Induced-Charge Electrokinetic Phenomena

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

Research Interests Electrokinetics Microfluidics = Electrically driven motion of particles and fluids Microfluidics Electrochemical systems Granular flow Applied mathematics

Induced-charge electrokinetics Acknowledgments Induced-charge electrokinetics 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), Postodoc: Yuxing Ben (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

Outline Linear electrokinetics Nonlinear “induced-charge” electrokinetics Preview of upcoming lectures

Electrokinetic particle motion Electrolyte (salt solution) e.g. clay particles in water, Reuss 1808 Non-conducting viscous liquid, e.g. oil drops in air, Millikan 1900 ?

The Electric Double Layer + quasi-neutral bulk liquid electrolyte solid Electrostatic potential Ion concentrations Gouy 1910 continuum region

Electrokinetics in electrolytes - - - - - - - - - - - - - - - - - Redo (a) tro show bulk flow (a) Electro-osmosis = fluid slip across the double layer, as an electric field pushes on the screening cloud (b) Electrophoresis = particle motion due to electro-osmosis

Linear Electrokinetics: 1. Fluids Response Helmholtz: electro-osmotic flow Onsager: streaming potential & current (inverse effects) Ajdari: transverse couplings (anisotropic surfaces) uniform zeta, thin double layers: potential flow (no vortices) No net response to AC forcing

Application: DC EO pumps Small channels (porous media) lead to large pressure (>10atm) Disadvantages: High voltage (kV) Faradaic reactions Gas management Hard to miniaturize Porous Glass Yau et al, JCIS (2003)

Linear Electrokinetics: 2. Particles Smoluchowski: electrophoresis Onsager: sedimentation potential, induced dipole Dukhin, Deryaguin: surface conduction (large charge) Anderson, Ajdari: transverse motion, rotation uniform zeta, thin double layers: cannot separate particles!

Applications in microfluidics Apply E across the chip Advantages: EO plug flow has low hydrodynamic dispersion Many uses of linear EP in separation/detection Limitations: High voltage (kV) Often slow separations No local flow control “Table-top technology” From Todd Thorsen

Outline Linear electrokinetics Nonlinear “induced-charge” electrokinetics Preview of upcoming lectures

Nonlinear Electrokinetic Phenomena Some early examples Dielectric liquids dielectrophoresis (DEP): acts on induced dipole Taylor (1966): deformation & flow in oil drops Melcher (1960s): Traveling-wave AC pumping Electrolytes Shilov (1976): double-layer effects in DEP Murtsovkin (1986): flows around polarizable particles Dukhin (1986): 2nd kind EP at large current Saville (1997): AC colloidal self-assembly on electrodes Ramos (1999): AC electro-osmosis Ajdari (2000): ACEO pumping with electrode arrays

“Induced-Charge Electro-osmosis” = nonlinear electro-osmotic slip at a polarizable surface Example: An uncharged metal cylinder in a suddenly applied DC field Refs at end ICEO flow persists in an AC field (< charging frequency). Gamayunov, Murtsovkin, Dukhin, Colloid J. USSR (1986) - flow around a metal sphere Bazant & Squires, Phys, Rev. Lett. (2004) - general theory, broken symmetries, microfluidics

Double-layer polarization and ICEO flow A conducting cylinder in a suddenly applied uniform E field. Electric field ICEO velocity Movies from a finite-element simulation by Yuxing Ben (2005) Solving the Poisson-Nernst-Planck/Navier-Stokes eqns l/a=0.005

Experimental Observation of ICEO Jeremy Levitan, PhD Thesis in Mechanical Engineering, MIT (2005) 100 mm Pt wire on channel wall Viewing plane PDMS polymer microchannel Bottom view of optical slice Inverted optics microscope Micro-particle image velocimetry (mPIV) to map the velocity profile

Simulated flow (side view) ICEO Experiments J. A. Levitan, S. Devasenathipathy, V. Studer, Y. Ben, T. Thorsen, T. M. Squires & M. Z. Bazant, Colloids and Surfaces (2005) Collapse of experimental data Movie: 5 m optical slice sweeping 100 m Pt cylinder (top view) 100 V/cm, 300 Hz, 0.1 mM KCl

Examples of ICEO in Microfluidics Flow around a metal post Fixed-potential ICEO DC jet at a dielectric corner AC electro-osmosis Thamida & Chang (2002) Ramos et al (1999), Ajdari (2000)

A pioneer, ahead of his time Vladimir A. Murtsokvin (work from 1983 to 1996) “ICEO” flow around an metal particle (courtesy of Andrei Dukhin)

Induced-Charge Electrophoresis = ICEO swimming by broken symmetry Bazant & Squires, Phys. Rev. Lett. (2004); Yariv, Phys. Fluids (2005) 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

Experimental observation of induced-charge electrophoresis S. Gangwal, O. Cayre, MZB, O.Velev, Phys Rev. Lett. 100, 058302 (2008).

Outline Linear electrokinetics Nonlinear “induced-charge” electrokinetics Preview of upcoming lectures

Lecture 2: ICEP in Colloids Thursday 10 Jan. 2pm Theory Field-dependent EO mobility Shape-dependent ICEP motion Wall interactions ICEP & DEP in non-uniform fields Applications in separation, assembly

Some examples... E u The ICEO pinwheeel Non-uniform fields

Lecture 3: ACEO in Microfluidics Thursday 17 Jan. 2pm Theory ICEO mixers ACEO flow over electrode arrays Fast (> mm/s), low-voltage (< 3V), high-pressure (10% atm) ACEO pumps Applications to portable/implantable labs-on-a-chip, drug delivery

Some examples... The “Fluid Conveyor Belt” Scientific American, Oct. 2007. The “Fluid Conveyor Belt”

Lecture 4: Theory at large voltages Postponed… Experimental puzzles Strongly nonlinear dynamics Breakdown of dilute-solution theory Modified theories for ion crowding New phenomena and open questions

Experimental puzzles in ACEO V. Studer et al., Analyst (2004) MZB et al., MicroTAS (2007) High-frequency flow reversal Concentration dependence Ion specificity Classical theory breaks down…

Ion crowding at large voltages Crucial new physics: Ion crowding at large voltages MZB, MS Kilic, B Storey, A Ajdari (2007) Poisson-Boltzman/ Dilute-solution theory ICEO experiments, New theory needed

Conclusion Induced-charge electrokinetics provides many opportunities for new science and new applications Papers, slides… http://math.mit.edu/~bazant/ICEO