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Induced-Charge Electrokinetic Phenomena

Paris-Sciences Chair Lecture Series 2008, ESPCI. Induced-Charge Electrokinetic Phenomena. Introduction ( 7/1) Induced-charge electrophoresis in colloids (10/1) AC electro-osmosis in microfluidics (17/1) Theory at large applied voltages (14/2). Martin Z. Bazant

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Induced-Charge Electrokinetic Phenomena

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  1. Paris-Sciences Chair Lecture Series 2008, ESPCI Induced-Charge Electrokinetic Phenomena Introduction (7/1) Induced-charge electrophoresis in colloids (10/1) AC electro-osmosis in microfluidics (17/1) Theory at large applied voltages (14/2) Martin Z. Bazant Department of Mathematics, MIT ESPCI-PCT & CNRS Gulliver

  2. Acknowledgments Induce-charge electrokinetics: Colloids CURRENT Students:Sabri Kilic, Damian Burch, JP Urbanski (Thorsen) Postdoc: Chien-Chih Huang Faculty: Todd Thorsen (Mech Eng) Collaborators: Armand Ajdari (St. Gobain) Brian Storey (Olin College) Orlin Velev (NC State), Henrik Bruus (DTU) Antonio Ramos (Sevilla) FORMER PhD: Jeremy Levitan, Kevin Chu (2005), Postodocs: Yuxing Ben, Hongwei Sun (2004-06) Interns: Kapil Subramanian, Andrew Jones, Brian Wheeler, Matt Fishburn Collaborators: Todd Squires (UCSB), Vincent Studer (ESPCI), Martin Schmidt (MIT), Shankar Devasenathipathy (Stanford) • Funding: • Army Research Office • National Science Foundation • MIT-France Program • MIT-Spain Program

  3. Outline • Linear electrophoresis • Induced-charge electrophoresis • Heterogeneous particles

  4. Electrophoresis in a dielectric liquid Lab frame Particle frame Size-dependent velocity Long-range flow perturbation

  5. Electrophoresis in an electrolyte Smoluchowski (1907) Electro-osmotic slip Electrophoretic mobility Zeta potential force-free motion Size-independent velocity short-range flow perturbation

  6. Electrophoresis of a colloid Morrison (1970) Solution for uniform mobility: potential flow No relative motion!

  7. Non-uniform surface charge (1) Anderson 1984 An inhomogeneous sphere rotates to align dipole with E Force-free ICEP enhances forced dielectrophoresis (DEP)

  8. Non-uniform surface charge (2) Anderson 1984 Transverse EP is possible, but only for certain orientations EP mobility is not related to total or average charge!

  9. Non-spherical & non-uniform particles Ajdari 1995, Long & Ajdari 1998 A particle can exhibit transverse EP for any orientation: Continuous rotation is also possible, but only around a special axis, with chiral, charged grooves

  10. Outline • Linear electrophoresis • Induced-charge electrophoresis • Heterogeneous particles

  11. Electrophoresis of Polarizable Particles Classical result, e.g. Levich (1956): Electrophoretic mobility depends on the total charge, but not on the induced dipole moment …BUT this only holds for linear response to small E Induced dipole

  12. Stotz-Wien-Dukhin Effect For nonlinear double-layer capacitance, the mobility depends on E, since induced charge must redistribute to maintain the same the total charge (AS Dukhin 1992) Can exploit for separation in “unbalanced” AC fields (SS Dukhin et al 1986, R Chimenti, patent 1986)

  13. Ion-specific mobility Bazant, Kilic, Storey, Ajdari, in preparation 2008 Dukhin effect in an asymmetric electrolyte Mobility must depend on ion charges, sizes, etc. Even an uncharged sphere can move, if it is polarizable Its apparent charge is that of ions which screen at higher density

  14. Induced-Charge Electro-osmosis Gamayunov, Murtsovkin, Dukhin, Colloid J. USSR (1986) - flow around a metal sphere Bazant & Squires, Phys, Rev. Lett. (2004) - general theory, broken symmetries, microfluidics Example: An uncharged metal particle in a DC (or AC) field

  15. First studies of “ICEO” flow Vladimir A. Murtsokvin (work from 1983 to 1996) with Andrei Dukhin, Mantrov, Gamayunov Nonlinear flow induced around a tin particle (albeit in the “wrong” direction at large sizes…) Also studied interactions between particles

  16. Thin-DL, low-voltage theory Squires & Bazant, JFM 2004, 2006; Yariv 2005 Ohm’s law Total charge constraint “RC circuit” boundary condition ICEO slip Solve Stokes flow with for particle set by force=torque=0

  17. Dielectrophoresis Maxwell (1891), Pohl (1958) Maxwell-Wagner induced dipole moment Time-averaged force and torque Velocity in Stokes flow

  18. Dipolophoresis = DEP + ICEP Shilov & Simonova, Colloid J. USSR (1981, 2001). Metal sphere “dipolophoresis” Squires & Bazant, J. Fluid Mech. (2006). General problem of DEP + ICEP • In an electrolyte, ICEP opposes DEP for highly polarizable particles • Both effects have the same scaling Electric Field Fluid Streamlines

  19. General solution for any 2d shape in any non-uniform E field bycomplex analysis… Electric Field Fluid Streamlines

  20. Outline • Linear electrophoresis • Induced-charge electrophoresis • Heterogeneous particles

  21. Electrokinetic motion of rod-like metal particles Perturbation theory: Squires & Bazant, JFM (2006) Rose & Santiago, Phys Rev E (2006): Experiments on alignment of “nano-barcode” particles Saintillan, Darve & Shaqfeh, J Fluid Mech (2006): theory for spheroids + simulations Field off Field on

  22. ICEP of Irregular Shapes ICEP can separate particles of the same material and same size by shape alone. Any direction is possible. Expts on quartz particles: Gamayunov & Murtsovkin (1992). Theory: Bazant & Squires (2004) Tensor relations: Yariv (2005); Perturbation analysis: Squires & Bazant (2006).

  23. ICEP of Asymmetric Shapes Squires & Bazant, J. Fluid Mech. (2006). ICEP can separate polarizable colloids by shape and size in a uniform DC or AC electric field, while normal (linear) electrophoresis cannot. • long axis rotates to align with E • a “thin arrow” swims parallel to E, • towards its “blunt” end • a “fat arrow” swims transverse to E • towards its “pointed” end Perturbation analysis E u An asymmetric metal post can pump fluid in any direction in a uniform DC or AC field, but ICEO flow has quadrupolar rolls, very different from normal EOF. FEMLAB finite-element simulation (Yuxing Ben)

  24. ICEP of Inhomogeneous Particles Bazant & Squires, Phys. Rev. Lett. (2004); Squires & Bazant, J. Fluid Mech (2006) Example: Janus particle A metal/dielectric sphere in a uniform E field always moves toward its dielectric face, which rotates to perpendicular to E. The particle swims sideways. Stable Unstable

  25. An even more surprising example (Squires & Bazant J Fluid Mech 2006): An Electrophoretic Pinwheel • Responds to any electric field by rotating ( ) • Could be used to apply torques to molecules or cells?

  26. ICEP Experiments S. Gangwal, O. Cayre, MZB, O.Velev, Phys Rev. Lett (2008). Gold/latex Janus spheres in NaCl

  27. Experimental data 0.1 mM 300 V/cm Good fit to theory for but particles move near the wall… why?

  28. ICEO wall interactions Zhao & Bau, Langmuir (2007) We expect repulsion from non-polarizable walls, but the Janus particles are attracted to the wall. Why?

  29. ICEP of Janus particles near a wall Kilic & Bazant, preprint, arXiv:0712.0453 Without tilting, the particle is indeed repelled, but it always rotates to meet the wall and can translate with stable angle.

  30. Simulations of Janus-Wall interaction Strong ICEO flows make particle face the wall and get stuck. Weaker ICEO flows produce tilted translation as observed (due to DEP).

  31. Conclusion Induced-charge electrophoresis leads to many new phenomena in colloids with applications to separation, manipulation, self-assembly. Better theories needed. ACEO pumps in Lecture 3… Papers, slides… http://math.mit.edu/~bazant/ICEO

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