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Non-Newtonian fluid flow induced by pressure gradient and time-periodic electroosmosis in a microtube

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Abstract

Non-Newtonian fluid flow, based on the Carreau–Yasuda model, is studied in a circular microchannel which is driven by combined pressure gradient and alternating current electroosmosis. Smaller values of the flow behavior index correspond to the larger degrees of shear-thinning, and so the velocity field contracts. The flow field is strongly influenced by the dimensionless frequency. When viscous diffusion is faster than the period of oscillation, the bulk fluid has sufficient time to respond to alternating current electric field, and quasi-steady plug-like velocity profiles may be observed for sufficient large values of the flow behavior index; while a major part of the flow field may be immobile at sufficiently high dimensionless frequencies. When a pressure gradient is applied along the microchannel, the periodic velocity field deviates from the centerline and hence, a non-zero pulsating flow rate is attained. The non-linearity of the fluid behavior is enhanced by the Weissenberg number through the model time constant. Large or small values of shear stress during one period can lead to sharp variation of viscosity. Using non-Newtonian fluids, the voltage and current required to attain desirable characteristics, and therefore, the detrimental effects of Joule heating may be reduced.

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Abbreviations

a :

A dimensionless parameter

\( D \) :

Time ratio

\( {\text{d}}p/{\text{d}}z \) :

Pressure gradient

\( e \) :

Electron charge (C)

\( E_{z} \) :

Electrical field strength along axial direction (V/m)

\( k_{\text{B}} \) :

Boltzmann constant (J/K)

\( K \) :

Flow consistency index

\( n \) :

Flow behavior index

\( n_{0} \) :

Bulk ion concentration (m−3)

\( r \) :

Radial coordinate (m)

\( \Re \) :

The microchannel radius (m)

\( R \) :

Dimensionless radial coordinate

\( t \) :

Time (s)

\( T \) :

Absolute temperature (K)

\( V \) :

Dimensionless axial velocity

\( V_{z} \) :

Axial velocity (m/s)

\( V_{\text{HS}} \) :

The Helmholtz–Smoluchowski velocity

\( Wi \) :

Weissenberg number

\( z \) :

Axial coordinate (m)

\( Z \) :

Dimensionless potential at the wall

\( \aleph \) :

Valence of ionic species

\( \chi \) :

The electro-kinetic radius

\( \varepsilon \) :

Electric permittivity of solution (F/m)

\( \eta_{0} \) :

Zero-shear-rate viscosity (Pa s)

\( \eta_{\infty } \) :

Infinite-shear-rate viscosity (Pa s)

\( \eta_{\text{vr}} \) :

Viscosity ratio

\( \kappa \) :

Debye–Hückel parameter (m−1)

\( \lambda \) :

A time constant (s)

\( \theta \) :

Dimensionless time

\( \rho \) :

Fluid density (kg/m3)

\( \rho_{e} \) :

Net volume charge density (C m−3)

\( \tau \) :

Time scale

\( \omega \) :

Frequency (s−1)

\( \gamma \) :

Force ratio

\( \dot{\varUpsilon } \) :

Rate-of-strain tensor (s−1)

\( \varOmega \) :

Dimensionless frequency

\( \psi \) :

Electrical potential (V)

\( \varPsi \) :

Dimensionless electrical potential

\( \zeta \) :

Zeta potential at the outer wall (V)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahrood University of Technology, P.O. Box 316, Shahrood, Iran

    Ali Jabari Moghadam & Pooria Akbarzadeh

Authors
  1. Ali Jabari Moghadam
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  2. Pooria Akbarzadeh
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Correspondence to Ali Jabari Moghadam.

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Technical Editor: Cezar Negrao.

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Moghadam, A.J., Akbarzadeh, P. Non-Newtonian fluid flow induced by pressure gradient and time-periodic electroosmosis in a microtube. J Braz. Soc. Mech. Sci. Eng. 39, 5015–5025 (2017). https://doi.org/10.1007/s40430-017-0876-8

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  • DOI: https://doi.org/10.1007/s40430-017-0876-8

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