A study on the bifurcation of the peristaltic driven flow of Ellis fluid

Abstract

In this work, a bifurcation analysis is presented for the transport of Ellis fluid model due to peristaltic activity. The position, qualitative nature and bifurcations of stagnation-points are deliberated through the dynamical system approach. An exact expression for stream function is found by using the lubrication approach. Based on the stream function, a system of autonomous differential equations is established to analyze the equilibrium-points. Three kinds of flows are observed, namely backward flow, trapping and augmented flow. The transition of one flow into other represents a bifurcation. In the first bifurcation, a saddle point bifurcates into two centers in the normal direction while the second bifurcation emerges where nearby saddle nodes join under the wave trough and then split into two branches in the transverse direction. Ramifications of different embedded parameters on the bifurcations and nature of stagnation-points are explored through graphical representations. It is found that bifurcations transpire earlier for viscous fluids as compared to shear-thinning fluids. Further, bifurcations appear at low flow rate for small values of the material parameter . Moreover, in Newtonian fluids, as opposed to shear-thinning fluids, the trapping starts earlier and the backward region expands for larger values of the material parameter .