When a particle is moving inside a channel, its hydrodynamic interaction with channel walls increases its drag coefficient, causing a diffusivity reduction. For charged particles moving in an electrolytic solution, there is an additional drag due to the distortion of an electrical double layer caused by particle motion known as the relaxation effect. Effects of relaxation on drag forces on spheres confined in rectangular channels are computed employing perturbations involving particle Peclet number and surface charge densities. Results indicate that confinement amplifies electrokinetic retardation; increasing the relative particle size or decreasing the channel cross section area enhances the relaxation effect. With the relative particle size kept constant, the relaxation effect on the drag exerted on charged spheres in cylindrical pores with its smaller cross section area is stronger than that on charged spheres in rectangular channels and slit pores. However, for certain values of Debye length and particle size, the ratio between excess drag due to relaxation on confined charged spheres and hydrodynamic drag on uncharged spheres confined at the same location is higher for particles in rectangular channels, resulting in higher percentages of diffusivity reduction. Diffusivity reduction due to relaxation of charged particles in square ducts displays a maximum as a function of relative particle size, whereas that of charged particles in rectangular channels with higher cross section aspect ratio increases monotonically as particle size increases.

References

References
1.
Kang
,
Y.
, and
Li
,
D.
,
2009
, “
Electrokinetic Motion of Particles and Cells in Microchannels
,”
Microfluid. Nanofluid.
,
6
(
4
), pp.
431
460
.
2.
Ai
,
Y.
, and
Qian
,
S.
,
2011
, “
Electrokinetic Particle Translocation Through a Nanopore
,”
Phys. Chem. Chem. Phys.
,
13
(
9
), pp.
4060
4071
.
3.
Ai
,
Y.
, and
Qian
,
S.
,
2011
, “
Direct Numerical Simulation of Electrokinetic Translocation of a Cylindrical Particle Through a Nanopore Using a Poisson-Boltzmann Approach
,”
Electrophoresis
,
32
(
9
), pp.
996
1005
.
4.
Yeh
,
L. H.
,
Zhang
,
M.
,
Joo
,
S. W.
,
Qian
,
S.
, and
Hsu
,
J. P.
,
2012
, “
Controlling pH-Regulated Bionanoparticles Translocation Through Nanopores With Polyelectrolyte Brushes
,”
Anal. Chem.
,
84
(
21
), pp.
9615
9622
.
5.
Aksimentiev
,
A.
,
Heng
,
J. B.
,
Timp
,
G.
, and
Schulten
,
K.
,
2004
, “
Microscopic Kinetics of DNA Translocation Through Synthetic Nanopores
,”
Biophys. J.
,
87
(
3
), pp.
2086
2097
.
6.
Heng
,
J. B.
,
Ho
,
C.
,
Kim
,
T.
,
Timp
,
R.
,
Aksimentiev
,
A.
,
Grinkova
,
Y. V.
,
Sligar
,
S.
,
Schulten
,
K.
, and
Timp
,
G.
,
2004
, “
Sizing DNA Using a Nanometer-Diameter Pore
,”
Biophys. J.
,
87
(
4
), pp.
2905
2911
.
7.
Zhang
,
M.
,
Yeh
,
L. H.
,
Qian
,
S.
,
Hsu
,
J. P.
, and
Joo
,
S. W.
,
2012
, “
DNA Electrokinetic Translocation Through a Nanopore: Local Permittivity Environment Effect
,”
J. Phys. Chem. C
,
116
(
7
), pp.
4793
4801
.
8.
Stone
,
H. A.
,
Stroock
,
A. D.
, and
Ajdari
,
A.
,
2004
, “
Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-a-Chip
,”
Annu. Rev. Fluid Mech.
,
36
(
1
), pp.
381
411
.
9.
Bazant
,
M. Z.
, and
Squire
,
T. M.
,
2004
, “
Induced-Charge Electrokinetic Phenomena: Theory and Microfluidic Applications
,”
Phys. Rev. Lett.
,
92
(
6
), p.
066101
.
10.
Chin
,
C. D.
,
Linder
,
V.
, and
Sia
,
S. K.
,
2007
, “
Lab-on-a-Chip Devices for Global Health: Past Studies and Future Opportunities
,”
Lab Chip
,
7
(
1
), pp.
41
57
.
11.
Batchelor
,
G.
,
1974
Transport Properties of Two-Phase Materials With Random Structure
,”
Annu. Rev. Fluid Mech.
,
6
, pp.
227
255
.
12.
Deen
,
W. M.
,
1987
, “
Hindered Transport of Large Molecules in Liquid-Filled Pores
,”
AIChE J.
,
33
(
9
), pp.
1409
1425
.
13.
Pozrikidis
,
C.
,
1992
,
Boundary Integral and Singularity Methods for Linearized Viscous Flow
,
Cambridge University Press
,
New York
.
14.
Brenner
,
H.
, and
Gaydos
,
L. J.
,
1977
, “
The Constrained Brownian Movement of Spherical Particles in Cylindrical Pores of Comparable Radius
,”
J. Colloid Interface Sci.
,
58
(
2
), pp.
312
356
.
15.
Smith
,
F. G.
, and
Deen
,
W. M.
,
1983
, “
Electrostatic Effects on the Partition of Spherical Colloids Between Dilute Bulk Solution and Cylindrical Pores
,”
J. Colloid Interface Sci.
,
91
(
2
), pp.
571
590
.
16.
Otani
,
H.
,
Akinaga
,
T.
, and
Sugihara-seki
,
M.
,
2011
, “
The Charge Effect on the Hindrance Factors for Diffusion and Convection of a Solute in Pores: I
,”
Fluid Dyn. Res.
,
43
(
6
), pp.
1
12
.
17.
Akinaga
,
T.
,
Otani
,
H.
, and
Sugihara-seki
,
M.
,
2012
, “
The Charge Effect on the Hindrance Factors for Diffusion and Convection of a Solute in Pores: II
,”
Fluid Dyn. Res.
,
44
(
6
), pp.
1
14
.
18.
Chun
,
M.
, and
Phillips
,
R. J.
,
1997
, “
Electrostatic Partitioning in Slit Pores by Gibbs Ensemble Monte Carlo Simulation
,”
AIChE J.
,
43
(
5
), pp.
1194
1203
.
19.
Hsu
,
J. P.
, and
Liu
,
B.
,
1999
, “
Electrical Interaction Energy between Two Charged Entities in an Electrolyte Solution
,”
J. Colloid Interface Sci.
,
217
(
2
), pp.
219
236
.
20.
Booth
,
F.
,
1954
, “
Sedimentation Potential and Velocity of Solid Spherical Particles
,”
J. Chem. Phys.
,
22
(
12
), pp.
1956
1968
.
21.
Stigter
,
D.
,
1980
, “
Sedimentation of Highly Charged Colloidal Spheres
,”
J. Phys. Chem.
,
84
(
21
), pp.
2758
2762
.
22.
Ohshima
,
H.
,
Healy
,
T. W.
, and
White
,
L. R.
,
1984
, “
Sedimentation Velocity and Potential of Dilute of Charged Spherical Colloidal Particles
,”
J. Chem. Soc., Faraday Trans. 2
,
80
(
10
), pp.
1299
1317
.
23.
Lee
,
E.
,
Chu
,
J. W.
, and
Hsu
,
J. P.
,
1999
, “
Sedimentation Potential of a Concentrated Spherical Colloidal Suspension
,”
J. Chem. Phys.
,
110
(
23
), pp.
11643
11651
.
24.
Keh
,
H. J.
, and
Ding
,
J. M.
,
2000
, “
Sedimentation Velocity and Potential in Concentrated Suspensions of Charged Spheres With Arbitrary Double-Layer Thickness
,”
J. Colloid Interface Sci.
,
227
(
2
), pp.
540
552
.
25.
Yeh
,
P. H.
,
Hsu
,
J. P.
, and
Teng
,
S.
,
2014
, “
Influence of Polyelectrolyte Shape on Its Sedimentation Behavior: Effect of Relaxation Electric Field
,”
Soft Matter
,
10
(
44
), pp.
8864
8874
.
26.
Booth
,
F.
,
1950
, “
The Cataphoresis of Spherical, Solid Non-Conducting Particles in a Symmetrical Electrolyte
,”
Proc. R. Soc. London A
,
203
(
1075
), pp.
514
533
.
27.
Wiersama
,
P. H.
,
Loeb
,
A. L.
, and
Overbeek
,
J. T. G.
,
1966
, “
Calculation of the Electrophoretic Mobility of a Spherical Colloid Particle
,”
J. Colloid Interface Sci.
,
22
(
1
), pp.
78
99
.
28.
O'Brien
,
R. W.
, and
White
,
L. R.
,
1978
, “
Electrophoretic Mobility of a Spherical Colloidal Particle
,”
J. Chem. Soc., Faraday Trans. 2
,
74
, pp.
1607
1626
.
29.
Ohshima
,
H.
,
2011
, “
Electrophoretic Mobility of a Highly Charged Soft Particle: Relaxation Effect
,”
Colloids Surf. A: Physicochem. Eng. Aspects
,
36
(
1–3
), pp.
72
75
.
30.
Pujar
,
N. S.
, and
Zydney
,
A. L.
,
1996
, “
Boundary Effects on the Sedimentation and Hindered Diffusion of Charged Particles
,”
AIChE J.
,
42
(
8
), pp.
2101
2111
.
31.
Lee
,
E.
,
Yen
,
C. B.
, and
Hsu
,
J. P.
,
2000
, “
Sedimentation of a Nonconducting Sphere in a Spherical Cavity
,”
J. Phys. Chem. B
,
104
(
29
), pp.
6815
6820
.
32.
Keh
,
H. J.
, and
Cheng
,
T. F.
,
2011
, “
Sedimentation of a Charged Colloidal Sphere in a Charged Cavity
,”
J. Chem. Phys.
,
135
(
21
), p.
214706
.
33.
Dechadilok
,
P.
, and
Deen
,
W. M.
,
2009
, “
Electrostatic and Electrokinetic Effects on Hindered Diffusion in Pores
,”
J. Membr. Sci.
,
336
(
1–2
), pp.
7
16
.
34.
Yalcin
,
S. E.
,
Lee
,
S. Y.
,
Joo
,
S. W.
,
Baysal
,
O.
, and
Qian
,
S.
,
2010
, “
Electrodiffusiophoretic Motion of a Charged Spherical Particles in a Nanopore
,”
J. Phys. Chem. B.
,
114
(
11
), pp.
4082
4093
.
35.
Zhang
,
M.
,
Ye
,
A.
,
Kim
,
D. S.
,
Jeong
,
J. H.
,
Joo
,
S. W.
, and
Qian
,
S.
,
2011
, “
Electrophoretic Motion of a Soft Spherical Particle in a Nanopore
,”
Colloid Surf. B
,
88
(
1
), pp.
165
174
.
36.
Wang
,
N.
,
Yee
,
C. P.
,
Chen
,
Y. Y.
,
Hsu
,
J. P.
, and
Tseng
,
S.
,
2013
, “
Electrophoresis of a pH-Regulated Zwitterionic Nanoparticle in a pH-Regulated Zwitterionic Capillary
,”
Langmuir
,
29
(
23
), pp.
7162
7169
.
37.
Qiu
,
Y.
,
Yang
,
C.
,
Hinkle
,
P.
,
Vlassiouk
,
I. V.
, and
Siwy
,
Z. S.
,
2015
, “
Anomalous Mobility of Highly Charged Particles in Pores
,”
Anal. Chem.
,
87
(
16
), pp.
8517
8523
.
38.
Van de Ven
,
T. G. M.
,
1989
,
Colloidal Hydrodynamics
,
Academic Press
,
San Diego, CA
.
39.
Ilic
,
V.
,
Tullock
,
D.
,
Phan-Thien
,
N.
, and
Graham
,
A. L.
,
1992
, “
Translation and Rotation of Spheres Settling in Square and Circular Conduits: Experiments and Numerical Predictions
,”
Int. J. Multiphase Flow
,
18
(
6
), pp.
1061
1075
.
40.
Feng
,
Z.
, and
Michaelides
,
E. E.
,
2002
, “
Hydrodynamic Forces on Spheres in Cylindrical and Prismatic Enclosures
,”
Int. J. Multiphase Flow
,
28
(
3
), pp.
479
496
.
41.
Gentile
,
F. S.
,
De Santo
,
I.
,
D'Avino
,
G.
,
Rossi
,
L.
,
Romeo
,
G.
,
Greco
,
F.
,
Netti
,
P. A.
, and
Maffettone
,
P. L.
,
2015
, “
Hindered Brownian Diffusion in a Square-Shaped Geometry
,”
J. Colloid Interface Sci.
,
447
, pp.
25
32
.
42.
Ganatos
,
P.
,
Pfeffer
,
R.
, and
Weinbaum
,
S.
,
1980
, “
A Strong Interaction Theory for the Creeping Motion of a Sphere Between Plane Parallel Boundaries. 2. Parallel Motion
,”
J. Fluid Mech.
,
99
(
4
), pp.
755
783
.
43.
Weinbaum
,
S.
,
1981
, “
Strong Interaction Theory for Particle Motion through Pores and Near Boundaries in Biological Flows at Low Reynolds Number
,”
Some Mathematical Questions in Biology
, S. Childress, ed., The American Mathematical Society, Providence, RI, pp.
119
146
.
44.
Happel
,
J.
, and
Brenner
,
H.
,
1983
,
Low Reynolds Number Hydrodynamics
,
Martinus Nijhoff
,
The Hague, The Netherlands
.
45.
Staben
,
M. E.
,
Zinchenko
,
A. Z.
, and
Davis
,
R. H.
,
2003
, “
Motion of a Particle Between Two Parallel Plane Walls in Low-Reynolds-Number Poiseuille Flow
,”
Phys. Fluids.
,
15
(
6
), pp.
1711
1733
.
46.
Gupta
,
M.
,
2004
, “
Polymer and Sphere Diffusion in Confinement
,” M.S. thesis, Massachusetts Institute of Technology, Cambridge, MA.
47.
Dechadilok
,
P.
, and
Deen
,
W. M.
,
2006
, “
Hindrance Factors for Diffusion and Convection in Pores
,”
Ind. Eng. Chem. Res.
,
45
(
21
), pp.
6953
6959
.
48.
Johnson
,
K. A.
,
Westermann-Clark
,
G. B.
, and
Shah
,
D. O.
,
1989
, “
Diffusion of Charged Micelles through Charged Microporous Membranes
,”
Langmuir
,
5
(
4
), pp.
932
938
.
49.
Verway
,
E. J. W.
, and
Overbeek
,
J. Th. G.
,
1948
,
Theory of the Stability of Lyophobic Colloids
,
Elsevier
,
Amsterdam, The Netherlands
.
You do not currently have access to this content.