Streaming-potential-mediated pressure-driven transport of Phan-Thien–Tanner fluids in a microchannel

Sandip Sarkar
Phys. Rev. E 101, 053104 – Published 18 May 2020

Abstract

Streaming potential mediated pressure driven electrokinetic transport of Phan-Thien–Tanner fluids in a slit type parallel plate microchannel is studied analytically and semianalytically. Without adopting the traditional considerations of Debye–Hückel linearization approximation for low surface potentials, exact analytical solutions are obtained for the electrostatic potential distribution, velocity, and volumetric flow rates taking into account the full Poisson-Boltzmann equation. The influences of interfacial electrokinetics and viscoelasticity on the streaming potential development, polymeric stress components, shear viscosity, and the hydroelectric energy conversion efficiency are incorporated concurrently. Major findings indicate that the magnitude of the induced streaming potential, volumetric flow rates, and the energy conversion efficiency increases up to a threshold limit of zeta potential of ζ6, however, it follows an asymptotic reduction at the other end of higher zeta potentials 6<ζ10. The polymeric stress components and shear viscosity follow a similar trend in the regime of 1ζ10, which is primarily governed by the streaming potential field. In contrast, the transverse averaged shear viscosity in the range 1ζ10 obeys an opposite trend by yielding an inverted parabolic shape. Amplification in the Stern layer conductivity yields a progressive reduction in the streaming potential magnitude and the hydroelectric energy conversion efficiency. The effect of the fluid viscoelasticity designated by the Weissenberg number exhibits a linear enhancement in streaming potential, flow rates, and the energy conversion efficiency. Moreover, we show that with the optimal combinations of surface charging and fluid viscoelasticity, it is possible to accomplish a giant augmentation in the hydroelectric energy conversion efficiency and flow rates. The analytical and semianalytical results presented in this investigation are believed to be worthy not only to cater deeper understanding in micro- and nanofluidic transport characteristics but also will act as functional design instrument for the future generation of energy efficient narrow fluidic devices.

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  • Received 5 December 2019
  • Revised 25 March 2020
  • Accepted 20 April 2020

DOI:https://doi.org/10.1103/PhysRevE.101.053104

©2020 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Sandip Sarkar*

  • Department of Mechanical Engineering, Jadavpur University, Kolkata 700 032, India

  • *thesandipsarkar3@gmail.com

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Vol. 101, Iss. 5 — May 2020

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