The electrokinetic transports of viscoelastic fluids are investigated in different channel geometries. The fluid elasticity is responsible for the generation of resonance behaviors under periodic pressure gradient driving. We introduce a universal Deborah number defined by the surface-to-volume ratio of the channel, and thereby a critical value Dec = 1/4 can be applied to different channel geometries. Above this threshold, the resonances occur at particular frequencies and result in a dramatic increase in the amplitudes of the flow rate, streaming potential, and energy conversion efficiency. The locations of resonant peaks are determined by the ratio of the effective characteristic size of the channel to the wavelength of viscoelastic shear waves. Interestingly, in the annular geometry with small effective size, even order resonances are suppressed significantly relative to odd order resonances. For the maximum energy conversion efficiency in steady flows in different geometries, we find that the annular geometry is optimal, which has a 20% increase in the maximum efficiency compared to the cylindrical geometry.
References
1.
S. H.
Sadek
and F. T.
Pinho
, “Electro-osmotic oscillatory flow of viscoelastic fluids in a microchannel
,” J. Non-Newtonian Fluid Mech.
266
, 46
–58
(2019
).2.
D.
Stein
, M.
Kruithof
, and C.
Dekker
, “Surface charge governed ion transport in nanofluidic channels
,” Phys. Rev. Lett.
93
(3
), 035901
(2004
).3.
C.
Pini
, T.
Baier
, and M.
Dietzel
, “Energy conversion by surface-tension-driven charge separation
,” Microfluid. Nanofluid.
19
, 721
–735
(2015
).4.
L. L.
Ferrás
, A. M.
Afonso
, M. A.
Alves
, J. M.
Nóbrega
, and F. T.
Pinho
, “Electro-osmotic and pressure-driven flow of viscoelastic fluids in microchannels: Analytical and semi-analytical solutions
,” Phys. Fluids
28
(9
), 093102
(2016
).5.
U.
Ghosh
, “Electrokinetic effects in helical flow of non-linear viscoelastic fluids
,” Phys. Fluids
32
(5
), 052004
(2020
).6.
B.
Mahapatra
and A.
Bandopadhyay
, “Numerical analysis of combined electroosmotic-pressure driven flow of a viscoelastic fluid over high zeta potential modulated surfaces
,” Phys. Fluids
33
, 12001
(2021
).7.
S.
Chakraborty
and S.
Das
, “Streaming-field-induced convective transport and its influence on the electroviscous effects in narrow fluidic confinement beyond the Debye-Hückel limit
,” Phys. Rev. E
77
(3
), 037303
(2008
).8.
R.
Sarma
, N.
Deka
, K.
Sarma
, and P. K.
Mondal
, “Electroosmotic flow of Phan-Thien-Tanner fluids at high zeta potentials: An exact analytical solution
,” Phys. Fluids
30
(6
), 062001
(2018
).9.
B.
Mahapatra
and A.
Bandopadhyay
, “Electroosmosis of a viscoelastic fluid over non-uniformly charged surfaces: Effect of fluid relaxation and retardation time
,” Phys. Fluids
32
(3
), 032005
(2020
).10.
S.
Das
, A.
Guha
, and S. K.
Mitra
, “Exploring new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with overlapping electric double layers
,” Anal. Chim. Acta
804
, 159
–166
(2013
).11.
Y.
Daghighi
and D.
Li
, “Numerical study of a novel induced-charge electrokinetic micro-mixer
,” Anal. Chim. Acta
763
, 28
–37
(2013
).12.
N.
Ali
, S.
Hussain
, and K.
Ullah
, “Theoretical analysis of two-layered electro-osmotic peristaltic flow of FENE-P fluid in an axisymmetric tube
,” Phys. Fluids
32
(2
), 023105
(2020
).13.
O.
Schnitzer
and E.
Yariv
, “Streaming-potential phenomena in the thin-Debye-layer limit. Part 3. Shear-induced electroviscous repulsion
,” J. Fluid Mech.
786
, 84
–109
(2016
).14.
X.
Xuan
and D.
Li
, “Thermodynamic analysis of electrokinetic energy conversion
,” J. Power Sources
156
(2
), 677
–684
(2006
).15.
J. F.
Osterle
, “Electrokinetic energy conversion
,” J. Appl. Mech.
31
, 161
–164
(1964
).16.
H.
Daiguji
, P.
Yang
, A.
Szeri
, and A.
Majumdar
, “Electrochemomechanical energy conversion in nanofluidic channels
,” Nano Lett.
4
, 2315
–2322
(2004
).17.
F. H.
van der Heyden
, D. J.
Bonthuis
, D.
Stein
, C.
Meyer
, and C.
Dekker
, “Electrokinetic energy conversion efficiency in nanofluidic channels
,” Nano Lett.
6
(10
), 2232
–2237
(2006
).18.
F. H.
van der Heyden
, D. J.
Bonthuis
, D.
Stein
, C.
Meyer
, and C.
Dekker
, “Power generation by pressure-driven transport of ions in nanofluidic channels
,” Nano Lett.
7
(4
), 1022
–1025
(2007
).19.
M.
Wang
and Q.
Kang
, “Electrochemomechanical energy conversion efficiency in silica nanochannels
,” Microfluid. Nanofluid
9
(2-3
), 181
–190
(2010
).20.
C. C.
Chang
and R. J.
Yang
, “Electrokinetic energy conversion efficiency in ion-selective nanopores
,” Appl. Phys. Lett.
99
(8
), 083102
(2011
).21.
A.
Siria
, P.
Poncharal
, A. L.
Biance
, R.
Fulcrand
, X.
Blase
, S. T.
Purcell
, and L.
Bocquet
, “Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube
,” Nature
494
(7438
), 455
–458
(2013
).22.
S.
Pennathur
, J. C. T.
Eijkel
, and A.
van den Berg
, “Energy conversion in microsystems: Is there a role for micro/nanofluidics?
,” Lab Chip
7
(10
), 1234
–1237
(2007
).23.
J.
Yang
, F.
Lu
, L. W.
Kostiuk
, and D. Y.
Kwok
, “Electrokinetic microchannel battery by means of electrokinetic and microfluidic phenomena
,” J. Micromech. Microeng.
13
, 963
–970
(2003
).24.
H.
Daiguji
, Y.
Oka
, T.
Adachi
, and K.
Shirono
, “Theoretical study on the efficiency of nanofluidic batteries
,” Electrochem. Commun.
8
(11
), 1796
–1800
(2006
).25.
C.
Davidson
and X.
Xuan
, “Electrokinetic energy conversion in slip nanochannels
,” J. Power Sources
179
(1
), 297
–300
(2008
).26.
Y.
Ren
and D.
Stein
, “Slip-enhanced electrokinetic energy conversion in nanofluidic channels
,” Nanotechnology
19
(19
), 195707
(2008
).27.
S.
Chanda
, S.
Sinha
, and S.
Das
, “Streaming potential and electroviscous effects in soft nanochannels: Towards designing more efficient nanofluidic electrochemomechanical energy converters
,” Soft Matter
10
(38
), 7558
–7568
(2014
).28.
J.
Patwary
, G.
Chen
, and S.
Das
, “Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density
,” Microfluid. Nanofluid.
20
(2
), 37
(2016
).29.
J.
Zhang
, K.
Zhan
, S.
Wang
, and X.
Hou
, “Soft interface design for electrokinetic energy conversion
,” Soft Matter
16
, 2915
–2927
(2020
).30.
A.
Bandopadhyay
and S.
Chakraborty
, “Steric-effect induced alterations in streaming potential and energy transfer efficiency of non-Newtonian fluids in narrow confinements
,” Langmuir
27
(19
), 12243
–12252
(2011
).31.
P.
Goswami
and S.
Chakraborty
, “Energy transfer through streaming effects in time-periodic pressure driven-nanochannel flows with interfacial slip
,” Langmuir
26
(1
), 581
–590
(2010
).32.
T.
Nguyen
, Y.
Xie
, L. J. D.
Vreede
, A.
van den Berg
, and J. C. T.
Eijkel
, “Highly enhanced energy conversion from the streaming current by polymer addition
,” Lab Chip
13
(16
), 3210
–3216
(2013
).33.
L.
Mei
, L.-H.
Yeh
, and S.
Qian
, “Buffer anions can enormously enhance the electrokinetic energy conversion in nanofluidics with highly overlapped double layers
,” Nano Energy
32
, 374
–381
(2017
).34.
F.
Munshi
and S.
Chakraborty
, “Hydroelectrical energy conversion in narrow confinements in the presence of transverse magnetic fields with electrokinetic effects
,” Phys Fluids
21
(12
), 122003
(2009
).35.
D.
Gillespie
, “High energy conversion efficiency in nanofluidic channels
,” Nano Lett.
12
(3
), 1410
–1416
(2012
).36.
A.
Bandopadhyay
and S.
Chakraborty
, “Giant augmentations in electro-hydro-dynamic energy conversion efficiencies of nanofluidic devices using viscoelastic fluids
,” Appl. Phys. Lett.
101
(4
), 043905
(2012
).37.
Z.
Ding
and Y.
Jian
, “Electrokinetic oscillatory flow and energy conversion of viscoelastic fluids in microchannels: A linear analysis
,” J. Fluid Mech.
(submitted; arXiv:2101.12517.38.
A. J.
O'Connor
, H. R. C.
Pratt
, and G. W.
Stevens
, “Electrophoretic mobilities of proteins and protein mixtures in porous membranes
,” Chem. Eng. Sci.
51
(13
), 3459
–3477
(1996
).39.
V. P.
Andreev
, S. B.
Koleshko
, D. A.
Holman
, L. D.
ScampaviA
, and G. D.
Christian
, “Hydrodynamics and mass transfer of coaxial jet mixer in flow injection analysis
,” Anal. Chem.
71
, 2199
(1999
).40.
R. C.
Wu
and K. D.
Papadopoulos
, “Electro-osmotic flow through porous media: Cylindrical and annular models
,” Colloids Surf., A
161
, 469
–476 (
2000
).41.
A. N.
Morozov
and W.
van Saarloos
, “An introductory essay on subcritical instabilities and the transition to turbulence in visco-elastic parallel shear flows
,” Phys. Rep.
447
, 112
–143
(2007
).42.
L.
Casanellas
and J.
Ortín
, “Laminar oscillatory flow of Maxwell and Oldroyd-B fluids: Theoretical analysis
,” J. Non-Newtonian Fluid Mech.
166
(23-24
), 1315
–1326
(2011
).43.
44.
J. H.
Masliyah
and S.
Bhattacharjee
, Electrokinetic and Colloid Transport Phenomena
(John Wiley & Sons
, 2006
).45.
Z.
Ding
, Y.
Jian
, and W.
Tan
, “Electrokinetic energy conversion of two-layer fluids through nanofluidic channels
,” J. Fluid Mech.
863
, 1062
–1090
(2019
).46.
F. W. J.
Olver
, D. W.
Lozier
, R. F.
Boisvert
, and C. W.
Clark
, NIST Handbook of Mathematical Functions
(Cambridge University Press
, 2010
).47.
Y. A.
Andrienko
, D. A.
Siginer
, and Y. G.
Yanovsky
, “Resonance behavior of viscoelastic fluids in Poiseuille flow and application to flow enhancement
,” Int. J. Non-Linear Mech.
35
(1
), 95
–102
(2000
).48.
S. K.
Griffiths
and R. H.
Nilson
, “The efficiency of electrokinetic pumping at a condition of maximum work
,” Electrophoresis
26
(2
), 351
–361
(2005
).© 2021 Author(s).
2021
Author(s)
You do not currently have access to this content.
