Embryological transport features a very interesting and complex application of peristaltic fluid dynamics. Electro-osmotic phenomena are also known to arise in embryo transfer location. The fluid dynamic environment in embryological systems is also known to be non-Newtonian and exhibits strong viscoelastic properties. Motivated by these applications, the present article develops a new mathematical model for simulating two-dimensional peristaltic transport of a viscoelastic fluid in a tapered channel under the influence of electro-osmosis induced by asymmetric zeta potentials at the channel walls. The robust Jeffrey viscoelastic model is utilized. The finite Debye layer electro-kinetic approximation is deployed. The moving boundary problem is transformed to a steady boundary problem in the wave frame. The current study carries significant physiological relevance to an ever-increasing desire to study intrauterine fluid flow motion in an artificial uterus. The consequences of this model may introduce a new mechanical factor for embryo transport to a successful implantation site. Hydrodynamic characteristics are shown to be markedly influenced by the electro-osmosis, the channel taper angle, and the phase shift between the channel walls. Furthermore, it is demonstrated that volumetric flow rates and axial flow are both enhanced when the electro-osmotic force aids the axial flow for specific values of zeta potential ratio. Strong trapping of the bolus (representative of the embryo) is identified in the vicinity of the channel central line when the electro-osmosis opposes axial flow. The magnitude of the trapped bolus is observed to be significantly reduced with increasing tapered channel length whereas embryo axial motility is assisted with aligned electro-osmotic force.

References

References
1.
Lang
,
R. J.
,
Davidson
,
M. E.
, and
Exintaris
,
B.
,
2002
, “
Pyeloureteral Motility and Ureteral Peristalsis: Essential Role of Sensory Nerves and Endogenous Prostaglandins
,”
Exp Physiol.
,
87
(
2
), pp.
129
146
.
2.
Ezzati
,
M.
,
Djahanbakhch
,
O.
,
Arian
,
S.
, and
Carr
,
B. R.
,
2014
, “
Tubal Transport of Gametes and Embryos: A Review of Physiology and Pathophysiology
,”
J. Assisted Reprod. Genet.
,
31
(
10
), pp.
1337
1347
.
3.
Yaniv
,
S.
,
Elad
,
D.
,
Jaffa
,
A. J.
, and
Eytan
,
O.
,
2003
, “
Biofluid Aspects of Embryo Transfer
,”
Ann. Biomed. Eng.
,
31
(
10
), p.
1255
.
4.
Bulletti
,
C.
, and
de Ziegler
,
D.
,
2005
, “
Uterine Contractility and Embryo Implantation
,”
Curr. Opin. Obstet. Gynecol.
,
17
(
3
), pp.
265
276
.
5.
Eytan
,
O.
, and
Elad
,
D.
,
1999
, “
Analysis of Intra-Uterine Fluid Motion Induced by Uterine Contractions
,”
Bull. Math. Biol.
,
61
(
2
), pp.
221
238
.
6.
Zhu
,
L.
,
Li
,
Y.
, and
Xu
,
A.
,
2012
, “
Influence of Controlled Ovarian Hyper-Stimulation on Uterine Peristalsis in Infertile Women
,”
Hum Reprod.
,
27
(
9
), pp.
2684
2689
.
7.
Zhu
,
L.
,
Che
,
H. S.
,
Xiao
,
L.
, and
Li
,
Y. P.
,
2014
, “
Uterine Peristalsis Before Embryo Transfer Affects the Chance of Clinical Pregnancy in Fresh and Frozen-Thawed Embryo Transfer Cycles
,”
Hum. Reprod.
,
29
(
6
), pp.
1238
1243
.
8.
Aranda
,
V.
,
Cortez
,
R.
, and
Fauci
,
L.
,
2015
, “
A Model of Stokesian Peristalsis and Vesicle Transport in a Three-Dimensional Closed Cavity
,”
J. Biomech.
,
48
(9), pp. 1631–1638.
9.
Eytan
,
O.
,
Jaffa
,
A. J.
, and
Elad
,
D.
,
2001
, “
Peristaltic Flow in a Tapered Channel: Application to Embryo Transport Within the Uterine Cavity
,”
Med. Eng. Phys.
,
23
(
7
), pp.
475
484
.
10.
Eytan
,
O.
,
Elad
,
D.
,
Zaretsky
,
U.
, and
Jaffa
,
A. J.
,
2004
, “
A Glance Into the Uterus During In Vitro Simulation of Embryo Transfer
,”
Hum. Reprod.
,
19
(
3
), pp.
562
569
.
11.
Yao
,
S.
, ed.,
2008
,
Electro-Osmotic Pump Technologies: Theory, Design and Demonstration
,
VDM Verlag
,
Saarbrücken, Germany
.
12.
Dainty
,
J.
,
Croghan
,
P. C.
, and
Fensom
,
D. S.
,
1963
, “
Electro-Osmosis, With Some Applications to Plant Physiology
,”
Can. J. Botany
,
41
(
6
), pp.
953
966
.
13.
Kalmijn
,
A. J.
,
1971
, “
The Electric Sense of Sharks and Rays
,”
Exp. Biol.
,
55
(
2
), pp.
371
383
.http://jeb.biologists.org/content/55/2/371.article-info
14.
Tandon
,
T.
, and
Kirby
,
B. J.
,
2008
, “
Zeta Potential and Electroosmotic Mobility in Microfluidic Devices Fabricated From Hydrophobic Polymers—2: Slip and Interfacial Water Structure
,”
Electrophoresis
,
29
(
5
), pp.
1102
1114
.
15.
Brown
,
M.
, and
Meinhart
,
C.
,
2006
, “
AC Electroosmotic Flow in a DNA Concentrator
,”
Microfluid. Nanofluid.
,
2
(6), pp.
513
523
.
16.
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
.
17.
Sheu
,
T. W. H.
,
Huang
,
V. C.
, and
Rani
,
H. P.
,
2008
, “
Development of an Electro-Osmotic Flow Model to Study the Dynamic Behaviour in Human Meridian
,”
Int. J. Numer. Methods Fluids
,
56
(
6
), pp.
739
751
.
18.
Ghosal
,
S.
,
2002
, “
Lubrication Theory for Electro-Osmotic Flow in a Microfluidic Channel of Slowly Varying Cross-Section and Wall Charge
,”
J. Fluid Mech.
,
459
, pp.
103
128
.
19.
Bengtsson
,
K.
, and
Robinson
,
N. D.
,
2017
, “
A Large-Area, All-Plastic, Flexible Electroosmotic Pump
,”
Microfluid. Nanofluid.
,
21
, p.
178
.
20.
Bohme
,
G.
, ed.,
1987
,
Non-Newtonian Fluid Mechanics
,
North Holland
,
Amsterdam, The Netherlands
.
21.
Bég
,
O. A.
,
Zueco
,
J.
, and
Ghosh
,
S. K.
,
2010
, “
Unsteady Hydromagnetic Natural Convection of a Short-Memory Viscoelastic Fluid in a Non-Darcian Regime: Network Simulation
,”
Chem. Eng. Commun.
,
198
(2), pp.
172
190
.
22.
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
348
.
23.
Norouzi
,
M.
,
Davoodi
,
M.
,
Bég
,
O. A.
, and
Joneidi
,
A. A.
,
2013
, “
Analysis of the Effect of Normal Stress Differences on Heat Transfer in Creeping Viscoelastic Dean Flow
,”
Int. J. Therm. Sci.
,
69
, pp.
61
69
.
24.
Tripathi
,
D.
, and
Bég
,
O. A.
,
2013
, “
Mathematical Modelling of Heat Transfer Effects on Swallowing Dynamics of Viscoelastic Flood Bolus Through the Human Oesophagus
,”
Int. J. Therm. Sci.
,
70
, pp.
41
53
.
25.
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
.http://www.lifesciencesite.com/lsj/life1107/024_22013life110714_197_206.pdf
26.
Sadeghi
,
A.
,
Saidi
,
M. H.
, and
Mozafari
,
A. A.
,
2011
, “
Heat Transfer Due to Electroosmotic Flow of Viscoelastic Fluids in a Slit Microchannel
,”
Int. J. Heat Mass Transfer
,
54
(
17–18
), pp.
4069
4077
.
27.
Berli
,
C. L. A.
, and
Olivares
,
M.
,
2008
, “
Electrokinetic Flow of Non-Newtonian Fluids in Microchannels
,”
J. Colloid Interface Sci.
,
320
(
2
), pp.
582
589
.
28.
Ferrás
,
L. L.
,
Afonso
,
A. M.
,
Alves
,
M. A.
,
Nóbrega
,
J. M.
, and
Pinho
,
F. T.
,
2014
, “
Analytical and Numerical Study of the Electro-Osmotic Annular Flow of Viscoelastic Fluids
,”
J. Colloid Interface Sci.
,
420
, pp.
152
157
.
29.
Jiang
,
Y.
,
Qi
,
H.
,
Xu
,
H.
, and
Jiang
,
X.
,
2017
, “
Transient Electroosmotic Slip Flow of Fractional Oldroyd-B Fluids
,”
Microfluid. Nanofluid.
,
21
, p.
7
.
30.
Misra
,
J. C.
,
Chandra
,
S.
,
Shit
,
G. C.
, and
Kundu
,
P. K.
,
2014
, “
Electroosmotic Oscillatory Flow of Micropolar Fluid in Microchannels: Application to Dynamics of Blood Flow in Microfluidic Devices
,”
Appl. Math. Mech.
,
35
(
6
), pp.
749
766
.
31.
Kirby
,
B. J.
, and
Hasselbrink
,
E. F.
,
2004
, “
Zeta Potential of Microfluidic Substrates—II: Data for Polymers
,”
Electrophoresis
,
25
(
2
), pp.
203
213
.
32.
Bandopadhyay
,
A.
,
Tripathi
,
D.
, and
Chakraborty
,
S.
,
2016
, “
Electroosmosis-Modulated Peristaltic Transport in Microfluidic Channels
,”
Phys. Fluids
,
28
(
5
), p.
052002
.
33.
Huh
,
D.
,
Matthews
,
B. D.
,
Mammoto
,
A.
,
Montoya-Zavala
,
M.
,
Hsin
,
H. Y.
, and
Ingber
,
D. E.
,
2010
, “
Reconstituting Organ-Level Lung Functions on a Chip
,”
Sci.
,
328
(
5986
), pp.
1662
1668
.
34.
Kim
,
H. J.
,
Huh
,
D.
,
Hamilton
,
G.
, and
Ingber
,
D. E.
,
2012
, “
Human Gut-on-a-Chip Inhabited by Microbial Flora That Experiences Intestinal Peristalsis-Like Motions and Flow
,”
Lab Chip.
,
12
(
12
), pp.
2165
2174
.
35.
Wei-Xuan
,
L.
,
Guang-Tie
,
L.
,
Wei
,
Y.
,
Qiong
,
Z.
,
Wei
,
W.
,
Xiao-Mian
,
Z.
, and
Da-Yu
,
L.
,
2013
, “
Artificial Uterus on a Microfluidic Chip
,”
Chin. J. Anal. Chem.
,
41
(
4
), pp.
467
472
.
36.
Pozrikidis
,
C.
,
1987
, “
A Study of Peristaltic Flow
,”
J. Fluid Mech.
,
180
(
1
), pp.
515
527
.
37.
Yaniv
,
S.
,
Jaffa
,
A. J.
, and
Elad
,
D.
,
2012
, “
Modeling Embryo Transfer Into a Closed Uterine Cavity
,”
ASME J. Biomech. Eng.
,
134
(
11
), p.
111003
.
38.
Shaked
,
S.
,
Jaffa
,
A. J.
,
Grisaru
,
D.
, and
Elad
,
D.
,
2015
, “
Uterine Peristalsis-Induced Stresses Within the Uterine Wall May Sprout Adenomyosis
,”
Biomech. Model. Mechanobiol.
,
14
(
3
), pp.
437
444
.
39.
Payan
,
Y.
, and
Ohayon
,
J.
,
2017
,
Biomechanics of Living Organs: Hyperelastic Constitutive Laws for Finite Element Modeling
,
Academic Press
,
New York
.
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