Bifurcation and stability analysis of stagnation points for an asymmetric peristaltic transport

• Published in: Canadian journal of physics Vol. 98; no. 2; pp. 172 - 182
• Main Authors: Ullah, Kaleem, Ali, Nasir
• Format: Journal Article
• Language: English
• Published: Ottawa NRC Research Press 01.02.2020; Canadian Science Publishing NRC Research Press
• Subjects: Amplitudes; asymmetric channel; Asymmetry; bifurcation; Bifurcation theory; Bifurcations; canal asymétriquem; Differential equations; Exact solutions; Flow augmentation; Flow stability; Fluid dynamics; Fluid flow; non-linear dynamical system; Nonlinear differential equations; Nonlinear equations; peristaltic flow; Physics; Reynolds number; Stability analysis; Stagnation; streamline topologies; Systems stability; système dynamique non linéaire; topologies des lignes de courant; Topology; Transport; Trapping; Walls; Wave propagation; Wave velocity; écoulement–flot péristaltique; Pakistan
• ISSN: 0008-4204; 1208-6045
• DOI: 10.1139/cjp-2019-0062

This paper investigates the streamline topologies and stability of stagnation points and their bifurcations for an asymmetric peristaltic flow. The asymmetry of channel is due to the propagation of peristaltic waves with different phases and amplitudes on the flexible channel walls. An exact analytic solution of the flow problem subject to the constraints of low Reynolds number and long wavelength is obtained in wave frame of reference moving with wave velocity. A system of nonlinear differential equations is established to locate and classify the stagnation points in the flow domain. Different flow situations, manifested in the flow field, are categorized as: backward flow, trapping, and augmented flow. The transition from one situation to the other corresponds to bifurcation, which is explored graphically through local and global bifurcation diagrams. This analysis discloses the stability status of stagnation points and ranges of involved parameters in which various flow conditions appear in the flow field. It is concluded that the trapping in an asymmetric peristaltic transport can be reduced by increasing the phase difference of the channel walls. It is also found that the augmented flow region shrinks and the trapping region expands by increasing the amplitude ratio of the channel walls.