Key Concepts for section IV (Electrokinetics and Forces)

1: Debye layer, , Electrokinetics 2: , Electroosmosis 3: Dielectrophoresis 4: Inter-Debye layer force, Van-Der Waals forces 5: Coupled systems, Scaling, Dimensionless Number

Goals of Part IV: (1) Understand and apply them in (natural or artificial) biosystems (2) Understand various driving forces and be able to identify dominating forces in coupled systems Helmholtz model Guoy-Chapman model Stern model (1924) (1853) (1910-1913) slip boundary + - + - + - - + - + + + + - + + - + - - + - - + - + + + - + - + - + + + - + + + - + - + - + + + - + - + - - + + - - + - + - + - + - + - + - + - + - + + - + + - + - + - + - - −1 −1 κ −1 κ κ

Φ Φ Φ 0 0 0 ξ (zeta potential)

−1 −1 κ x κ −1 x κ x

Debye layer is a extraordinary capacitor! http://www.nesscap.com/

Image removed due to copyright restrictions. Graph of power vs. energy characteristics of energy storage devices.

From NessCAP Inc. website Image removed due to copyright restrictions. Datasheet for NESSCAP Ultracapacitor 3500F/2.3V Motion of DNA in Channels

35.7 V/cm (surface charges) - - - - - electroosmosis - - - - + + + + + + +- + + - - - - - (cathode) electrophoresis - + + +++ + + + (anode) ++ ------

E field

Source: Prof. Han’s Ph.D thesis DNA electrophoresis in a channel

Velocity of DNA in obstacle-free channel 40 10X TBE 20

m/sec) 0 μ 0 0.25 0.5 0.75 1 -20

Velocity ( -40 T7 T2 -60 0.5X TBE Buffer concentration(M) 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. 1 2 3 4

Figure by MIT OCW. Image removed due to copyright restrictions. Schematic of electroosmotic flow of water in a porous charged medium. Figure 6.5.1 in Probstein, R. F. Physicochemical Hydrodynamics: An Introduction. New York: NY, John Wiley & Sons, 1994.

http://www.moldreporter.org/vol1no5/drytronic Gels and Tissues

Nanoporous materials

Extra-Cellular matrix

Microfluidic system

Electrokinetic pumping http://www.eksigent.com/ Courtesy of Daniel J. Laser. Used with permission.

http://micromachine.stanford.edu/~dlaser/research_pages/silicon_eo_pumps.html Electroosmosis Streaming potential

E field (ΔΦ) + + + + + + + + + + + + + + + v fluid flow (Q) generates v P1 P0 generates fluid flow (Q) + + + + + + + + + + + + + + E-field (ΔΦ)

+ v

+ E field (ΔΦ) + + + + + + + + + particle generates + + + + + + particle motion (v) motion (v) v E E v generates v E v E-field (ΔΦ)

Electrophoresis Sedimentation potential Figure by MIT OCW. Fick’s law of diffusion Maxwell’s equation Electrophoresis Concentration(c) E and B field ρ ( ) ρ, J : source

Convection Osmosis Electroosmosis Streaming potential

(aqueous) medium,

Flow velocity (vm)

Navier-Stokes’ equation Stern layer (Realistic Debye layer model)

Particle Surface Stern Plane

Surface of Shear + + + + + + Stern Layer + + + + + + + + + + + + + Diffuse Layer

φ w φ

, l a i t n

e φ

t δ ζ o P

0 λ δ D Distance

Structure of electric double layer with inner Stern layer (after Shaw, 1980.) Figure by MIT OCW. Sheer boundary, zeta potential v E EEO z x x

+ + + −1 + ~ κ + + Slip (shear) boundary δ + + + + + + + + + + + ------Φ(0) ξ Φ vz Stern layer Zeta potential Stern layer : adsorbed ions, linear potential drop Gouy-Chapman layer : diffuse-double layer exponential drop

Shear boundary : vz=0 Navier-Stokes equation New term dvr r ρμρ=−∇pvE + ∇2 r + ≅0 dt e ∇⋅vr =0( incompressible) ε ⎛⎞22−Δ =−()ζ −Φ − Rr P vrzz() ()r Eo⎜⎟ μμ⎝⎠4 L 144424443 1442443 electroosmotic flow Poiseuille flow

Poiseuille flow Δ≠PE0, = 0 : z parabolic flow profile

Electroosmotic flow Δ=PE0, ≠ 0 : z flat (plug-like) profile

εζ v=− E =μ E (outside of the Debye layer) EEO μ zzEEO μ EEO : electroosmotic 'mobility' Paul’s experiment

Figure by MIT OCW. After Paul, et al. Anal Chem 70 (1998): 2459.

Pressure-driven 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 pulse-exposing 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.

http://www.ca.sandia.gov/microfluidics/research/pdfs/paul98.pdf εζ R2 ΔP vE=− v =− EEO μ z Poiseuille 8μ L (averaged over r)

Electroosmotic flow velocity Pressure-driven flow velocity is independent of the size (and is a strong function of R. shape) of the tube.

R=1μmR=10μmR=1m

εζ εζ εζ =− vE=− vE=− vEEEO z EEO μ z EEO μ z μ ?