Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

doi:10.1088/1674-1056/23/6/064701

中国物理B ›› 2014, Vol. 23 ›› Issue (6): 64701-064701.doi: 10.1088/1674-1056/23/6/064701

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

Z. Asghar, N. Ali

Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan

收稿日期:2013-09-05 修回日期:2013-10-30 出版日期:2014-06-15 发布日期:2014-06-15

Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

Z. Asghar, N. Ali

Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan

Received:2013-09-05 Revised:2013-10-30 Online:2014-06-15 Published:2014-06-15
Contact: Z. Asghar E-mail:zaheer_asghar@yahoo.com

摘要/Abstract

摘要： We discuss the effects of the surface slip on streamline patterns and their bifurcations for the peristaltic transport of a Newtonian fluid. The flow is in a two-dimensional symmetric channel or an axisymmetric tube. An exact expression for the stream function is obtained in the wave frame under the assumptions of long wavelength and low Reynolds number for both cases. For the discussion of the particle path in the wave frame, a system of nonlinear autonomous differential equations is established and the methods of dynamical systems are used to discuss the local bifurcations and their topological changes. Moreover, all types of bifurcations and their topological changes are discussed graphically. Finally, the global bifurcation diagram is used to summarize the bifurcations.

关键词: viscous fluid, slip condition, streamline topologies, bifurcation

Abstract: We discuss the effects of the surface slip on streamline patterns and their bifurcations for the peristaltic transport of a Newtonian fluid. The flow is in a two-dimensional symmetric channel or an axisymmetric tube. An exact expression for the stream function is obtained in the wave frame under the assumptions of long wavelength and low Reynolds number for both cases. For the discussion of the particle path in the wave frame, a system of nonlinear autonomous differential equations is established and the methods of dynamical systems are used to discuss the local bifurcations and their topological changes. Moreover, all types of bifurcations and their topological changes are discussed graphically. Finally, the global bifurcation diagram is used to summarize the bifurcations.

Key words: viscous fluid, slip condition, streamline topologies, bifurcation

中图分类号: (Laminar flows)

47.15.-x

47.10.ad (Navier-Stokes equations) 05.45.-a (Nonlinear dynamics and chaos)

Z. Asghar, N. Ali. Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid[J]. 中国物理B, 2014, 23(6): 64701-064701.

Z. Asghar, N. Ali. Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid[J]. Chin. Phys. B, 2014, 23(6): 64701-064701.

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Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

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