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Mechanics of liquid–liquid interfaces and mixing enhancement in microscale flows

Published online by Cambridge University Press:  19 May 2010

STÉPHANE VERGUET ,
CHUANHUA DUAN ,
ALBERT LIAU ,
VEYSEL BERK ,
JAMIE H. D. CATE ,
ARUN MAJUMDAR  and
ANDREW J. SZERI
STÉPHANE VERGUET
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
CHUANHUA DUAN
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
ALBERT LIAU
Affiliation:
Biophysics Program, University of California, Berkeley, CA 94720, USA
VEYSEL BERK
Affiliation:
California Institute for Quantitative Biosciences, University of California, Berkeley, CA 94720, USA
JAMIE H. D. CATE
Affiliation:
Department of Molecular and Cell Biology, University of California, Berkeley, CA 94720, USA Department of Chemistry, University of California, Berkeley, CA 94720, USA Physical Biosciences Division, Lawrence Berkeley National Laboratory, CA 94720, USA
ARUN MAJUMDAR
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, CA 94720, USA
ANDREW J. SZERI*
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
*
†Email address for correspondence: [email protected]
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Abstract

Experimental work on mixing in microfluidic devices has been of growing importance in recent years. Interest in probing reaction kinetics faster than the minute or hour time scale has intensified research in designing microchannel devices that would allow the reactants to be mixed on a time scale faster than that of the reaction. Particular attention has been paid to the design of microchannels in order to enhance the advection phenomena in these devices. Ultimately, in vitro studies of biological reactions can now be performed in conditions that reflect their native intracellular environments. Liau et al. (Anal. Chem., vol. 77, 2005, p. 7618) have demonstrated a droplet-based microfluidic mixer that induces improved chaotic mixing of crowded solutions in milliseconds due to protrusions (‘bumps’) on the microchannel walls. Liau et al. (2005) have shown it to be possible to mix rapidly plugs of highly concentrated protein solutions such as bovine hemoglobin and bovine serum albumin. The present work concerns an analysis of the underlying mechanisms of shear stress transfer at liquid–liquid interfaces and associated enhanced mixing arising from the protrusions along the channel walls. The role of non-Newtonian rheology and surfactants is also considered within the mixing framework developed by Aref, Ottino and Wiggins in several publications. Specifically, we show that proportional thinning of the carrier fluid lubrication layer at the bumps leads to greater advection velocities within the plugs, which enhances mixing. When the fluid within the plugs is Newtonian, mixing will be enhanced by the bumps if they are sufficiently close to one another. Changing either the rheology of the fluid within the plugs (from Newtonian to non-Newtonian) or modifying the mechanics of the carrier fluid-plug interface (by populating it with insoluble surfactants) alters the mixing enhancement.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 652 , 10 June 2010 , pp. 207 - 240
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Andreas, J. M., Hauser, E. A. & Tucker, W. B. 1938 Boundary tension by pendant drops. J. Phys. Chem. 42, 1001–1019.Google Scholar
Aref, H. 1984 Stirring by chaotic advection. J. Fluid. Mech. 143, 1–21.CrossRefGoogle Scholar
Aref, H. 2002 The development of chaotic advection. Phys. Fluids 14, 1315–1325.CrossRefGoogle Scholar
Behrens, R. A., Crochet, M. J., Denson, C. D. & Metzner, A. B. 1987 Transient free-surface flows: motion of a fluid advancing in a tube. AIChE J. 33, 1178–1186.CrossRefGoogle Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids. Wiley.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.CrossRefGoogle Scholar
Bringer, M. R., Gerdts, J. C., Song, H., Tice, J. D. & Ismagilov, R. F. 2004 Microfluidic systems for chemical kinetics that rely on chaotic mixing in droplets. Phil. Trans. R. Soc. Lond. A 362, 1087–1104.CrossRefGoogle ScholarPubMed
Chang, C. H. & Franses, E. I. 1995 Adsorption dynamics of surfactants at the air/water interface - a critical review of mathematical models, data, and mechanisms. Colloids Surf. A: Physichochem. Engng Asp. 100, 1–45.CrossRefGoogle Scholar
Coyle, D. J., Blake, J. W. & Macosko, C. W. 1987 The kinematics of fountain flow in mold-filling. AIChE J. 33, 1168–1177.CrossRefGoogle Scholar
D'Alessandro, D., Dahleh, M. & Mezic, I. 1999 Control of mixing in fluid flow: a maximum entropy approach. IEEE Trans. Autom. Control 44, 1852–1863.CrossRefGoogle Scholar
Deen, W. 1998 Analysis of Transport Phenomena. Oxford University Press.Google Scholar
Duffy, D. C., McDonald, J. C., Schueller, O. J. A. & Whitesides, G. M. 1998 Rapid prototyping of microfluidic systems in poly(dimethylsiloxane). Anal. Chem. 70, 4974–4984.Google Scholar
Edwards, D., Brenner, H. & Wasan, D. 1991 Interfacial Transport Processes and Rheology. Butterworth–Heinemann.Google Scholar
Eggleton, C. D., Pawar, Y. P. & Stebe, K. J. 1999 Insoluble surfactants on a drop in an extensional flow: a generalization of the stagnated surface limit to deforming interfaces. J. Fluid Mech. 385, 79–99.Google Scholar
Ellis, R. J. 2001 Macromolecular crowding: obvious but underappreciated. Trends Biochem. Sci. 26, 597–604.CrossRefGoogle ScholarPubMed
Graham, D. E. & Phillips, M. C. 1979 a Proteins at liquid interfaces 1. Kinetics of adsorption and surface denaturation. J. Colloid Interface Sci. 70, 403–414.CrossRefGoogle Scholar
Graham, D. E. & Phillips, M. C. 1979 b Proteins at liquid interfaces 2. Adsorption-isotherms. J. Colloid Interface Sci. 70, 415–426.CrossRefGoogle Scholar
Hall, D. & Minton, A. P. 2003 Macromolecular crowding: qualitative and semi quantitative successes, quantitative challenges. Biochem. Biophys. Acta 1649, 127–139.Google Scholar
Hodges, S. R., Jensen, O. E. & Rallison, J. M. 2004 The motion of a viscous drop through a cylindrical tube. J. Fluid Mech. 501, 279–301.Google Scholar
Ikeda, S. & Nishinari, K. 2000 Intermolecular forces in bovine serum albumin solutions exhibiting solidlike mechanical behaviours. Biomacromolecules 1, 757–763.CrossRefGoogle Scholar
Jacob, A. M. & Gaver, D. P. 2005 An investigation of the influence of cell topography on epithelial mechanical stresses during pulmonary airway reopening. Phys. Fluids 17, 031052-1–031052-11.CrossRefGoogle ScholarPubMed
Jensen, O. E., Chini, G. P. & King, J. R. 2004 Thin-film flows near isolated bumps and interior corners. J. Engng Math. 50, 289–309.Google Scholar
Jensen, O. E. & Grotberg, J. B. 1999 The spreading of heat or soluble surfactant along a thin liquid film. Phys. Fluids A5, 58–68.Google Scholar
Liau, A., Karnik, R., Majumdar, A. & Cate, J. H. D. 2005 Mixing crowded biological solutions in milliseconds. Anal. Chem. 77, 7618–7625.CrossRefGoogle ScholarPubMed
Liu, R. H., Stremler, M. A., Sharp, K. V., Olsen, M. G., Santiago, J. G., Adrian, R. J., Aref, H. & Beebe, D. J. A. 2000 Passive mixing in a three-dimensional serpentine channel. J. Microelectromech. Syst. 9, 190–197.Google Scholar
Minton, A. P. 2001 The influence of macromolecular crowding and macromolecular confinement on biochemical reactions in physiological media. J. Biol. Chem. 276, 10577–10580.Google Scholar
Monkos, K. 1994 Viscometric study of human, bovine, equine and ovine hemoglobin in aqueous solution. Intl J. Biol. Macromol. 16, 31–35.CrossRefGoogle ScholarPubMed
Monkos, K. 1996 Viscosity of bovine serum albumin aqueous solutions as a function of temperature and concentration. Intl J. Biol. Macromol. 18, 61–68.CrossRefGoogle ScholarPubMed
Muradoglu, M. & Stone, H. A. 2005 Mixing in a droplet moving through a serpentine channel: a computational study. Phys. Fluids 18, 073305-1–073305-9.Google Scholar
Muradoglu, M. & Stone, H. A. 2007 Motion of large bubbles in curved channels. J. Fluid Mech. 570, 455–466.Google Scholar
Ottino, J. M. 1989 The kinematics of mixing: stretching, chaos and transport. Cambridge University Press.Google Scholar
Ottino, J. M. & Wiggins, S. 2004 Introduction: Mixing in microfluidics. Phil. Trans. R. Soc. Lond. A 362, 923–935.CrossRefGoogle ScholarPubMed
Park, C-W. 1992 Influence of soluble surfactants on the motion of a finite bubble in a capillary tube. Phys. Fluids A4, 2335–2347.CrossRefGoogle Scholar
Roy, R. V., Roberts, A. J. & Simpson, M. E. 2002 A lubrication model of coating flows over a curved substrate in space. J. Fluid Mech. 454, 235–261.CrossRefGoogle Scholar
Satyanarayana, S., Karnik, R. & Majumdar, A. 2005 Stam-and-stick room-temperature bonding technique for microdevices. J. Microelectromech. Syst. 14, 392–399.CrossRefGoogle Scholar
Song, H. & Ismagilov, R. F. 2003 Millisecond kinetics on a microfluidic chip using nanoliters of reagents. J. Am. Chem. Soc. 125, 14613–14619.CrossRefGoogle ScholarPubMed
Song, H., Tice, J. D. & Ismagilov, R. F. 2003 A microfluidic system for controlling reaction networks in time. Angew. Chem. Intl Ed. 42, 768–772.CrossRefGoogle ScholarPubMed
Stauffer, C. E. 1965 Measurement of surface tension by pendant drop technique. J. Phys. Chem. 69, 1933–1938.CrossRefGoogle Scholar
Stroock, A. D., Dertinger, S. K. W., Ajdari, A., Mezic, I., Stone, H. A. & Whitesides, G. M. 2002 Chaotic mixer for microchannels. Science 295, 647–651.CrossRefGoogle ScholarPubMed
Sturman, R., Ottino, J. M. & Wiggins, S. 2006 The Mathematical Foundations of Mixing: The Linked Twist Map as a Paradigm in Applications: Micro to Macro, Fluids to Solids. Cambridge University Press.CrossRefGoogle Scholar
Wiggins, S. & Ottino, J. M. 2004 Foundations of chaotic mixing. Phil. Trans. R. Soc. Lond. A 362, 937–970.CrossRefGoogle ScholarPubMed
Wolfram Research, Inc. 2005 Mathematica Edition: Version 5.2. Wolfram Research, Inc.Google Scholar