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Electrokinetic oscillatory flow and energy conversion of viscoelastic fluids in microchannels: a linear analysis

Published online by Cambridge University Press:  26 May 2021

Zhaodong Ding  and
Yongjun Jian Open the ORCID record for Yongjun Jian [Opens in a new window]
Zhaodong Ding
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, PR China
Yongjun Jian*
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, PR China
*
†Email address for correspondence: jianyj@imu.edu.cn
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Abstract

We studied the electrokinetic flow of viscoelastic fluids subjected to an oscillatory pressure gradient. Under the assumption of laminar unidirectional flow, the constitutive and motion equations of fluids are in the linear regime. Since the surface potentials are assumed to be small, the Poisson–Boltzmann equation is linearised. Resonance behaviours appear in the flow when the elastic effect of fluids is dominant. Based on the interaction of viscoelastic shear waves, we explain the mechanism of resonance and derive the critical Deborah number, Dec = 1/4, which dictates the occurrence of resonance. Using the Maxwell fluid model, the resonance enhances the electrokinetic effects and dramatically increases the electrokinetic energy conversion efficiency. However, by employing the Oldroyd-B fluid model, we reveal that the amplification of efficiency is suppressed even for a very small Newtonian solvent contribution. This could be one of the reasons for the unavailability of reports on experimental verification regarding the high efficiency predicted by Bandopadhyay & Chakraborty (Appl. Phys. Lett., vol. 101, 2012, 043905). The damping effect of solvent viscosity is more significant for higher-order resonances. The effects of multiple relaxation times on the resonance behaviours are investigated and the results indicate that Dec still dominates the occurrence of resonances for streaming potential field and flow rate.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Non-Newtonian Flows: Viscoelasticity

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JFM Papers
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Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A20
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© The Author(s), 2021. Published by Cambridge University Press

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