中国物理B ›› 2006, Vol. 15 ›› Issue (11): 2644-2650.doi: 10.1088/1009-1963/15/11/031

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇    下一篇

Velocity overshoot of start-up flow for a Maxwellfluid in a porous half-space

谭文长   

  1. State Key Laboratory of Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
  • 收稿日期:2005-10-20 修回日期:2006-06-28 出版日期:2006-11-20 发布日期:2006-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10372007 and 10572006) and the New Century Training Programme Foundation for the Talents by Chinese Ministry of Education.

Velocity overshoot of start-up flow for a Maxwellfluid in a porous half-space

Tan Wen-Chang(谭文长)†   

  1. State Key Laboratory of Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
  • Received:2005-10-20 Revised:2006-06-28 Online:2006-11-20 Published:2006-11-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10372007 and 10572006) and the New Century Training Programme Foundation for the Talents by Chinese Ministry of Education.

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摘要： Stokes' first problem has been investigated for a Maxwell fluid in a porous half-space for gaining insight into the effect of viscoelasticity on the start-up flow in a porous medium. An exact solution was obtained by using the Fourier sine transform. It was found that at large values of the relaxation time the velocity overshoot occurs obviously and the system exhibits viscoelastic behaviours. On the other hand, for short relaxation time the velocity overshoot disappears and the system exhibits viscous behaviours. A critical value of the relaxation time was obtained for the emergence of the velocity overshoot. Furthermore, it was found that the velocity overshoot is caused by both the viscoelasticity of the Maxwell fluid and the Darcy resistance resulting from the structure of the micropore in the porous medium.

Abstract: Stokes' first problem has been investigated for a Maxwell fluid in a porous half-space for gaining insight into the effect of viscoelasticity on the start-up flow in a porous medium. An exact solution was obtained by using the Fourier sine transform. It was found that at large values of the relaxation time the velocity overshoot occurs obviously and the system exhibits viscoelastic behaviours. On the other hand, for short relaxation time the velocity overshoot disappears and the system exhibits viscous behaviours. A critical value of the relaxation time was obtained for the emergence of the velocity overshoot. Furthermore, it was found that the velocity overshoot is caused by both the viscoelasticity of the Maxwell fluid and the Darcy resistance resulting from the structure of the micropore in the porous medium.

Key words: Maxwell fluid, porous media, velocity overshoot

中图分类号:  (Flows through porous media)

  • 47.56.+r
47.10.-g (General theory in fluid dynamics) 47.50.-d (Non-Newtonian fluid flows)