Chaotic mixing in thermocapillary-driven microdroplets

Liquid microdroplets represent a convenient system for studies of mixing by chaotic advection in discrete microscopic volumes. The mixing properties of the flows in microdroplets are governed by their symmetries, which give rise to invariant surfaces serving as barriers to transport. Thorough mixing via chaotic advection requires destruction of all such invariant surfaces. To illustrate this idea, we demonstrate that quick and thorough mixing inside a spherical microdroplet suspended in a layer of substrate fluid can be obtained by moving the droplet along a two-dimensional path using temperature-induced surface tension gradients. The use of flow invariants also provides a convenient way to analyze the mixing properties of flows in many other experimental implementations.

[1]  Helen Song,et al.  A microfluidic system for controlling reaction networks in time. , 2003, Angewandte Chemie.

[2]  S. C. Hardy,et al.  The motion of bubbles in a vertical temperature gradient , 1979 .

[3]  Geoffrey Ingram Taylor,et al.  The Viscosity of a Fluid Containing Small Drops of Another Fluid , 1932 .

[4]  H. Stone,et al.  Chaotic streamlines in steady bounded three-dimensional Stokes flows , 1999 .

[5]  Michael F Schatz,et al.  Optical manipulation of microscale fluid flow. , 2003, Physical review letters.

[6]  C. Kim,et al.  Enhancement of mixing by droplet-based microfluidics , 2002, Technical Digest. MEMS 2002 IEEE International Conference. Fifteenth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.02CH37266).

[7]  Phil Paik,et al.  Rapid droplet mixers for digital microfluidic systems. , 2003, Lab on a chip.

[8]  M. Burns,et al.  Thermocapillary Pumping of Discrete Drops in Microfabricated Analysis Devices , 1999 .

[9]  A. Neishtadt,et al.  Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow. , 1996, Chaos.

[10]  G. Taylor.  Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  G. Whitesides,et al.  Flexible Methods for Microfluidics , 2001 .

[12]  S. Cho,et al.  Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits , 2003 .

[13]  Chen.  Movement of a Fluid Sphere in the Vicinity of a Flat Plane with Constant Temperature Gradient. , 2000, Journal of colloid and interface science.

[14]  Note on chaotic advection in an oscillating drop , 2003 .

[15]  Sigurd Wagner,et al.  Microfluidic actuation by modulation of surface stresses , 2003 .

[16]  Sandra M. Troian,et al.  Patterning liquid flow on the microscopic scale , 1999, Nature.

[17]  Robin H. Liu,et al.  Passive mixing in a three-dimensional serpentine microchannel , 2000, Journal of Microelectromechanical Systems.

[18]  G. Homsy,et al.  Electrohydrodynamically driven chaotic mixing in a translating drop. II. Experiments , 2003 .

[19]  Arpad Bergh,et al.  The Promise and Challenge of Solid-State Lighting , 2001 .

[20]  S. Wiggins,et al.  On the integrability and perturbation of three-dimensional fluid flows with symmetry , 1994 .

[21]  Howard Brenner,et al.  The Stokes resistance of a slightly deformed sphere , 1964 .

[22]  T. Fujii,et al.  Handling of Picoliter Liquid Samples in a Poly(dimethylsiloxane)-Based Microfluidic Device , 1999 .

[23]  J. Ottino.  The Kinematics of Mixing: Stretching, Chaos, and Transport , 1989 .

[24]  R. Fair,et al.  Electrowetting-based actuation of liquid droplets for microfluidic applications , 2000 .

[25]  S. Strogatz,et al.  Chaotic streamlines inside drops immersed in steady Stokes flows , 1991, Journal of Fluid Mechanics.

[26]  H. K. Moffatt,et al.  On a class of steady confined Stokes flows with chaotic streamlines , 1990, Journal of Fluid Mechanics.

[27]  J. W. Parce,et al.  Electrokinetically controlled microfluidic analysis systems. , 2000, Annual review of biophysics and biomolecular structure.

[28]  I. Kang,et al.  Circulating flows inside a drop under time-periodic nonuniform electric fields , 2000 .

[29]  A. R. Kaiser,et al.  Microfabricated structures for integrated DNA analysis. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[30]  H. Aref.  Stirring by chaotic advection , 1984, Journal of Fluid Mechanics.

[31]  A. Neishtadt,et al.  Chaotic advection in a cubic Stokes flow , 1998 .

[32]  I. Mezić,et al.  Chaotic Mixer for Microchannels , 2002, Science.

[33]  Thomas Ward,et al.  Electrohydrodynamically driven chaotic mixing in a translating drop , 2001 .

[34]  Julyan H. E. Cartwright,et al.  Chaotic advection in three-dimensional unsteady incompressible laminar flow , 1995, Journal of Fluid Mechanics.

[35]  Mass-transfer enhancement via chaotic laminar flow within a droplet , 1999 .

[36]  Phil Paik,et al.  Electrowetting-based droplet mixers for microfluidic systems. , 2003, Lab on a chip.