In the present work, we attempt to analyze the electroosmotic flow of a viscoelastic fluid, following quasi-linear constitutive behavior, over charge modulated surfaces in narrow confinements. We obtain analytical solutions for the flow field for thin electrical double layer (EDL) limit through asymptotic analysis for small Deborah numbers. We show that a combination of matched and regular asymptotic expansion is needed for the thin EDL limit. We subsequently determine the modified Smoluchowski slip velocity for viscoelastic fluids and show that the quasi-linear nature of the constitutive behavior adds to the periodicity of the flow. We also obtain the net throughput in the channel and demonstrate its relative decrement as compared to that of a Newtonian fluid. Our results may have potential implications towards augmenting microfluidic mixing by exploiting electrokinetic transport of viscoelastic fluids over charge modulated surfaces.
REFERENCES
1.
M.
Brust
, C.
Schaefer
, R.
Doerr
, L.
Pan
, M.
Garcia
, P.
Arratia
, and C.
Wagner
, “Rheology of human blood plasma: Viscoelastic versus Newtonian behavior
,” Phys. Rev. Lett.
110
, 078305
(2013
).2.
T.
Das
and S.
Chakraborty
, “Perspective: Flicking with flow: Can microfluidics revolutionize the cancer research?
,” Biomicrofluidics
7
, 11811
(2013
).3.
J.
Dhar
, U.
Ghosh
, and S.
Chakraborty
, “Alterations in streaming potential in presence of time periodic pressure-driven flow of a power law fluid in narrow confinements with nonelectrostatic ion–ion interactions
,” Electrophoresis
35
, 662
(2014
).4.
G. C.
Georgiou
, “The time-dependent, compressible Poiseuille and extrudate-swell flows of a Carreau fluid with slip at the wall
,” J. Non-Newtonian Fluid Mech.
109
, 93
(2003
).5.
J.
Boyd
, J. M.
Buick
, and S.
Green
, “Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method
,” Phys. Fluids
19
, 093103
(2007
).6.
P. J.
Oliveira
and F. T.
Pinho
, “Analytical solution for fully developed channel and pipe flow of Phan-Thien–Tanner fluids
,” J. Fluid Mech.
387
, 271
(1999
).7.
A. M.
Afonso
, M. A.
Alves
, and F. T.
Pinho
, “Analytical solution of two-fluid electro-osmotic flows of viscoelastic fluids
,” J. Colloid Interface Sci.
395
, 277
(2013
).8.
A. M.
Afonso
, M. A.
Alves
, and F. T.
Pinho
, “Electro-osmotic flow of viscoelastic fluids in microchannels under asymmetric zeta potentials
,” J. Eng. Math.
71
, 15
(2010
).9.
A. M.
Afonso
, M. A.
Alves
, and F. T.
Pinho
, “Analytical solution of mixed electro-osmotic/pressure driven flows of viscoelastic fluids in microchannels
,” J. Non-Newtonian Fluid Mech.
159
, 50
(2009
).10.
N.
Aggarwal
and K.
Sarkar
, “Effects of matrix viscoelasticity on viscous and viscoelastic drop deformation in a shear flow
,” J. Fluid Mech.
601
, 63
(2008
).11.
F. T.
Akyildiz
and H.
Bellout
, “Viscoelastic lubrication with Phan-Thein-Tanner fluid (PTT)
,” J. Tribol.
126
, 288
(2004
).12.
A. M.
Ardekani
, D. D.
Joseph
, D.
Dunn-Rankin
, and R. H.
Rangel
, “Particle-wall collision in a viscoelastic fluid
,” J. Fluid Mech.
633
, 475
(2009
).13.
A.
Bandopadhyay
, U.
Ghosh
, and S.
Chakraborty
, “Time periodic electroosmosis of linear viscoelastic liquids over patterned charged surfaces in microfluidic channels
,” J. Non-Newtonian Fluid Mech.
202
, 1
(2013
).14.
P. C.-H.
Chan
and L. G.
Leal
, “The motion of a deformable drop in a second-order fluid
,” J. Fluid Mech.
92
, 131
(2006
).15.
S.
Dhinakaran
, A. M.
Afonso
, M. A.
Alves
, and F. T.
Pinho
, “Steady viscoelastic fluid flow between parallel plates under electro-osmotic forces: Phan-Thien-Tanner model
,” J. Colloid Interface Sci.
344
, 513
(2010
).16.
Y.
Fan
, R. I.
Tanner
, and N.
Phan-Thien
, “Fully developed viscous and viscoelastic flows in curved pipes
,” J. Fluid Mech.
440
, 327
(2001
).17.
L. L.
Ferrás
, A. M.
Afonso
, M. A.
Alves
, J. M.
Nóbrega
, and F. T.
Pinho
, “Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids
,” J. Colloid Interface Sci.
420
, 152
(2014
).18.
J.-W.
Ha
and S.-M.
Yang
, “Deformation and breakup of a second-order fluid droplet in an electric field
,” Korean J. Chem. Eng.
16
, 585
(1999
).19.
M. A.
Hanyk
and R. E.
Khayat
, “Steady and transient thin-jet flow of a viscoelastic fluid
,” Phys. Rev. E
88
, 053005
(2013
).20.
D.
Khismatullin
and A.
Nadim
, “Shape oscillations of a viscoelastic drop
,” Phys. Rev. E
63
, 061508
(2001
).21.
L. G.
Leal
, “The slow motion of slender rod-like particles in a second-order fluid
,” J. Fluid Mech.
69
, 305
(2006
).22.
L.
Liu
and L.
Lu
, “Instability of viscoelastic annular liquid jets in a radial electric field
,” J. Fluids Eng.
136
, 081202
(2014
).23.
S.
Mukherjee
and K.
Sarkar
, “Viscoelastic drop falling through a viscous medium
,” Phys. Fluids
23
, 013101
(2011
).24.
S.
Mukherjee
and K.
Sarkar
, “Effects of matrix viscoelasticity on the lateral migration of a deformable drop in a wall-bounded shear
,” J. Fluid Mech.
727
, 318
(2013
).25.
T. C.
Niederkorn
and J. M.
Ottino
, “Mixing of a viscoelastic fluid in a time-periodic flow
,” J. Fluid Mech.
256
, 243
(2006
).26.
M. L.
Olivares
, L.
Vera-Candioti
, and C. L. A.
Berli
, “The EOF of polymer solutions
,” Electrophoresis
30
, 921
(2009
).27.
N.
Phan-Thien
and R. I.
Tanner
, “Viscoelastic squeeze-film flows–Maxwell fluids
,” J. Fluid Mech.
129
, 265
(1983
).28.
S. B.
Pillapakkam
, P.
Singh
, D.
Blackmore
, and N.
Aubry
, “Transient and steady state of a rising bubble in a viscoelastic fluid
,” J. Fluid Mech.
589
, 215
(2007
).29.
S.
Saprykin
, R. J.
Koopmans
, and S.
Kalliadasis
, “Free-surface thin-film flows over topography: Influence of inertia and viscoelasticity
,” J. Fluid Mech.
578
, 271
(2007
).30.
B. Z.
Vamerzani
, M.
Norouzi
, and B.
Firoozabadi
, “Analytical solution for creeping motion of a viscoelastic drop falling through a Newtonian fluid
,” Korea-Aust. Rheol. J.
26
, 91
(2014
).31.
A.
Bandopadhyay
, U.
Ghosh
, and S.
Chakraborty
, “Capillary filling dynamics of viscoelastic fluids
,” Phys. Rev. E
89
, 053024
(2014
).32.
J.
Dhar
, A.
Bandopadhyay
, and S.
Chakraborty
, “Electro-osmosis of electrorheological fluids
,” Phys. Rev. E
88
, 053001
(2013
).33.
S.
Das
and S.
Chakraborty
, “Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian bio-fluid
,” Anal. Chim. Acta
559
, 15
(2006
).34.
C.-O.
Ng
and C.
Qi
, “Electroosmotic flow of a power-law fluid in a non-uniform microchannel
,” J. Non-Newtonian Fluid Mech.
208-209
, 118
(2014
).35.
A.
Ajdari
, “Electro-osmosis on inhomogeneously charged surfaces
,” Phys. Rev. Lett.
75
, 755
(1995
).36.
U.
Ghosh
and S.
Chakraborty
, “Patterned-wettability-induced alteration of electro-osmosis over charge-modulated surfaces in narrow confinements
,” Phys. Rev. E
85
, 046304
(2012
).37.
C.-O.
Ng
and H. C. W.
Chu
, “Electrokinetic flows through a parallel-plate channel with slipping stripes on walls
,” Phys. Fluids
23
, 102002
(2011
).38.
S. S.
Bahga
, O. I.
Vinogradova
, and M. Z.
Bazant
, “Anisotropic electro-osmotic flow over super-hydrophobic surfaces
,” J. Fluid Mech.
644
, 245
(2010
).39.
A.
Ajdari
, “Generation of transverse fluid currents and forces by an electric field: Electro-osmosis on charge-modulated and undulated surfaces
,” Phys. Rev. E
53
, 4996
(1996
).40.
C.-K.
Chen
and C.-C.
Cho
, “Electrokinetically-driven flow mixing in microchannels with wavy surface
,” J. Colloid Interface Sci.
312
, 470
(2007
).41.
C.-C.
Chang
and R.-J.
Yang
, “Chaotic mixing in a microchannel utilizing periodically switching electro-osmotic recirculating rolls
,” Phys. Rev. E
77
, 056311
(2008
).42.
H.
Sugioka
, “Chaotic mixer using electro-osmosis at finite Péclet number
,” Phys. Rev. E
81
, 036306
(2010
).43.
J.
Zhang
, G.
He
, and F.
Liu
, “Electro-osmotic flow and mixing in heterogeneous microchannels
,” Phys. Rev. E
73
, 056305
(2006
).44.
T.
Nguyen
, Y.
Xie
, L. J.
de Vreede
, A.
van den Berg
, and J. C. T.
Eijkel
, “Highly enhanced energy conversion from the streaming current by polymer addition
,” Lab Chip
13
, 3210
(2013
).45.
C. L. A.
Berli
, “Electrokinetic energy conversion in microchannels using polymer solutions
,” J. Colloid Interface Sci.
349
, 446
(2010
).46.
C.
Zhao
and C.
Yang
, “Electrokinetics of non-Newtonian fluids: A review
,” Adv. Colloid Interface Sci.
201-202
, 94
(2013
).47.
A.
Bandopadhyay
and S.
Chakraborty
, “Giant augmentations in electro-hydro-dynamic energy conversion efficiencies of nanofluidic devices using viscoelastic fluids
,” Appl. Phys. Lett.
101
, 043905
(2012
).48.
K.
Yeleswarapu
and M.
Kameneva
, “The flow of blood in tubes: Theory and experiment
,” Mech. Res. Commun.
25
, 257
(1998
).49.
R. G.
Owens
, “A new microstructure-based constitutive model for human blood
,” J. Non-Newtonian Fluid Mech.
140
, 57
(2006
).50.
T.
Bodnár
, a.
Sequeira
, L.
Pirkl
, T. E.
Simos
, G.
Psihoyios
, and C.
Tsitouras
, “Numerical simulations of blood flow in a stenosed vessel under different flow rates using a generalized Oldroyd-B model
,” AIP Conf. Proc.
1168
, 645
(2009
).51.
A.
Vissink
and H.
Waterman
, “Rheological properties of saliva substitutes containing mucin, carboxymethylcellulose or polyethylenoxide
,” J. Oral Pathol.
13
(1
), 22
(1984
).52.
A.
Ajdari
, “Transverse electrokinetic and microfluidic effects in micropatterned channels: Lubrication analysis for slab geometries
,” Phys. Rev. E
65
, 1
(2001
).53.
L. M.
Quinzani
, “Modeling the rheology of polyisobutylene solutions
,” J. Rheol.
34
, 705
(1990
).54.
R. B.
Bird
, R. C.
Armstrong
, and O.
Hassager
, in Dynamics of Polymeric Liquids: Fluid Mechanics
(John Wiley & Sons
, 1987
), Vol. 1
.55.
J.
Escandón
, F.
Santiago
, O.
Bautista
, and F.
Méndez
, “Hydrodynamics and thermal analysis of a mixed electromagnetohydrodynamic-pressure driven flow for Phan–Thien–Tanner fluids in a microchannel
,” Int. J. Therm. Sci.
86
, 246
(2014
).56.
W.
Tan
and T.
Masuoka
, “Stokes’ first problem for an Oldroyd-B fluid in a porous half space
,” Phys. Fluids
17
, 023101
(2005
).57.
Q.
Liu
, Y.
Jian
, and L.
Yang
, “Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel
,” Phys. Fluids
23
, 102001
(2011
).58.
M.
Kilic
, M.
Bazant
, and A.
Ajdari
, “Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations
,” Phys. Rev. E
75
, 021503
(2007
).59.
L. G.
Leal
, Advanced Transport Phenomena
(Cambridge University Press
, Cambridge
, 2007
).60.
© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
You do not currently have access to this content.
