1: Debye layer, Zeta potential, Electrokinetics

2: Electrophoresis, Electroosmosis

3: Dielectrophoresis

4: Inter-Debye layer force, Van-Der 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

Key Concepts for section IV (Electrokinetics and Forces)

Helmholtz model(1853)

Guoy-Chapman model(1910-1913)

Stern model (1924)

+ -+++++++++++

-----------

1κ −

1κ −

0Φ

x

+ -+++++++++++

--

--

-

- --

- --1κ −

1κ − x

0Φ

+

+

+

++

++

-

+++++++++++

-

-

--

-

--

-

--

-1κ −

+

+

+

+

+

+

1κ −

0Φ

x

-

--

slip boundary

(zeta potential)ξ

Jongyoon HanText BoxkT

From NessCAP Inc. website

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.

http://www.nesscap.com/

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

Motion of DNA in Channels

35.7 V/cm

-(cathode)+

(anode)

electroosmosis

electrophoresis

- - -

--

--

-

-

- - - - - -

- - - - - -- - -

+ + + + + ++ + +

+ + + + + ++ + +

(surface charges)

E field

Source: Prof. Han’s Ph.D thesis

-60

-40

-20

0

20

40

0 0.25 0.5 0.75 1

Buffer concentration(M)

Velo

city

( μm

/sec

)

T7 T20.5X TBE

10X TBE

Velocity of DNA in obstacle-free channel

DNA electrophoresis in a channel

• 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 viscousdrag.

Electroosmosis

Figure by MIT OCW.

1 2 3 4

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/

http://www.eksigent.com/

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

Courtesy of Daniel J. Laser. Used with permission.

Electroosmosis Streaming potential

Electrophoresis Sedimentation potentialFigure by MIT OCW.

E field (ΔΦ)generates fluid flow (Q)

E field (ΔΦ)generates particle motion (v)

fluid flow (Q) generates E-field (ΔΦ)

particle motion (v)generatesE-field (ΔΦ)

+ + + + + + +

+ ++

++++

+

v v

+ + + + + + +

++ + + + + + +

P0P1

+ ++

++++

+

EE

E

v

vv

v

+

+ + + + + + +

v

Concentration(c)(ρ)

Maxwell’s equationFick’s law of diffusion

E and B field

Navier-Stokes’ equation

ρ, J : source

Osmosis

(aqueous) medium, Flow velocity (vm)

Convection

Electrophoresis

Streamingpotential

Electroosmosis

Stern layer (Realistic Debye layer model)

+

++

++

+

++

++

+++++++++

Distance

Pote

ntia

l, φ

Diffuse Layer

Stern Layer

φδ

δ

φw

Particle Surface Stern Plane

Surface of Shear

ζ

λD0

Structure of electric double layer with innerStern layer (after Shaw, 1980.)

Figure by MIT OCW.

Sheer boundary, zeta potential

1~ κ −

x

Φξ-+

+

++- - - - - - - - - - - - - - - - - - -+ + + + +

+

+

++

++

++

Stern layer

Slip (shear) boundary

zv

x

δ

(0)Φ

Zeta potential

EEOvzE

Stern layer : adsorbed ions, linear potential dropGouy-Chapman layer : diffuse-double layer

exponential dropShear boundary : vz=0Navier-Stokes equation

2 0

0 ( )

edv p v Edtv incompressible

ρ μ ρ= −∇ + ∇ + ≅

∇ ⋅ =

r rr

r

New term

Poiseuille flowparabolic flow profile

( )2 2

( ) ( )4z zo

electroosmotic flow Poiseuille flow

R r Pv r r EL

ε ζμ μ

⎛ ⎞− Δ= − − Φ −⎜ ⎟⎝ ⎠1444244431442443

0, 0 :zP EΔ ≠ =

Electroosmotic flowflat (plug-like) profile0, 0 :zP EΔ = ≠

:

z zEEO EEO

EEO

v E E (outside of the Debye layer)

electroosmotic 'mobility'

εζ μμμ

= − =

Paul’s experiment

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

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

EEO zv Eεζμ

= −2

8PoiseuilleR Pv

LμΔ= −

(averaged over r)

Electroosmotic flow velocity is independent of the size (and shape) of the tube.

Pressure-driven flow velocity is a strong function of R.

R=1μm R=10μm R=1m

EEO zv Eεζμ

= − EEO zv Eεζμ

= − EEO zv Eεζμ

= −

?

Key Concepts for section IV (Electrokinetics and Forces)Motion of DNA in ChannelsImage removed due to copyright restrictions.��Schematic of electroosmotic flow of water in a porous charged medium. ��Figure 6Stern layer (Realistic Debye layer model) Sheer boundary, zeta potentialPaul’s experiment