Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis -...

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Lecture 6- Electrokine0cs and microfluidics

Transcript of Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis -...

Page 1: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Lecture6-Electrokine0csandmicrofluidics

Page 2: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

1) Electrophoresis

Page 3: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Electrophoresis

qE −Fv =mdUdt

≈ 0

FV = 6πRµU

! ≪ !!

r E

q

V = µeEwith

µe =q

6πRµ

Page 4: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Application: electronic paper (Kindle)

ΤiO2 (négative)

Positive charges (Carbon)

Ε

Page 5: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Application: electronic paper

Page 6: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

V = µe Eoù

µe =q

6πRη

Separation based on the ratio q/m

Electrophoretic separation

Page 7: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Electrochromatogram

Page 8: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Not possible with DNA

The ratio q/m is the same for all strands

Page 9: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

N ~ µEELD

Number of theoretical plates

Q ~ KΔTl ~ σE 2l3

E ~ l−1

Advantage of miniaturization

Maximum of Electric field that can be applied

Page 10: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

N~ l0

tR~ L/V ~l2

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

Advantage of miniaturization

Page 11: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

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

Interest of miniaturizing

Page 12: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming
Page 13: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Agilent DNA analyser

Page 14: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming
Page 15: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

2) Dielectrophoresis

Page 16: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Dielectrophoresis

Page 17: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

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

Positive diélectrophoresis

Page 18: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

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

La diélectrophorèse négative

Page 19: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Continuous field (or small frequencies)

F =12α∇E 2

Alternative field

F = 2πa2K∇E 2

Clausius Mosotti factor

Page 20: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Application: droplet sorter

200 µm

Page 21: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

3) Electrokinetics

Page 22: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Electrokinetics of charged media

+

+++

++

++

+ +

+

++

++ ++

++ +++

+

+

+++

++

++

+++

++

+

V

Ε

Page 23: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

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

Page 24: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

∂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

Page 25: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

The Debye layer

z

ρe

Page 26: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

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

Page 27: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

The Debye layer

Page 28: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Ε

z

x

Debye layer

Electroosmosis

Page 29: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

0 = − ∂p∂x+ µ

∂ 2u∂z2

− εExd2ψdz2

up = −εExψ0

µ= −

εExζµ€

u(z) =εEx

µ(ψ −ψ0)

Electroosmosis without slippage

Page 30: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

up = −εExζµ

Helmoltz-Smoluchowsky velocity

Electroosmotic mobility

µEOF =εζµ

Electroosmosis without slippage

Page 31: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

A flow generates an electric field

U Ε

Streaming potential

Page 32: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

Streaming potential: application

Soleil

Pot. Ecoul.

Page 33: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming

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

Page 34: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming
Page 35: Lecture 6- Electrokine0cs and microfluidics...Pot. Ecoul. What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming