Bifurcation and stability analysis of critical/stagnation points for peristaltic transport of a power-law fluid in a tube

The stability of critical/stagnation points and streamline topologies along with their local and global bifurcations for peristaltic flow of an incompressible power-law model have been investigated. The flow is analyzed in an axisymmetric tube subject to the constraints of long wavelength and low Reynolds number, and an exact analytic solution is found in a moving frame of reference. Nonlinear autonomous differential equations are developed to unveil the particle paths and position of critical points in the flow. Stability of obtained critical points and streamline patterns along with their local bifurcations are inspected by using the theory of dynamical system. Three different flow distributions are found in the flow: backward flow, trapping and augmented flow. The transitions between these flow situations correspond to bifurcations in the flow field where non-hyperbolic degenerate points change their behavior to form heteroclinic connection between saddles. The nature and stability of these bifurcations and corresponding topological changes are explored graphically. A global bifurcation diagram is used to epitomize these bifurcations. The fluid behavior index has a significant impact on the stability of critical points and the ranges of flow regions. The backward flow region and trapping region are observed to shrink and expand, respectively, with an increase in the fluid behavior index. The findings of present article are verified by comparing them with the results already existing in the literature.