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Lecture6-Electrokine0csandmicrofluidics
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1) Electrophoresis
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Electrophoresis
qE −Fv =mdUdt
≈ 0
FV = 6πRµU
! ≪ !!
r E
q
V = µeEwith
µe =q
6πRµ
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Application: electronic paper (Kindle)
ΤiO2 (négative)
Positive charges (Carbon)
Ε
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Application: electronic paper
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V = µe Eoù
µe =q
6πRη
Separation based on the ratio q/m
Electrophoretic separation
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Electrochromatogram
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Not possible with DNA
The ratio q/m is the same for all strands
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€
N ~ µEELD
Number of theoretical plates
€
Q ~ KΔTl ~ σE 2l3
E ~ l−1
Advantage of miniaturization
Maximum of Electric field that can be applied
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N~ l0
tR~ L/V ~l2
Same performances, faster (record : 800 µs, Jacobson et al)
Advantage of miniaturization
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- Small volumes - Intégration et parallelisation - Excellent efficiency - Much faster
Interest of miniaturizing
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Agilent DNA analyser
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2) Dielectrophoresis
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Dielectrophoresis
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Positive dielectrophoresis : Particle more polarizable than the environment. Force directed towards high eletric fields
Positive diélectrophoresis
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Negative dielectrophoresis : Particle less polarizable than the environment. Force directed towards small eletric fields
La diélectrophorèse négative
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Continuous field (or small frequencies)
€
F =12α∇E 2
Alternative field
€
F = 2πa2K∇E 2
Clausius Mosotti factor
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Application: droplet sorter
200 µm
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3) Electrokinetics
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Electrokinetics of charged media
+
+++
++
++
+ +
+
++
++ ++
++ +++
+
+
+++
++
++
+++
++
+
V
Ε
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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
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∂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
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The Debye layer
z
ρe
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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
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The Debye layer
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Ε
z
x
Debye layer
Electroosmosis
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0 = − ∂p∂x+ µ
∂ 2u∂z2
− εExd2ψdz2
€
up = −εExψ0
µ= −
εExζµ€
u(z) =εEx
µ(ψ −ψ0)
Electroosmosis without slippage
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up = −εExζµ
Helmoltz-Smoluchowsky velocity
Electroosmotic mobility
€
µEOF =εζµ
Electroosmosis without slippage
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A flow generates an electric field
U Ε
Streaming potential
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Streaming potential: application
Soleil
Pot. Ecoul.
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What must be learned: - Electrophoresis - Dielectrophoresis - Equations of EHD - Debye layer - Electroosmosis - Streaming Potential
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