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Research Papers

Electro-Osmosis Modulated Viscoelastic Embryo Transport in Uterine Hydrodynamics: Mathematical Modeling

[+] Author and Article Information
V. K. Narla

Department of Mathematics,
GITAM (Deemed to be University),
Hyderabad 502329, India
e-mail: vknarla@gmail.com

Dharmendra Tripathi

Department of Sciences and Humanities,
National Institute of Technology,
Uttarakhand 246174, India
e-mail: dtripathi@nituk.ac.in

O. Anwar Bég

Aeronautical and Mechanical Engineering,
University of Salford,
Manchester M54WT, UK
e-mail: O.A.Beg@salford.ac.uk

Manuscript received June 13, 2018; final manuscript received October 24, 2018; published online November 30, 2018. Assoc. Editor: Ching-Long Lin.

J Biomech Eng 141(2), 021003 (Nov 30, 2018) (10 pages) Paper No: BIO-18-1278; doi: 10.1115/1.4041904 History: Received June 13, 2018; Revised October 24, 2018

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.

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Figures

Grahic Jump Location
Fig. 1

(a) Human uterus wall structure and (b) schematic view of the physical problem

Grahic Jump Location
Fig. 2

Instantaneous flow rates for (a) various phase shifts θ when Rζ = −0.5, and (b) zeta-potential ratios Rζ during a single period when θ = π/2 (L = 1, ϕ = 0.7, λ1 = 1, α = 0.035, UHS = −1, κ = 5)

Grahic Jump Location
Fig. 3

The total flow rate over one period for (a) angle of inclination between the channel walls α when Rζ = 0.5, and (b) zeta-potential ratios when α = 0.035

Grahic Jump Location
Fig. 4

Local pressure distribution along the channel axis for different inclination angle α and viscoelastic parameter (λ1) with L = 2, ϕ = 0.7, θ = 0, UHS = −1, κ = 2, Rζ = 0.5

Grahic Jump Location
Fig. 5

Local pressure distribution along the channel axis for various phase shifts (θ) and electro-osmotic velocity (UHS) with L = 2, ϕ = 0.7, α = 0.04, λ1 = 1, κ = 2, Rζ = 0.5

Grahic Jump Location
Fig. 6

Maximum-to-minimum pressure differences in a non-uniform channel during two periods for various zeta potential ratios (Rζ) and Debye–Hückel parameter (κ) with L = 2, ϕ = 0.7, α = 0.04, λ1 = 1, θ = π/2, ΔPL = 0, UHS = −1

Grahic Jump Location
Fig. 7

Spatial variation of the wall shear stress for various zeta potential rations (Rζ) when there are different inclination angles (α) between the walls with L = 2, ϕ = 0.7, ΔPL = 0, θ = π/4, λ1 = 1, UHS = −1, κ = 2: (a) α = 0.04 and (b) α = 0.3

Grahic Jump Location
Fig. 8

Axial velocity for different (a) UHS(1,0,−1) and (b) θ(0,π/2,π) when ϕ = 0.7, λ1 = 1, Rζ = 1, κ = 2, QT/QT,Max = 0.01: (a) α = 0.04 and (b) α = 0.5

Grahic Jump Location
Fig. 9

Stream line patterns for different (a) UHS(1,0,−1) and (b) Rζ(0.5, 1, −0.5) when ϕ = 0.7, θ = 0, λ1 = 1, κ = 2, QT = 0.95: (a) α = 0.04 and (b) α = 0.5

Grahic Jump Location
Fig. 10

Particle trajectories during one period (T) when there are different (a) UHS(0.25, 0, −0.25) and (b) α (0.04, 0.3) with ϕ = 0.7, λ1 = 1, Rζ = 0.5, κ = 2, QT/QT,Max = 0.01: (a) α = 0.04 and (b) α = 0.3

Grahic Jump Location
Fig. 11

Particle trajectories during one period (T) when there are various phase shifts (θ) when ϕ = 0.7, α = 0.5, λ1 = 0, Rζ = 0.5, κ = 2, QT/QT,Max = 0.01: (a) UHS = 0 and (b) UHS = 0.25

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