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Rheologica Acta

, Volume 58, Issue 9, pp 603–618 | Cite as

Peristaltic flow of Phan-Thien-Tanner fluid: effects of peripheral layer and electro-osmotic force

  • Sadaqut HussainEmail author
  • Nasir Ali
  • Kaleem Ullah
Original Contribution
  • 41 Downloads

Abstract

The two-layered electro-osmotic peristaltic flow of Phan-Thien-Tanner (PTT) fluid in a flexible cylindrical tube is analyzed. The core (inner) layer fluid satisfies the constitutive equation of PTT fluid model and the peripheral (outer) layer is characterized as a Newtonian fluid. For each region, the two-dimensional conservation equations for mass and momentum with electro-osmotic body forces are transformed from the fixed frame to the moving frame of reference. These equations are further simplified by invoking the constraints of long wavelength and low Reynolds number. Closed-form expressions for velocity and stream function are derived and then employed to investigate the pressure variations, trapping, interface region, and reflux for a variety of the involved parameters. The analysis reveals that the reflux and trapping can be restrained by appropriately tuning the electro-kinetic slip parameter and Deborah number. Further, the pumping efficacy can also be improved by adjusting the rheological and the electro-kinetic effects. These results may be helpful for improving the performance of the microfluidic peristaltic pump.

Keywords

Peristaltic flow PTT fluid Electro-osmosis Trapping Reflux 

Nomenclature

u, w

Velocity components

τ

Shear stress

λ

Wavelength

μr

Viscosity ratio between two regions

μ1

Viscosity in the core region

μ2

Viscosity in the peripheral region

f

Linear function

R1

Interface between the two fluids

R0

Boundary of the tube wall

q1

Flow rate over the inner cross-section

q

Flow rate over the outer cross-section

ϵc

Dielectric constant in the inner region

ϵN

Dielectric constant in the outer region

De

Deborah number

κ

Relaxation time

U

Velocity of the peristaltic wall

Re

Reynolds number

k

Height of the interface at z = 0

ϕoc

Occlusion parameter

ψ

Stream function in the fixed frame

ψ

Stream function in the wave frame

ρe

Total charge density

r0

Characteristics radius of the tube

δ

Ratio of the characteristics radial length to the characteristics axial length scale

TP

Complete period

Subscripts:

c

Core region

N

Peripheral region

Notes

Acknowledgments

The authors are thankful to the reviewer for his valuable comments and suggestions to improve the quality of the manuscript.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsInternational Islamic UniversityIslamabadPakistan

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