Мікро- та наносенсори / L2
.7.pdf
Principles of Electronic Nanobiosensors
Unit 2: Settling Time
Lecture 2.7: Beating the Diffusion Limit:
Enhanced Diffusion and Fluid Flow
By Muhammad A. Alam
Professor of Electrical and Computer Engineering Purdue University
alam@purdue.edu
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Outline
• Diffusion in multiple dimensions
• Sensor in flow channel: theory
• Sensor in flow channel: characteristics
• Conclusion
Alam, Principles of Nanobiosensors, 2013 |
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dimensions
ρ3
I3 |
I |
LA |
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I1 |
I3 =×CD,ss− (ρ3 |
ρ0 ) |
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I3 = I1 |
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I =−4π D (×a−1 |
r −1 )−1 |
ρ |
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I |
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(ρ3 − ρ1 ) |
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Isphere |
= 4π D3aρ3 |
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(ρ − ρ |
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in
ρ1 )
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LA |
J (x)dx |
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LA |
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2π a |
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=− LA (D x) (ρ ρ |
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∫0 |
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1 0 |
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L |
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ρ1 |
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J(x) |
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I ≡ C |
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(ρ − ρ |
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I1 |
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ρ0 |
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2,1 |
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Alam, Principles of Nanobiosensors, 2013
Fast di usion in mul7ple dimensions
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T. Hu And Shklovkii, 2006 |
I3 =−C3,2 (ρ3 |
ρ1 ) |
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Richer and M. Eigen, Biophys. Chem. 2, 255, 1974 |
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Berg,Winter, von Hippel, Biochemistry, 20,6929, 1981 |
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I1 ≡ C2,1 (ρ1 − ρ0 ) |
I1 = I3 |
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I = C ρ = |
C2,1C3,2 |
ρ |
3 |
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1 |
1 |
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C2,1 |
+ C3,2 |
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→ C3,2 ρ3 |
D1 ? D3 |
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I1 |
2π D L |
ρ |
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Isphere |
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L |
A |
1 |
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L |
A |
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Isphere |
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= → |
3 |
A ×3 |
= |
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a |
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ln(r a) |
a |
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ln(r a) |
2 |
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Catches like a cylinder, but integrates to a point (LA~micron, a~10s nm)
Alam, Principles of Nanobiosensors, 2013 |
5 |
Aside: Inspira7ons
Looking for a target |
Looking for a lost |
on a DNA |
child in a city |
Alam, Principles of Nanobiosensors, 2013 |
6 |
Outline
• Diffusion in multiple dimensions
• Sensor in flow channel: theory
• Sensor in flow channel: characteristics
• Conclusion
Alam, Principles of Nanobiosensors, |
7 |
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2013 |
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in
Top view |
Side view |
W
Alam, Principles of Nanobiosensors, 2013
Total flux to a disk with fluid flow
the balance between convective and diffusive
P = |
6Q a 2 |
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e |
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4 − 0 |
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P3 |
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e |
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1− 0 |
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I = ρ0aD |
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3.55 |
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2.157 |
P + |
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e |
6 |
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for
for
depletion |
w |
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zone |
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Flow volume
<1
>1
Will see how this comes about? |
9 |
*W. Zhang et al. J. Phys. Chem. 100 (1996) 9462 |
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I =+ρ+aD |
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P |
3.55 |
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2.157 3 |
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0 |
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P |
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e |
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I |
Is |
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I =− |
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Is =−4 |
δ )−1 )−1 |
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ISmax = 4Dρ0 |
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= 4 |
δ |
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IS |
= |
a + δ |
= 1 |
+ |
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a |
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IS ,max |
δ |
δ |
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