Mathematical modelling of two-fluid electro-osmotic peristaltic pumping of an Ellis fluid in an axisymmetric tube
Department of Mathematics and Statistics, International Islamic University, 44000, Islamabad, Pakistan
2 Department of Aeronautical/Mechanical Engineering, Salford University, M54WT, Manchester, UK
* e-mail: email@example.com
Accepted: 2 January 2019
Published online: 10 April 2019
This article explores analytically the dynamics of two-fluid electro-osmotic peristaltic flow through a cylindrical tube. The rheology of the fluid in the central core (inner region or core region) is captured through the Ellis equation. The region adjacent to the wall (outer region or peripheral region) is occupied by a Newtonian fluid. The equations governing the flow in each region are modeled by using the appropriate suppositions of long wavelength and low Reynolds number. Closed form expressions for the stream function corresponding to each region are obtained and utilized to determine the axial pressure gradient and the interface between the inner and the outer regions. The pumping characteristics, trapping and reflux phenomena are investigated in detail with reference to the Ellis model parameters and the electro-kinetic slip velocity. The present model also generalizes earlier studies from the literature which can be retrieved as special cases. The analysis shows that pressure drop at zero volumetric flow rate is elevated with increasing occlusion parameter. Trapping and reflux phenomena are mitigated with increasing electro-osmotic slip and shear-thinning effects. At larger value of the occlusion parameter an increase in the power-law index reduces the magnitude of the pressure drop. Increasing Ellis rheological parameter reduces the pressure drop over the entire range of occlusion parameters for the case when the peripheral region fluid viscosity exceeds that of the core region fluid. The results obtained may be applicable in the modulation of peristaltic pumping in the efficient operation of various industrial and bio-medical devices.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019