Lecture 5: Mixing, mass transfer, adsorption, NP transport · Lecture 5: Mixing, mass transfer,...
Transcript of Lecture 5: Mixing, mass transfer, adsorption, NP transport · Lecture 5: Mixing, mass transfer,...
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Lecture 5: Mixing, mass transfer, adsorption, NP transport
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1) Basics of diffusion, dispersion
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Microscopic description of diffusion processes
x = li1
n
∑li
x2 = li1
n
∑⎛
⎝⎜
⎞
⎠⎟
2
≈ l2n ≈ Dt
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Continuous approach
C(x, t) = δmδV
J = δmδtδA
J = −D∇C
Area δAVolumeδV
Fick’s law
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∂C∂t
= DΔC
Diffusion equation
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C(x, t) =C04πDt
exp −x2
4Dt# $ %
& ' (
The gaussian distribution
C
x
C
x
t=0 t
STD σ = (2Dt)1/2
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€
DCDt
=∂C∂t
+ u∇C = DΔC
Equation of diffusion-advection
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The Peclet number
Pe =UlD~ advectiondiffusion
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(a) (b) (c)
u∇C = 0u∇C ≠ 0;u uniform
u∇C ≠ 0;u_non_uniform
Basic situations in microfluidics
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Slow mixing in side-to-side flows
100 µm
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Dispersion in a uniform flow
C(x,t) =C0δ2πσ
exp −(x −Ut)2
2σ 2
%
& ' (
) with σ2=2Dt
x=0
xU
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Dispersion in a pure shear flow
C(x, y, t) = Q2πσ x 2Dt
exp −(x −Ut)2
2σ x2
⎛
⎝⎜
⎞
⎠⎟
with σ x2 = 2Dt (1+α
2
12t2 )
hyperdiffusion
U=αy
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Dispersion of Taylor-Aris
From Kirby
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∂C
∂t= DeffΔC
DC
Dt=∂C
∂t+ (U(z)− V)
∂C
∂x'= D
∂2C
∂x'2
DC
Dt=∂C
∂t+U(z)
∂C
∂x= DΔC
t >> d2/D
Deff = D(1+ αPe2 )
Dispersion of Taylor-Aris
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2) Mixing
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Perfectly mixed system: when the concentration is homogeneous The mixing process: process that leads to a perfectly mixed system Two mechanisms play a role in any mixing process:
- Diffusion - Advection
Notion of mixing
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Diffusion based mixing
€
τ =l2
D
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Nanofluidics does not need nanomixers
€
τ =l2
D
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Mixing by scale reduction
R.Austin et al (1999)
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w
Residence time: tR=L/UDiffusion time : tD=w2/DMixing quality: A = tR/tD
Distributed micromixer
L
w’=w/N
Mixing quality : A’ = t’R/tD=N2A >> A
U
Mixing by scale reduction
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Manz (2004)
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L ~ Pe √Dt
Mixers based on Taylor Aris dispersion
Length of the spot at Pe>>1 :
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The circular micromixer
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The rotary mixer
Quake, Scherer (2001)
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A chip for DNA purification
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Chaotic mixers
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The most popular chaotic micromixer
A. Strooke et al, Science (2002)
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A. Strooke et al, Science (2002)
The most popular chaotic micromixer
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Review on micro/mini mixers
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Universal diagram of micromixers
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3) Mixing in droplets
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Mixing in digital microfluidics
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Mixing in droplet based microfluidics
Ismagilov group
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Application to the measurement of chemical kinetics
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4) Mass manipulations in microfluidics
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Measurement of diffusion constants
P. Yager (Seattle)
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Filtering of particles
P. Yager (Seattle)
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Gradient formation
Q
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Ismagilov et al, Anal Chem (2001)
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Liquid liquid extraction
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5) Adsorption phenomena
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Adsorption phenomena
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Isotherm of Langmuir
Langmuir, I.,. J. Am. Chem. Soc, 1918. 40: p. 1399-1400.
Choc sans adsorption
Choc avec adsorption
Désorption
€
Γ =KaC1+ KaC
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Scaling laws indicate that adsorption phenomena are important in microfluidics
€
Qadsorbée ≈ KaCS ~ l2
Qtransportée ≈ CV ~ l3
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6) Microfluidic chromatography
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Basics of chromatography
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N =traveldis tance
width⎛
⎝⎜
⎞
⎠⎟2
N ~ L2
Deff L /U( )~ ULDeff
Basis of chromatography
Number of theoretical plates
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U
l ≈ √Deff t
Estimation à la Taylor-Aris :
Deff≈ Pe2D ≈ U2b2/D
U
Estimate of the efficiency of a chromatographic column
€
N ~ ULDeff
~ ULDU 2b2
~ LDUb2
~ µL2DΔPb4
~ L2
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Pro/con of miniaturisation of chromatographic columns
Pilot Plant preparation column chromatography Genzyme Pharmaceuticals
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Pro/con of miniaturisation of chromatographic columns
Pro - Small samples - Intégration - Parallelism Con Degradation of analytical performances
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7) Transport of nanoparticles in microfluidic channels
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PFF – Pinched flow fractionation
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x
z
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Behavior of a particle close to the wall
- Hindered diffusion: D⊥ ≈z− rr
D;D// ≈ D 1− 9r16z
+...⎛
⎝⎜
⎞
⎠⎟
- Van der Waals forces:
- Electrostatic forces:
!!"#! −!
6!(! − !)!
!! = ! !!!/!!
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