 177, 184 (1991).
26. C. N. Baroud, F. Okkels, L. Menetrier, and P. Tabeling, "Reaction-diffusion dynamics: Confrontation between theory and experiment in a microfluidic reactor," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.67.060104 67, 060104 (2003).
27. R. K. Shah and A. L. London, Laminar Flow Forced Convection in Ducts (Academic, New York, 1978).
28. J. Crank, The Mathematics of Diffusion, 2nd ed. (Clarendon, Oxford, 1975).
29. E. L. Cussler, Diffusion: Mass Transfer in Fluid Systems, 2nd ed. (Cambridge University Press, New York, 1997).
30. J. C. McDonald, D. C. Duffy, J. R. Anderson, D. T. Chiu, H. K. Wu, O. J. A. Schueller, and G. M. Whitesides, "Fabrication of microfluidic systems in poly(dimethylsiloxane)," Electrophoresis ELCTDN0173-083510.1002/ (SICI)1522-2683(20000101)21:1<27::AID-ELPS27>3.3.CO;2-3 21, 27 (2000).
31. S. Inoue and K. R. Spring, Video Microscopy:THe Fundamentals (Plenum, New York, 1997).
32. A. Minta, J. P. Y. Kao, and R. Y. Tsien, "Fluorescent indicators for cytosolic calcium based on rhodamine and fluorescein chromophores," J. Biol. Chem. JBCHA30021-9258 264, 8171 (1989).
33. M. Naraghi, "T-jump study of calcium binding kinetics of calcium chelators," Cell Calcium CECADV0143-416010.1016/ S0143-4160(97)90064-6 22, 255 (1997).