In the present study, we investigate the combined interplay of streaming potential and substrate compliance with sliding dynamics on the load carrying capacity of a planar slider bearing. We relax previously utilized simplifying assumptions to model the electrokinetic effects and demonstrate that the streaming potential may augment the load carrying capacity of the bearing to a considerable extent. Interestingly, we also reveal that the electrokinetically augmented load carrying capacity exhibits strong dependencies on a combination of the compliance and the sliding dynamics, which have, hitherto, not been extensively explored. This rich interplay reveals certain parametric regimes of interest, which are significant from the viewpoint of practical design considerations.
REFERENCES
1.
2.
J. M.
Skotheim
and L.
Mahadevan
, “Soft lubrication
,” Phys. Rev. Lett.
92
, 245509
(2004
).3.
J. M.
Skotheim
and L.
Mahadevan
, “Soft lubrication: The elastohydrodynamics of nonconforming and conforming contacts
,” Phys. Fluids
17
, 092101
(2005
).4.
X.
Yin
and S.
Kumar
, “Lubrication flow between a cavity and a flexible wall
,” Phys. Fluids
17
, 063101
(2005
).5.
J.
Urzay
, S. G.
Llewellyn Smith
, and B. J.
Glover
, “The elastohydrodynamic force on a sphere near a soft wall
,” Phys. Fluids
19
, 103106
(2007
).6.
A.
Shinkarenko
, Y.
Kligerman
, and I.
Etsion
, “The validity of linear elasticity in analyzing surface texturing effect for elastohydrodynamic lubrication
,” J. Tribol.
131
, 021503
(2009
).7.
M.
Abkarian
, C.
Lartigue
, and A.
Viallat
, “Tank treading and unbinding of deformable vesicles in shear flow: Determination of the lift force
,” Phys. Rev. Lett.
88
, 068103
(2002
).8.
J.
Beaucourt
, T.
Biben
, and C.
Misbah
, “Optimal lift force on vesicles near a compressible substrate
,” Eur. Phys. Lett.
67
, 676
(2004
).9.
James
P.
Butler
and Stephen H.
Loring
, “A potential elastohydrodynamic origin of load-support and Coulomb-like friction in lung/chest wall lubrication
,” J. Tribol.
130
, 041201
(2008
).10.
M.
Jones
, G.
Fulford
, C.
Please
, D.
McElwain
, and M.
Collins
, “Elastohydrodynamics of the eyelid wiper
,” Bull. Math. Biol.
70
, 323
(2008
).11.
A. J.
Szeri
, S. C.
Park
, S.
Verguet
, A.
Weiss
, and D. F.
Katz
, “A model of transluminal flow of an anti-HIV microbicide vehicle: Combined elastic squeezing and gravitational sliding
,” Phys. Fluids
20
, 083101
(2008
).12.
C.
de Loubens
, A.
Magnin
, M.
Doyennette
, I. C.
Tr
éléa, and I. Souchon, “A biomechanical model of swallowing for understanding the influence of saliva and food bolus viscosity on flavor release
,” J. Theor. Biol.
280
, 180
(2011
).13.
14.
H. A.
Stone
, A. D.
Stroock
, A.
Ajdari
, “Engineering flow in small devices: Microfluidics toward a Lab-on-a-Chip
,” Ann. Rev. Fluid Mech.
36
, 381
(2004
) and references therein.15.
T. M.
Squires
and S. R.
Quake
, “Microfluidics: Fluid physics at the nanoliter scale
,” Rev. Mod. Phys.
77
, 977
(2005
) and references therein.16.
17.
S.
Chakraborty
, in Encyclopedia of Microfluidics and Nanofluidics
, edited by D.
Li
(Springer
, New York
, 2008
).18.
G. A. H.
Elton
and F. G.
Hirschler
, “Electroviscosity. IV. Some extensions of the theory of flow of liquids in narrow channels
,” Proc. R. Soc. London, Ser. A
198
, 581
(1949
).19.
D.
Burgreen
and F. R.
Nakache
, “Electrokinetic flow in ultrafine capillary slits
,” J. Phys. Chem.
68
, 1084
(1964
).20.
C. L.
Rice
and R.
Whitehead
, “Electrokinetic flow in a narrow cylindrical capillary
,” J. Phys. Chem.
69
, 4017
(1965
).21.
S.
Levine
, J. R.
Marriott
, G.
Neale
, and N.
Epstein
, “Theory of electrokinetic flow in fine cylindrical capillaries at high zeta-potentials
,” J. Colloid Interface Sci.
52
, 136
(1975
).22.
E.
Donath
and A.
Voigt
, “Streaming current and streaming potential on structured surfaces
,” J. Colloid Interface Sci.
109
, 122
(1986
).23.
W. R.
Bowen
and F.
Jenner
, “Electroviscous effects in charged capillaries
,” J. Colloid Interface Sci.
173
, 388
(1995
).24.
D.
Li
, “Electro-viscous effects on pressure-driven liquid flow in microchannels
,” Colloid Surf. A
195
, 35
(2001
).25.
J.
Yang
, J. H.
Masliyah
, and D. Y.
Kwok
, “Streaming potential and electroosmotic flow in heterogeneous circular microchannels with nonuniform zeta potentials: Requirements of flow rate and current continuities
,” Langmuir
20
, 3863
(2004
).26.
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
, 1
(2008
).27.
X.
Xuan
, “Streaming potential and electroviscous effect in heterogeneous microchannels
,” Microfluid. Nanofluid.
4
, 457
(2008
).28.
H. M.
Park
and J. Y.
Lim
, “Streaming potential for microchannels of arbitrary cross-sectional shapes for thin electric double layers
,” J. Colloid Interface Sci.
336
, 834
(2009
).29.
M.
Wang
, C.-C.
Chang
, and R.-J.
Yang
, “Electroviscous effects in nanofluidic channels
,” J. Chem. Phys.
132
, 024701
(2010
).30.
H.
Zhao
, “Streaming potential generated by a pressure-driven flow over superhydrophobic stripes
,” Phys. Fluids
23
, 022003
(2011
).31.
K.
Sadlej
, E.
Wajnryb
, J.
Blawzdziewicz
, M. L.
Ekiel
-Jezewska, and Z.
Adamczyk
, “Streaming current and streaming potential for particle covered surfaces: Virial expansion and simulations
,” J. Chem. Phys.
130
, 144706
(2009
).32.
J. D.
Sherwood
, “Streaming potential generated by two-phase flow in a capillary
,” Phys. Fluids
19
, 053101
(2007
).33.
J. D.
Sherwood
, “Streaming potential generated by a long viscous drop in a capillary
,” Langmuir
24
, 10011
(2008
).34.
E.
Lac
and J. D.
Sherwood
, “Streaming potential generated by a drop moving along the centerline of a capillary
,” J. Fluid Mech.
640
, 55
(2009
).35.
J. D.
Sherwood
, “Streaming potential generated by a small charged drop in Poiseuille flow
,” Phys. Fluids
21
, 013101
(2009
).36.
J. D.
Sherwood
, “Streaming potential generated by two-phase flow in a polygonal capillary
,” J. Colloid Interface Sci.
349
, 417
(2010
).37.
M.
Wang
and Q.
Kang
, “Electromechanical energy conversion efficiency in silica nanochannels
,” Microfluid. Nanofluid.
9
, 181
(2010
).38.
C.-
C.
Chang
and R.
-J.
Yang
, “Electrokinetic energy conversion in micrometer-length nanofluidic channels
,” Microfluid. Nanofluid.
9
, 225
(2010
).39.
X.
Xuan
, “Streaming potential effects on solute dispersion in nanochannels
,” Anal. Chem.
79
, 7928
(2007
).40.
X.
Xuan
and D.
Sinton
, “Hydrodynamic dispersion of neutral solutes in nanochannels: The effect of streaming potential
,” Microfluid. Nanofluid.
3
, 723
(2007
).41.
D.
Dutta
, “Solutal transport in rectangular nanochannels under pressure-driven flow conditions
,” Microfluid. Nanofluid.
10
, 691
(2011
).42.
B.
Zhang
and N.
Umehara
, “Hydrodynamic lubrication theory considering electric double layer for very thin water film lubrication of ceramics
,” Jpn. Soc. Mech. Eng. Int. J. Ser. C
41
, 285
(1998
).43.
P. L.
Wong
, P.
Huang
, and Y.
Meng
, “The effect of the electric double layer on a very thin water lubricating film
,” Tribol. Lett.
14
, 197
(2003
).44.
X.
Wang
, S.
Bai
, and P.
Huang
, “Theoretical analysis and experimental study on the influence of electric double layer on thin film lubrication
,” Front. Mech. Eng. China
3
, 370
(2006
).45.
A.
Steinberger
, C.
Cottin
-Bizonne, P.
Kleimann
, and E.
Charlaix
, “Nanoscale flow on a bubble mattress: Effect of surface elasticity
,” Phys. Rev. Lett.
100
, 5
(2008
).46.
J.
Chakraborty
and S.
Chakraborty
, “Influence of streaming potential on the elastic response of a compliant microfluidic substrate subjected to dynamic loading
,” Phys. Fluids
22
, 122002
(2010
).47.
M. S.
Kilic
, M. Z.
Bazant
, and A.
Ajdari
, “Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging
,” Phys. Rev. E
75
, 021502
(2007
).48.
J.
Cervera
, V.
Garc
ía-Morales, and J. Pellicer, “Ion size effects on the electrokinetic flow in nanoporous membranes caused by concentration gradients
,” J. Phys. Chem. B.
107
, 8300
(2003
).49.
J.
Cervera
, P.
Ram
írez, J. A. Manzanares, and S. Mafé, “Incorporating ionic size in the transport equations for charged nanopores
,” Microfluid. Nanofluid.
9
, 41
(2010
).50.
A. S.
Khair
and T. M.
Squires
, “Ion steric effects on electrophoresis of a colloidal particle
,” J. Fluid Mech.
640
, 343
(2009
).51.
K.
Muralidhar
and G.
Biswas
, Advanced Engineering Fluid Mechanics
(Narosa
, New Delhi
, 1996
).52.
S.V.
Patankar
, Numerical Heat Transfer and Fluid Flow
(Taylor & Francis
, Kundli
, 2004
).© 2011 American Institute of Physics.
2011
American Institute of Physics
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