lecture 6- electrokine0cs and microfluidics...pot. ecoul. what must be learned: - electrophoresis -...

Lecture6-Electrokine0csandmicrofluidics

1) Electrophoresis

Electrophoresis

qE −Fv =mdUdt

≈ 0

FV = 6πRµU

! ≪ !!

r E

q

V = µeEwith

µe =q

6πRµ

Application: electronic paper (Kindle)

ΤiO2 (négative)

Positive charges (Carbon)

Ε

Application: electronic paper

V = µe Eoù

µe =q

6πRη

Separation based on the ratio q/m

Electrophoretic separation

Electrochromatogram

Not possible with DNA

The ratio q/m is the same for all strands

€

N ~ µEELD

Number of theoretical plates

€

Q ~ KΔTl ~ σE 2l3

E ~ l−1

Advantage of miniaturization

Maximum of Electric field that can be applied

N~ l0

tR~ L/V ~l2

Same performances, faster (record : 800 µs, Jacobson et al)

Advantage of miniaturization

- Small volumes - Intégration et parallelisation - Excellent efficiency - Much faster

Interest of miniaturizing

Agilent DNA analyser

2) Dielectrophoresis

Dielectrophoresis

Positive dielectrophoresis : Particle more polarizable than the environment. Force directed towards high eletric fields

Positive diélectrophoresis

Negative dielectrophoresis : Particle less polarizable than the environment. Force directed towards small eletric fields

La diélectrophorèse négative

Continuous field (or small frequencies)

€

F =12α∇E 2

Alternative field

€

F = 2πa2K∇E 2

Clausius Mosotti factor

Application: droplet sorter

200 µm

3) Electrokinetics

Electrokinetics of charged media

+

+++

++

++

+ +

+

++

++ ++

++ +++

+

+

+++

++

++

+++

++

+

V

Ε

JD = −D∇ρe ; JT = ρeV ; Je = σ E

J = −D∇ρe + ρeV +σE

3 contributions

Charge gradient convection Diffusion (Ohm’s law)

Electrokinetics of charged media

∂ρ e

∂t+ divJ = 0; divu = 0

ρDuDt

= −∇p+ µΔu + ρeE ≈ 0

J = −D∇ρe + ρeu +σ E

Electrohydrodynamics

U

Ε

+ + + +

+ ++ +

+ + + +

+ + + +

+ + + +

8 EQUATIONS 8 Unknown

The Debye layer

z

ρe

0 = σEz − Ddρedz

ψ = −Dσρe

d2ψdz

2 = −ρeε

On déduit

€

ψ =ψ0e−z /λD

λD =Dεσ

(car E=-grad ψ)

(car div E = ρ/ε)

Longueur de Debye

The Debye layer

The Debye layer

Ε

z

x

Debye layer

Electroosmosis

0 = − ∂p∂x+ µ

∂ 2u∂z2

− εExd2ψdz2

€

up = −εExψ0

µ= −

εExζµ€

u(z) =εEx

µ(ψ −ψ0)

Electroosmosis without slippage

up = −εExζµ

Helmoltz-Smoluchowsky velocity

Electroosmotic mobility

€

µEOF =εζµ

Electroosmosis without slippage

A flow generates an electric field

U Ε

Streaming potential

Streaming potential: application

Soleil

Pot. Ecoul.

What must be learned: -  Electrophoresis -  Dielectrophoresis -  Equations of EHD -  Debye layer -  Electroosmosis -  Streaming Potential