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Viscoelastic liquid film flowing down a flexible tube

Published online by Cambridge University Press:  05 August 2016

Zhi-Qiang Zhou ,
Jie Peng ,
Yang-Jun Zhang  and
Wei-Lin Zhuge
Zhi-Qiang Zhou
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing, PR China
Jie Peng*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing, PR China
Yang-Jun Zhang
Affiliation:
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, PR China
Wei-Lin Zhuge
Affiliation:
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, PR China
*
†Email address for correspondence: peng-jie@tsinghua.edu.cn
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Abstract

This investigation addresses the dynamics of annular viscoelastic films flowing down a flexible tube. The fluid viscoelasticity is assumed to be weak in order to obtain approximate explicit expressions for the stresses. Based on Shkadov’s integral boundary layer method (Fluid Dyn., vol. 2(1), 1967, pp. 29–34), a set of nonlinear evolution equations is derived that is valid for flows with moderate Reynolds numbers. The linear stability property of the system is examined by using normal-mode analysis, which is verified by comparing the results with those resulting from the linearization of the full Navier–Stokes equations. The results indicate that the fluid viscoelasticity plays an unstable role in the stability of the annular film flow. The tube flexibility, which includes wall damping and wall tension, plays a dual role. A bifurcation analysis is performed, and the families of steady travelling waves are catalogued. It is found that the stiffness of the tube tends to stimulate the interfacial capillary ripples. The fluid viscoelasticity acts to strengthen the dispersion of the interfacial waves but weakens the interfacial capillary ripples. The spatio-temporal evolutions of the system are also solved numerically. When the tube radius is small enough, tube closure can be observed due to the Plateau–Rayleigh instability. The fluid viscoelasticity acts to promote tube closure while the tube radius is relatively small. However, it plays a role in postponing the closure of the tube with a large radius.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Interfacial Flows (free surface): Thin films Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 802 , 10 September 2016 , pp. 583 - 610
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Copyright
© 2016 Cambridge University Press 

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