Study of EDL phenomenon in Peristaltic pumping of a Phan-Thien-Tanner Fluid through asymmetric channel
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Study of EDL phenomenon in Peristaltic pumping of a Phan-Thien-Tanner Fluid through asymmetric channel J. Prakash1 and Dharmendra Tripathi2,* Department of Mathematics, Avvaiyar Government College for Women, Karaikal-609 602, Pondicherry –U.T., India 2 Department of Mathematics, National Institute of Technology Uttarakhand, Srinagar -246174, India (Received May 17, 2020; final revision received August 8, 2020; accepted September 21, 2020)
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This paper is mainly attained to examine the electric double layer (EDL) phenomena and rheological effects on peristaltic pumping through asymmetric microchannel in presence of Lorentz force. To examine the electroosmosis mechanism, Poisson–Boltzmann equation is considered. To describe the rheological behavior of the fluids, a Phan-Thien-Tanner model is taken into account. The governing equations are simplified by using scaling analysis with low Reynolds number and large wavelength approximations. The set of non-linear partial differential equations are solved by regular perturbation technique to find out the series solutions for stream function, axial velocity and pressure gradient. Furthermore, the shear stress at the channel wall is derived. The graphical results for velocity, pressure gradient, stream lines and shear stress are illustrated using the in-house code written in Mathematica software. It is revealed that velocity field, shear stress and trapping phenomenon are strongly altered with EDL thickness, electric and magnetic fields. It is further concluded that rheological parameter i.e. Weissenberg number significantly affects the physical mechanisms. This model can be applicable in various complex systems where the rheological fluids can be transported by novel microfluidics peristaltic pumps. Keywords: electroosmosis, peristaltic pumping, Phan-Thien-Tanner fluid, magnetic field, electric double layer, trapping
1. Introduction Rheological behaviors of the fluids/materials like viscosity, shear thinning, shear thickening, elasticity, plasticity, etc. describe the most of the complex fluids which are being utilized in Industries and many other researches (Steffe, 1996). Many models of the viscous fluids, viscoplastic fluids, and viscoelastic fluids are available in literature and these modes are being used by researchers to investigate some novel works of fluid dynamics (Cross, 1965; Glowinski and Wachs, 2011). However the viscoelastic nature (Denn, 1990; Ferry, 1980) of the materials represent the solidity and fluidity behavior of the materials such as gels, Mucus, sputum, synovial fluids liquid polymers, and glycerin, etc. The difference between the rheology and fluid dynamics of viscoelastic materials was also analyzed. Cilia beating viscoelastic fluids flow in the mucus-filled female reproductive tract was reported by Lauga (2007). He has discussed the effects of Deborah number and relaxation time on complex fluid transport. Viscoelastic fluids/materials are described through various models such as Maxwell model, Kelvin model, Jeffrey model
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