Induced-Charge Electro-osmosis Martin Z. Bazant Mathematics, MIT Supported by the Institute for Soldier Nanotechnologies Jeremy Levitan Todd Thorsen Mechanical Engineering, MIT Martin Schmidt Electrical Engineering, MIT Todd M. Squires Applied Math, Caltech

AC Electro-osmosis Ramos et. al (1998), Ajdari (2000) t = 0t = tt >> t Steady flow for AC period = t c c c How general is this phenomenon? Need electrode arrays? Need “AC”? Sudden DC voltage

Induced-Charge Electro-osmosis Bazant & Squires, Phys, Rev. Lett. 92, (2004). Squires & Bazant, J. Fluid. Mech. 509, 217 (2004). E-field, t = 0E-field, t » charging timeSteady ICEO flow Example: An uncharged metal cylinder in a suddenly applied DC field Nonlinear electrokinetic slip at a polarizable surface  induced ~ E a Same effect for metals and dielectrics, DC and AC fields…

Nonlinear Electrokinetic Phenomena AC electro-osmosis (+ colloidal aggregation?) at electrodes DC electrokinetic jet at a dielectric corner AC flows around metallic particles Dielectrophoresis in electrolytes Levich (1962); Simonov & Shilov (1977); Gamayunov, Murtsovkin, A. S. Dukhin (1984…). 1. Other examples of “ICEO” flows Thamida & Chang (2002…) Simonova, Shilov, Shramko (2001…) 2. Other “Non-equilibrium Electro-surface Phenomena” Surface conduction, non-equilibrium diffusio-osmosis Second-kind electro-osmosis, instability at limiting current S. S. Dukhin (1965); Deryaguin & S. S. Dukhin (1969…). S. S. Dukhin (1989…); Ben & Chang (2002); Rubinstein & Zaltzman (2000…) Ramos et al. (1998…); Ajdari (2000…); “EHD” Ristenpart, Saville (2004)… (3. Bulk “electrokinetic instability” ) Lin et al, Santiago (2001…)

ICEO in Microfluidics Cross-channel Reversible pump Post-array mixer T pump

Fixed-Potential ICEO Example: metal cylinder grounded to an electrode supplying an AC field. Fixed-potential ICEO mixer

Pumping by Broken Symmetry Inspired by Ajdari (2000): AC EO pumping with electrode arrays. Symmetric metal wire Asymmetric Stern layer Partial coating by an insulator Asymmetric shape Misalignment with field also drives torques to align.

More ICEO in Microfluidics Patterned surfaces Asymmetric posts Pumping transverse to a AC or DC field

Non-uniform Applied Fields ICEO pumps in a non-uniform AC or DC field Very sensitive to size, shape, and time-dependence Cancels DEP for a metal sphere (but not other shapes) All higher multipoles at infinity also pump in AC fields Simonova, Shilov, Shramko, Colloid J. USSR (2001) Squires & Bazant, in preparation.

Mathematical Theory of ICEO I. Diffuse-Charge Dynamics What is the time scale for charge screening? Bazant, Thornton, Ajdari, Phys. Rev. E (2004) Debye time, / D ? Diffusion time, L / D ? No! (and yes…) 2 2 Model problem

1. Weakly Nonlinear Dynamics Intermediate “RC time”: Effective boundary condition: Equivalent circuit at leading order, << L. 2. Strongly Nonlinear Dynamics V = 4 kT/e Transient bulk diffusion

Weakly Nonlinear ICEO Flow BC: 1. Electrochemical problem for the induced zeta potential 2. Stokes flow driven by ICEO slip Bazant, Thornton, Ajdari, Phys. Rev. E (2004) Green et al. (2000) ACEO Squires & Bazant (2004) J. Levitan’s experiment: Platinum wire in a polymer microchannel Electric field after double-layer charging Steady ICEO flow

Strongly Nonlinear ICEO/NESP Nernst-Planck Equations Deryaguin/Dukhin BC for double-layer ion adsorption Adsorption rate = bulk flux + surface flux + reactions Dukhin number: Stokes flow due to “first-kind” electro/diffusio-osmosis

Induced-Charge Electro-osmosis Nonlinear electro-osmosis at a polarizable surface Sensitive to size, shape, voltage, time-dependence,… Builds on ACEO, Russian colloid literature, etc. Open theoretical questions –“Strongly nonlinear” ICEO with large induced zeta –Effect of Faradaic reactions (e.g. Butler-Volmer) –Why theory over-predicts experimental velocities –Optimization of geometry & forcing for mixing & pumping Experiments & microfluidic applications –See talk by Jeremy Levitan at 2:20pm… Papers:

Example: Dielectric-coated metal cylinder at fixed potential in a suddenly applied DC field Surface capacitance ratio = dielectric thickness / Debye length Induced dipole moment

Experiments Jeremy Levitan Todd Thorsen, Martin Schmidt, Hongwei Sun, Shankar Devasenathipathy (MIT), Vincent Studer (ESPCI) First model system: Isolated 100 micron platinum wire in KCl in a 0.2 x 1 x 1 mm PDMS microchannel with electrode ends. Next generation: electroplated gold posts. E

Voltmeter Function Generator Viewing Resistor KCl in PDMS Microchannel Platinum Wire Inverted Optics Microscope Viewing Plane Bottom View 200 um X 1 mm X 1mm Channel

PIV Mean Velocity Data PIV measurement with 0.01% volume dielectric (fluorescent) tracer particles Fit velocity profile to ICEO simulation 25 microns from wire Correct scaling, but smaller magnitude by factor of 30, perhaps due to surface impurity Metal colloids: Gamayunov, Mantrov, Murtsovkin (1992)

Frequency Scaling Decay above the “RC time” Consistent with ICEO theory U ~ U 0 /(1 + (  /  c ) 2 )  c = 2  d a/D = 1/  c = 3 ms Experiments in 1 mM KCl at 75 V

Induced-Charge Electro-osmosis Nonlinear electro-osmosis at a polarizable surface Sensitive to size, shape, voltage, time-dependence,… Unifies & extends ACEO, Russian colloid literature,... Open theoretical questions –“Strongly nonlinear” ICEO with large induced zeta –Effect of Faradaic reactions (e.g. Butler-Volmer) –Why theory under-predicts experimental velocities –Optimization of geometry & forcing for mixing & pumping Experiments & microfluidic applications underway Papers: