Abstract

Mathematical modeling of mechanical system in microfluidics is an emerging area of interest in microscale engineering. Since microfluidic devices use the hair-like structure of artificial cilia for pumping, mixing, and sensing in different fields, electro-osmotic cilia-driven flow helps to generate the fluid velocity for the Newtonian and viscoelastic fluid. Due to the deployment of artificial ciliated walls, the present research reports the combined effect of an electro-osmotic flow and convective heat transfer on Jeffrey viscoelastic electrolytic fluid flow in a two-dimensional ciliated vertical channel. Heat generation/absorption and nonlinear radiation effects are included in the present mathematical model. After applying Debye–Huckel approximation and small Reynolds number approximation to momentum and energy equation, the system of nonlinear partial differential equation is reduced into nonhomogenous boundary value problem. The problem determines the velocity, pressure, and temperature profiles by the application of semi-analytical technique known as homotopy perturbation method (HPM) with the help of software Mathematica. The graphical results of the study suggest that HPM is a reliable methodology for thermo physical electro-osmotic rheological transport in microchannels.

References

1.
Dongqing
,
L.
,
2008
,
Encyclopedia of Microfluidics and Nanofluidics
,
Springer-Verlag
,
New York
.
2.
Yoo
,
K.
,
Shim
,
J.
, and
Dutta
,
P.
,
2014
, “
Effect of Joule Heating on Isoelectric Focusing of Proteins in a Microchannel
,”
Biomicrofluidics
,
8
(
6
), p.
064125
.10.1063/1.4904805
3.
Green
,
N. G.
,
Ramos
,
A.
, and
Organ
,
H.
,
2002
, “
Numerical Solution of the Dielectrophoretic and Travelling Wave Forces for Interdigitated Electrode Arrays Using the Finite Element Method
,”
J. Electrostatistics
,
56
(
2
), pp.
235
254
.10.1016/S0304-3886(02)00069-4
4.
Mauck
,
R. L.
,
Hung
,
C. T.
, and
Ateshian
,
G. A.
,
2003
, “
Modeling of Neutral Solute Transport in a Dynamically Loaded Porous Permeable Gel: Implications for Articular Cartilage Biosynthesis and Tissue Engineering
,”
ASME J. Biomech. Eng.
,
125
(
5
), pp.
602
614
.10.1115/1.1611512
5.
Wang
,
Y.
, and
Guo
,
J.
,
2018
, “
Effective Electroelastic Constants for Three-Phase Confocal Elliptical Cylinder Model in Piezoelectric Quasicrystal Composites
,”
Appl. Math. Mech.
39
(
6
), pp.
797
812
.10.1007/s10483-018-2336-9
6.
Liu
,
Y.
, and
Jian
,
Y.
,
2019
, “
Electroviscous Effect on Electromagnetohydrodynamic Flows of Maxwell Fluids in Parallel Plate Microchannels
,”
Appl. Math. Mech.
,
40
(
10
), pp.
1457
1470
.10.1007/s10483-019-2526-9
7.
Ooi
,
K. T.
,
Yang
,
C.
,
Chai
,
J. C.
, and
Wong
,
T. N.
,
2005
, “
Developing Electro-Osmotic Flow in Closed-End Micro-Channels
,”
Int. J. Eng. Sci.
,
43
(
17–18
), pp.
1349
1362
.10.1016/j.ijengsci.2005.05.015
8.
Tripathi
,
D.
,
Bhushan
,
S.
, and
Bég
,
O. A.
,
2017
, “
Analytical Study of Electro-Osmosis Modulated Capillary Peristaltic Hemodynamics
,”
J. Mech. Med. Biol.
,
17
(
3
), p.
1750052
.10.1142/S021951941750052X
9.
Ng
,
C. O.
,
2013
, “
Combined Pressure-Driven and Electroosmotic Flow of Casson Fluid Through a Slit Microchannel
,”
J. Non-Newtonian Fluid Mech.
,
198
, pp.
1
9
.10.1016/j.jnnfm.2013.03.003
10.
Ali
,
N.
,
Hussain
,
S.
,
Ullah
,
K.
, and
Bég
,
O. A.
,
2019
, “
Mathematical Modelling of Two-Fluid Electro-Osmotic Peristaltic Pumping of an Ellis Fluid in an Axisymmetric Tube
,”
Eur. Phys. J. Plus
,
134
(
4
), p.
141
.10.1140/epjp/i2019-12488-2
11.
Sánchez
,
S.
,
Arcos
,
J.
,
Bautista
,
O.
, and
Méndez
,
F.
,
2013
, “
Joule Heating Effect on a Purely Electroosmotic Flow of non-Newtonian Fluids in a Slit Microchannel
,”
J. Non-Newtonian Fluid Mech.
,
192
, pp.
1
9
.10.1016/j.jnnfm.2012.09.014
12.
Farooq
,
M.
,
Alsaedi
,
A.
, and
Hayat
,
T.
,
2015
, “
Note on Characteristics of Homogeneous-Heterogeneous Reaction in Flow of Jeffrey Fluid
,”
Appl. Math. Mech.
,
36
(
10
), pp.
1319
1328
.10.1007/s10483-015-1981-9
13.
Narla
,
V. K.
,
Tripathi
,
D.
, and
Bég
,
O. A.
,
2019
, “
Electro-Osmosis Modulated Viscoelastic Embryo Transport in Uterine Hydrodynamics: Mathematical Modeling
,”
ASME J. Biomech. Eng.
,
141
(
2
), p. 021003.10.1115/1.4041904
14.
Corey
,
D. P.
, and
Hudspeth
,
A. J.
,
1979
, “
Ionic Basis of the Receptor Potential in a Vertebrate Hair Cell
,”
Nature
,
281
(
5733
), pp.
675
–67
7
.10.1038/281675a0
15.
Wang
,
Z.
,
Wu
,
H. J.
,
Fine
,
D.
,
Schmulen
,
J.
,
Hu
,
Y.
,
Godin
,
B.
,
Zhang
,
J. X.
, and
Liu
,
X.
,
2013
, “
Ciliated Micropillars for the Microfluidic-Based Isolation of Nanoscale Lipid Vesicles
,”
Lab Chip
,
13
(
15
), pp.
2879
–28
82
.10.1039/c3lc41343h
16.
Vasudevan
,
M.
, and
Lange
,
C. F.
,
2005
, “
Property Dependence of Onset of Instability in Viscoelastic Respiratory Fluids
,”
Int. J. Eng. Sci.
,
43
(
15–16
), pp.
1292
8
.10.1016/j.ijengsci.2005.05.004
17.
Toonder
,
J. D.
,
Bos
,
F.
,
Broer
,
D.
,
Filippini
,
L.
,
Gillies
,
M.
,
de Goede
,
J.
,
Mol
,
T.
,
Reijme
,
M.
,
Talen
,
W.
,
Wilderbeek
,
H.
,
Khatavkar
,
V.
, and
Anderson
,
P.
,
2008
, “
Artificial Cilia for Active Micro-Fluidic Mixing
,”
Lab Chip
,
8
(
4
), pp.
533
541
.10.1039/b717681c
18.
Balazs
,
A. C.
,
Bhattacharya
,
A.
,
Tripathi
,
A.
, and
Shum
,
H.
,
2014
, “
Designing Bioinspired Artificial Cilia to Regulate Particle–Surface Interactions
,”
J. Phys. Chem. Lett.
,
5
(
10
), pp.
1691
1700
.10.1021/jz5004582
19.
Chateau
,
S.
,
Favier
,
J.
,
D'Ortona
,
U.
, and
Poncet
,
S.
,
2017
, “
Transport Efficiency of Metachronal Waves in 3D Cilium Arrays Immersed in a Two-Phase Flow
,”
J. Fluid Mech.
,
824
, pp.
931
61
.10.1017/jfm.2017.352
20.
Manzoor
,
N.
,
Bég
,
O. A.
,
Maqbool
,
K.
, and
Shaheen
,
S.
,
2019
, “
Mathematical Modelling of Ciliary Propulsion of an Electrically-Conducting Johnson-Segalman Physiological Fluid in a Channel With Slip
,”
Comput. Methods Biomech. Biomed. Eng.
,
22
(
7
), pp.
685
695
.10.1080/10255842.2019.1582033
21.
Manzoor
,
N.
,
Maqbool
,
K.
,
Bég
,
O. A.
, and
Shaheen
,
S.
,
2019
, “
Adomian Decomposition Solution for Propulsion of Dissipative Magnetic Jeffrey Biofluid in a Ciliated Channel Containing a Porous Medium With Forced Convection Heat Transfer
,”
Heat Transfer-Asian Res.
,
48
(
2
), pp.
556
581
.10.1002/htj.21394
22.
Maqbool
,
K.
,
Shaheen
,
S.
, and
Mann
,
A. B.
,
2016
, “
Exact Solution of Cilia Induced Flow of a Jeffrey Fluid in an Inclined Tube
,”
SpringerPlus
,
5
(
1
), pp.
1
6
.10.1186/s40064-016-3021-8
23.
Mercke
,
U.
,
1975
, “
The Influence of Varying Air Humidity on Mucociliary Activity
,”
Acta Oto-Laryngol.
,
79
(
1–2
), pp.
133
9
.10.3109/00016487509124665
24.
Prodromou
,
N. V.
,
Thompson
,
C. L.
,
Osborn
,
D. P.
,
Cogger
,
K. F.
,
Ashworth
,
R.
,
Knight
,
M. M.
,
Beales
,
P. L.
, and
Chapple
,
J. P.
,
2012
, “
Heat Shock Induces Rapid Resorption of Primary Cilia
,”
J. Cell Sci.
,
125
(
18
), pp.
4297
4305
.10.1242/jcs.100545
25.
Mills
,
Z. G.
,
Aziz
,
B.
, and
Alexeev
,
A.
,
2012
, “
Beating Synthetic Cilia Enhance Heat Transport in Microfluidic Channels
,”
Soft Matter
,
8
(
45
), pp.
11508
13
.10.1039/c2sm26919h
26.
Shaheen
,
S.
,
Maqbool
,
K.
, and
Siddiqui
,
A. M.
,
2020
, “
Micro Rheology of Jeffrey Nanofluid Through Cilia Beating Subject to the Surrounding Temperature
,”
Rheol. Acta
,
59
(
8
), pp.
565
73
.10.1007/s00397-020-01222-8
27.
Gul
,
F.
,
Maqbool
,
K.
, and
Mann
,
A. B.
,
2020
, “
Thermal Analysis of Electroosmotic Flow in a Vertical Ciliated Tube With Viscous Dissipation and Heat Source Effects
,”
J. Therm. Anal. Calorim.
,
1
.10.1007/s10973-020-09702-y
28.
Akbar
,
N. S.
,
Tripathi
,
D.
,
Bég
,
O. A.
, and
Khan
,
Z. H.
,
2016
, “
MHD Dissipative Flow and Heat Transfer of Casson Fluids Due to Metachronal Wave Propulsion of Beating Cilia With Thermal and Velocity Slip Effects Under an Oblique Magnetic Field
,”
Acta Astronaut.
,
128
, pp.
1
2
.10.1016/j.actaastro.2016.06.044
29.
Akbar
,
N. S.
,
Khan
,
L. A.
,
Khan
,
Z. H.
, and
Mir
,
N. A.
,
2017
, “
Natural Propulsion With Lorentz Force and Nanoparticles in a Bioinspired Lopsided Ciliated Channel
,”
J. Bionic Eng.
,
14
(
1
), pp.
172
181
.10.1016/S1672-6529(16)60388-8
30.
Hussain
,
Q.
,
Latif
,
T.
,
Alvi
,
N.
, and
Asghar
,
S.
,
2018
, “
Nonlinear Radiative Peristaltic Flow of Hydromagnetic Fluid Through Porous Medium
,”
Results Phys.
,
9
, pp.
121
134
.10.1016/j.rinp.2018.02.014
31.
Kothandapani
,
M.
, and
Prakash
,
J.
,
2015
, “
Influence of Heat Source, Thermal Radiation, and Inclined Magnetic Field on Peristaltic Flow of a Hyperbolic Tangent Nanofluid in a Tapered Asymmetric Channel
,”
IEEE Trans. Nanobiosci.
,
14
(
4
), pp.
385
392
.10.1109/TNB.2014.2363673
32.
Bég
,
O. A.
,
Beg
,
T. A.
,
Karim
,
I.
,
Khan
,
M. S.
,
Alam
,
M. M.
,
Ferdows
,
M.
, and
Shamshuddin
,
M. D.
,
2019
, “
Numerical Study of Magneto-Convective Heat and Mass Transfer From Inclined Surface With Soret Diffusion and Heat Generation Effects: A Model for Ocean Magnetic Energy Generator Fluid Dynamics
,”
Chin. J. Phys.
,
60
, pp.
167
79
.10.1016/j.cjph.2019.05.002
33.
He
,
J. H.
,
2003
, “
Homotopy Perturbation Method: A New Nonlinear Analytical Technique
,”
Appl. Math. Comput.
,
135
(
1
), pp.
73
9
.10.1016/S0096-3003(01)00312-5
34.
Tripathi
,
D.
, and
Bég
,
O. A.
,
2012
, “
A Numerical Study of Oscillating Peristaltic Flow of Generalized Maxwell Viscoelastic Fluids Through a Porous Medium
,”
Transp. Porous Media
,
95
(
2
), pp.
337
48
.10.1007/s11242-012-0046-5
35.
Alarabi
,
T.
,
Elsayed
,
A. F.
, and
Bég
,
O. A.
,
2014
, “
Homotopy Perturbation Method for Heat Transfer in Peristaltic Flow of Viscoelastic Fluid in an Eccentric Cylinder With Variable Effects
,”
Life Sci. J.
,
11
(
7
), pp.
197
206
. https://www.semanticscholar.org/paper/Homotopy-Perturbation-Method-For-Heat-Transfer-Of-Al-arabi-Elsayed/f135aca1a23b7a343f193af2fa326cfd7b9d5190
36.
Gebhart
,
B.
,
Jaluria
,
Y.
,
Mahajan
,
R. L.
, and
Sammakia
,
B.
,
1988
, “
Buoyancy-Induced Flows and Transport
,” Springer, Berlin, 227, pp.
692
693
.10.1017/S0022112091240306
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