This article presents the theoretical analysis of two-dimensional peristaltic transport of two-fluids in a flexible tube under the influence of electro-osmotic force. The flow domain is composed of two regions, namely, the core region and the peripheral region. The Newtonian and the FENE-P models are used to describe the rheology of fluids in the peripheral and the core regions, respectively. Governing flow equations corresponding to each region are developed under the assumption of long wavelength and low-Reynolds number. The interface between the two regions is computed numerically by employing a system of non-linear algebraic equations. The influence of relevant controlling parameters on pressure gradient, interface, trapping, and reflux is highlighted graphically and explained in detail. Special attention is given to estimate the effects of viscoelastic parameter of the core region fluid in the presence of electro-osmotic environment. Our investigation indicates an augmentation in the pressure loss at a zero volumetric flow rate with growing the viscoelastic and occlusion parameters. Moreover, trapping, reflux, and pumping efficiency are found to increase by increasing the electro-osmotic and viscoelastic parameters. The analysis presented here may be helpful in controlling the micro-vascular flow during the fractionation of blood into plasma (in the peripheral layer) and erythrocytes (core layer). This study may also have potential applications in areas such as electrophoresis, hematology, design, and improvement of bio-mimetic electro-osmotic pumps.
In this article, bifurcation analysis is performed to study the qualitative nature of stagnation points and various flow regions for a peristaltic transport of viscoelastic fluid through an axisymmetric tube. The rheological behavior of viscoelastic fluid is characterized by the simplified Phan–Than–Tanner fluid model. An analytic solution in a wave frame is obtained subject to the low Reynolds number and long wavelength approximations. The stagnation points and their bifurcations (critical conditions) are explored by developing a system of autonomous differential equations. The dynamical system theory is employed to examine the nature and bifurcations of obtained stagnation points. The ranges of various flow phenomena and their bifurcations are scrutinized graphically through global bifurcation diagrams. This analysis reveals that the bifurcation in the flow is manifested at large flow rate for high extensional parameter and Weissenberg number. Backward flow phenomenon enhances and trapping diminishes with an increase in the Weissenberg number. At the end, the results of present analysis are verified by making a comparison with the existing literature.
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