We theoretically examine the widespread hypothesis of an electroviscous origin of the increase in apparent viscosity observed in recent experiments on capillary filling of nanochannels. Including Debye-layer corrections to the hydraulic resistance, we find that the apparent viscosity reaches a maximum in the mesoscopic regime where the channel height (or more generally the hydraulic radius) is comparable to the screening length. However, for realistic estimates of central parameters, we find that the electroviscous contribution to the apparent viscosity is at most a 1% effect.

1.
J. O.
Tegenfeldt
,
C.
Prinz
,
H.
Cao
,
S.
Chou
,
W. W.
Reisner
,
R.
Riehn
,
Y. M.
Wang
,
E. C.
Cox
,
J. C.
Sturm
,
P.
Silberzan
, and
R. H.
Austin
,
Proc. Natl. Acad. Sci. U.S.A.
101
,
10979
(
2004
).
2.
W.
Reisner
,
K. J.
Morton
,
R.
Riehn
,
Y. M.
Wang
,
Z. N.
Yu
,
M.
Rosen
,
J. C.
Sturm
,
S. Y.
Chou
,
E.
Frey
, and
R. H.
Austin
,
Phys. Rev. Lett.
94
,
196101
(
2005
).
3.
J. P.
Fu
,
J.
Yoo
, and
J. Y.
Han
,
Phys. Rev. Lett.
97
,
018103
(
2006
).
4.
W.
Reisner
,
J. P.
Beech
,
N. B.
Larsen
,
H.
Flyvbjerg
,
A.
Kristensen
, and
J. O.
Tegenfeldt
,
Phys. Rev. Lett.
99
,
058302
(
2007
).
5.
X. G.
Liang
,
K. J.
Morton
,
R. H.
Austin
, and
S. Y.
Chou
,
Nano Lett.
7
,
3774
(
2007
).
6.
M.
Gersborg-Hansen
and
A.
Kristensen
,
Appl. Phys. Lett.
89
,
103518
(
2006
).
7.
H.
Bruus
,
Theoretical Microfluidics
, 1st ed. (
Oxford University Press
,
Oxford
,
2007
).
8.
E. W.
Wasburn
,
Phys. Rev.
17
,
273
(
1921
).
9.
N. R.
Tas
,
J.
Haneveld
,
H. V.
Jansen
,
M.
Elwenspoek
, and
A.
van den Berg
,
Appl. Phys. Lett.
85
,
3274
(
2004
).
10.
L. H.
Thamdrup
,
F.
Persson
,
H.
Bruus
,
A.
Kristensen
, and
H.
Flyvbjerg
,
Appl. Phys. Lett.
91
,
163505
(
2007
).
11.
N. A.
Mortensen
,
L. H.
Olesen
, and
H.
Bruus
,
New J. Phys.
8
,
37
(
2006
).
12.
N. A.
Mortensen
,
L. H.
Olesen
,
F.
Okkels
, and
H.
Bruus
,
Microscale Thermophys. Eng.
11
,
57
(
2007
).
13.
D.
Burgreen
and
F. R.
Nakache
,
J. Phys. Chem.
68
,
1084
(
1964
).
14.
F.
Persson
,
L. H.
Thamdrup
,
M. B. L.
Mikkelsen
,
S. E.
Jaarlgard
,
P.
Skafte-Pedersen
,
H.
Bruus
, and
A.
Kristensen
,
Nanotechnology
18
,
246301
(
2007
).
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