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


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.


Peristaltic flow PTT fluid Electro-osmosis Trapping Reflux 


u, w

Velocity components


Shear stress




Viscosity ratio between two regions


Viscosity in the core region


Viscosity in the peripheral region


Linear function


Interface between the two fluids


Boundary of the tube wall


Flow rate over the inner cross-section


Flow rate over the outer cross-section


Dielectric constant in the inner region


Dielectric constant in the outer region


Deborah number


Relaxation time


Velocity of the peristaltic wall


Reynolds number


Height of the interface at z = 0


Occlusion parameter


Stream function in the fixed frame


Stream function in the wave frame


Total charge density


Characteristics radius of the tube


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


Complete period



Core region


Peripheral region



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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