FFF: Complete Description of Coupled
Transport and Biomolecular Interactions
E
C
DiffusionReaction
Navier
Stokes
M
"E.Q.S."
+ ρeE +other
(incompressible fluid)
TODAY: start “fully coupled”
(materialexamples
derivative)
1
ELECTROKINETIC PHENOMENA
Macro-porous
media models
Nano-continuum
models
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2
Electroporation: transient permeabilization of cell
membrane for gene transfection/therapy; drug
delivery; tumor treatment, and cell-based therapy
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3
2012
• It is shown that, in the presence of an electric pulse,
electrokinetic effects (electroosmosis & electrophoresis)
significantly influence ionic mass transfer through the
nanopores, while the effect of diffusion is negligible....
• Increasing the pore radius intensifies the effect of convection
(electroosmosis) on ionic flux compared to electrophoresis.
4
2012
E.O.
Diff
E.P.
0
= ∇⋅ Ni = ̶ ∂c/∂t
5
6
Zeta Potential versus Total Double Layer Potential
(Poisson-Boltzmann)
charged
surface
no-slip
boundary
zeta
potential
Total
double
layer
potential
δ
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7
Double Layer Models
(1) Poisson-Boltzmann
(expon.-like decay)
Φ(x)
Φ(x)
~ Φ exp(-κx)
Φo
σd
σd
_
_
_
_
_
_
εΦo
σd ≈
(1/κ)
1/κ
x
B.C. at x = 0:
8
Double Layer Models
Φ(x)
Φ(x)
~ Φ exp(-κx)
Φo
(1) Poisson-Boltzmann:
σd
Φ(x)
charged
surface
no-slip
boundary
+
+
+
δ (1/κ)
1/κ
x
(2) Electrokinetics:
ζ
σeff
εΦo
σd ≈
(1/κ)
σd
εζ
σd→"σeff" ≈
(1/κ)
zeta
potential
X
Infer
Measure
9
Models of Elec. Double Layer
plane of closest
approach
“no-slip”
plane
reversal
of surf.
charge
(−)
"Helmholtz"
double layer
"Diffuse" P-B
double layer
P6.1; analytical
model
model
with ion
adsorption;
ζ potential
with molec.
adsorption;
ζ potential
Electrokinetics
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10
Zeta Potential (particle charge) Instruments
Measure ζ → infer "σeff"
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11
Electrophoresis: Techniques & Methods
I. "Free Electrophoresis" (i.e., in free solution)
• 1930's "Moving Boundary" (Tiselius)
• 1970's "Micro-electrophoresis" (cells, etc.)
• 1980's "Capillary Electrophoresis"
• 1990's
MEMS; channels; (E.O. & E.P)
• 2000+
NEMS
II. "Zone E.P. (w. medium to suppress convection)
• paper; gel (SDS-PAGE)
• 1980's "Capillary "zone" (gel in pore)
• 1990's
MEMS channels (with gel in channels)
• 1980s to 1990s: "Pulsed Field"; "Rotary Field"
• 2000+
Lab-on-a Chip
12
Tiselius, 1931
in Lehninger, Biochemistry
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13
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14
Capillary
Electrophoresis
Eoz ~ 105 V/m
Electrophoresis
w.r.t. moving fluid
driven by
electroosmosis
_
+
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15
© Royal Society of Chemistry. All rights reserved. This content is excluded from our Creative
Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
Source: Griebel, Anja et al. "Integrated polymer chip for two-dimensional capillary gel
electrophoresis." Lab on a Chip 4, no. 1 (2004): 18-23.
16
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Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
17
Physical Biochemistry
D. Freifelder, Freeman, 1982
Chap 9
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18
Protein Purification: Principles and Practice
R. Scopes, Springer Verlag, 1982
© Springer. All rights reserved. This content is excluded from our Creative Commons
license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
19
Methods in Molecular Biophysics:
Serdyuk, Zaccai and Zaccai, Cambridge Univ Press, 2007
Sec D.5.4.1 Charge and Electrophoretic Mobility
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Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
20
2014
Dr. Thomas Waigh
Textbook cover removed due to copyright restrictions.
Source: Waigh, Thomas Andrew. The Physics of Living Processes:
A Mesoscopic Approach. John Wiley & Sons, 2014.
School of Physics
and Astronomy
Photon Science
Institute
University of
Manchester, UK
21
“Thus, ……the mobility can be related to the charge (Z)
and the radius (R).”
© John Wiley & Sons. All rights reserved. This content is excluded from our Creative
Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
Source: textbook: Waigh, Thomas Andrew. The Physics of Living Processes: A
Mesoscopic Approach. John Wiley & Sons, 2014.
22
© Agilent Technologies, Inc. All rights reserved. This content
is excluded from our Creative Commons license. For more
information, see http://ocw.mit.edu/help/faq-fair-use/.
1980’s
23
Page 20
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information, see http://ocw.mit.edu/help/faq-fair-use/.
24
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is excluded from our Creative Commons license. For more
information, see http://ocw.mit.edu/help/faq-fair-use/.
25
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information, see http://ocw.mit.edu/help/faq-fair-use/.
26
Page 676
istry
Biophysical Chemistry
Cantor and Schimmel, Freeman, 1980
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Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
27
Biophysical Chemistry
Cantor and Schimmel, Freeman, 1980
© W. H. Freeman and Company. All rights reserved. This content is excluded from our Creative
Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
28
Biophysical Chemistry
Cantor and Schimmel, Freeman, 1980
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Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
29
PNAS 2007
1980's huge bench top instrument becomes a little chip:
_
_
_
_
_
_
− wall charge (SiO¯)
_
_
_
_
_
_
_
_
Na+
_
Courtesy of National Academy of Sciences. Used with permission.
Source: Van den Heuvel, M. G. L. et al. "Electrophoresis of
individual microtubules in microchannels." Proceedings of the
National Academy of Sciences 104, no. 19 (2007): 7770-7775.
30
d
© National Academy of Sciences. All rights reserved. This content is excluded from our Creative
Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
Source: Van den Heuvel, M. G. L. et al. "Electrophoresis of individual microtubules in microchannels."
Proceedings of the National Academy of Sciences 104, no. 19 (2007): 7770-7775.
31
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