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