Bifurcation analysis for a flow of viscoelastic fluid due to peristaltic activity

Abstract

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.