Key Concepts for section IV (Electrokinetics and Forces)

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1 Key Concepts for section IV (Electrokinetics and Forces) 1: Debye layer, Zeta potential, Electrokinetics 2: Electrophoresis, Electroosmosis 3: Dielectrophoresis 4: InterDebye layer force, VanDer Waals forces 5: Coupled systems, Scaling, Dimensionless Number Goals of Part IV: (1) Understand electrokinetic phenomena and apply them in (natural or artificial) biosystems (2) Understand various driving forces and be able to identify dominating forces in coupled systems

2 Helmholtz model (1853) GuoyChapman model ( ) Stern model (1924) κ 1 κ 1 Φ 0 x κ 1 1 κ x Φ 0 κ 1 κ 1 Φ 0 x slip boundary (zeta potential) ξ

5 Debye layer is a extraordinary capacitor! Image removed due to copyright restrictions. Graph of power vs. energy characteristics of energy storage devices. From NessCAP Inc. website

6 Image removed due to copyright restrictions. Datasheet for NESSCAP Ultracapacitor 3500F/2.3V

7 Motion of DNA in Channels (anode) 35.7 V/cm (surface charges) electroosmosis electrophoresis (cathode) E field Source: Prof. Han s Ph.D thesis

8 DNA electrophoresis in a channel Velocity of DNA in obstaclefree channel Velocity (μm/sec) X TBE T7 T2 0.5X TBE Buffer concentration(m)

9 Electroosmosis The oxide or glass surface become unprotonated (pk ~ 2) when they are in contact with water, forming electrical double layer. When applied an electric field, a part of the ion cloud near the surface can move along the electric field. The motion of ions at the boundary of the channel induces bulk flow by viscous drag Figure by MIT OCW.

10 Image removed due to copyright restrictions. Schematic of electroosmotic flow of water in a porous charged medium. Figure in Probstein, R. F. Physicochemical Hydrodynamics: An Introduction. New York: NY, John Wiley & Sons,

11 Gels and Tissues Nanoporous materials ExtraCellular matrix Microfluidic system Electrokinetic pumping

12 Courtesy of Daniel J. Laser. Used with permission.

13 Electroosmosis Streaming potential E field (ΔΦ) generates fluid flow (Q) v P 1 v P 0 fluid flow (Q) generates Efield (ΔΦ) v E field (ΔΦ) generates particle motion (v) v E v v E E v particle motion (v) generates Efield (ΔΦ) Electrophoresis Sedimentation potential Figure by MIT OCW.

14 Fick s law of diffusion Concentration(c) (ρ) Electrophoresis ρ, J : source E and B field Maxwell s equation Osmosis Convection Electroosmosis Streaming potential (aqueous) medium, Flow velocity (v m ) NavierStokes equation

15 Stern layer (Realistic Debye layer model) Particle Surface Stern Plane Stern Layer Surface of Shear Diffuse Layer φ w Potential, φ φ δ ζ 0 δ λ D Distance Structure of electric double layer with inner Stern layer (after Shaw, 1980.) Figure by MIT OCW.

16 Sheer boundary, zeta potential E z x x v EEO Slip (shear) boundary Stern layer Φ(0) ξ Zeta potential Stern layer : adsorbed ions, linear potential drop GouyChapman layer : diffusedouble layer exponential drop Shear boundary : v z =0 NavierStokes equation r dv 2r r ρ = p μ v ρee dt r v = 0( incompressible) 0 Φ New term δ ~ κ 1 v z

17 2 2 ε R r ΔP vz() r = ( ζ Φ() r ) Ezo μ 4μ L electroosmotic flow Poiseuille flow ΔP 0, E z = 0 : Poiseuille flow parabolic flow profile Δ P= 0, E z 0 : Electroosmotic flow flat (pluglike) profile εζ veeo = Ez = μeeoe z (outside of the Debye layer) μ μ : electroosmotic 'mobility' EEO

18 Paul s experiment Figure by MIT OCW. After Paul, et al. Anal Chem 70 (1998): Pressuredriven flow vs. Electroosmotic flow. These images were taken by caged dye techniques (Paul et al. Anal. Chem. 70, 2459 (1998)). At t=0, an initial flat fluorescent line is generated in microchannel by pulseexposing and breaking the caged dye, rendering them fluorescent. These dyes were transported by the fluid flow generated by pressure (left column) or electroosmosis (right column), demonstrating the flow profile.

19 v EEO εζ = E μ z 2 R ΔP vpoiseuille = 8μ L (averaged over r) Electroosmotic flow velocity is independent of the size (and shape) of the tube. Pressuredriven flow velocity is a strong function of R. R=1μm R=10μm R=1m v EEO εζ μ εζ μ = Ez veeo = E EEO z z v εζ = E μ?

Key Concepts for section IV (Electrokinetics and Forces)

Key Concepts for section IV (Electrokinetics and Forces) 1: Debye layer, Zeta potential, Electrokinetics 2: Electrophoresis, Electroosmosis 3: Dielectrophoresis 4: InterDebye layer force, VanDer Waals