Abstract
The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive model, including the relaxation time and retardation time, is utilized to describe the viscoelasticity of the fluid. Under the assumptions of long wavelength, low Reynolds number, and Debye-Hückel linearization, the analytical solutions of pressure gradient, stream function and axial velocity are explored in terms of Mittag-Leffler function by Laplace transform method. The corresponding solutions of fractional Maxwell fluid and generalized second grade fluid are also obtained as special cases. The numerical analysis of the results are depicted graphically, and the effects of electro-osmotic parameter, external electric field, fractional parameters and viscoelastic parameters on the peristaltic flow are discussed.
Highlights
The electro-osmotic transport in micro-channels and nano-channels recently attract much attentions of researchers because of the development of biomedical microelectromechanical systems (Bio-MEMS) and lab-on-a-chip technologies
Taking most biofluids such as blood emerge the viscoelastic feature into consideration, more and more interests are being shown in the electro-osmotic flow of non-Newtonian fluids
Based on the promising results achieved in the above literature review, this paper attempts to study the fractional Jeffreys model of electro-osmotic peristaltic flow in an infinite micro-channel, with an aim to analyze the effects of electro-osmosis and fractional parameter on peristaltic flow of fractional viscoelastic fluid
Summary
The electro-osmotic transport in micro-channels and nano-channels recently attract much attentions of researchers because of the development of biomedical microelectromechanical systems (Bio-MEMS) and lab-on-a-chip technologies. Bandopadhya et al [28] investigated the peristaltic motion of an aqueous electrolyte with an externally-applied electric field along a finite channel. They obtained the spatial distribution of pressure and wall shear stress for a continuous wave and single pulse peristaltic wave. Based on the promising results achieved in the above literature review, this paper attempts to study the fractional Jeffreys model of electro-osmotic peristaltic flow in an infinite micro-channel, with an aim to analyze the effects of electro-osmosis and fractional parameter on peristaltic flow of fractional viscoelastic fluid. The paper is structured as follows: Section 1 serves as an introduction; Section 2 deduces the basic equations of the fluid and presents the initial and boundary value problem for the flow; Section 3 discusses the analytical solution to the problem; Section 4 discusses the special cases and the numerical results; and Section 5 draws a conclusion for the whole paper
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