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Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (1): 137-154.doi: https://doi.org/10.1007/s10483-017-2156-6

• 论文 • 上一篇    

Interaction between compressibility and particulate suspension on peristaltically driven flow in planar channel

I. M. ELDESOKY1, S. I. ABDELSALAM2,3, R. M. ABUMANDOUR1, M. H. KAMEL4, K. VAFAI2   

  1. 1. Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Menoufia 32511, Egypt;
    2. Department of Mechanical Engineering, University of California, California 92521, U. S. A.;
    3. Basic Science Department, Faculty of Engineering, The British University in Egypt, Cairo 11837, Egypt;
    4. Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza 12613, Egypt
  • 收稿日期:2016-03-22 修回日期:2016-08-23 出版日期:2017-01-01 发布日期:2017-01-01
  • 通讯作者: S. I. ABDELSALAM,E-mail:sara.abdelsalam@bue.edu.eg E-mail:sara.abdelsalam@bue.edu.eg

Interaction between compressibility and particulate suspension on peristaltically driven flow in planar channel

I. M. ELDESOKY1, S. I. ABDELSALAM2,3, R. M. ABUMANDOUR1, M. H. KAMEL4, K. VAFAI2   

  1. 1. Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Menoufia 32511, Egypt;
    2. Department of Mechanical Engineering, University of California, California 92521, U. S. A.;
    3. Basic Science Department, Faculty of Engineering, The British University in Egypt, Cairo 11837, Egypt;
    4. Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza 12613, Egypt
  • Received:2016-03-22 Revised:2016-08-23 Online:2017-01-01 Published:2017-01-01
  • Contact: S. I. ABDELSALAM E-mail:sara.abdelsalam@bue.edu.eg

摘要:

The peristaltic pumping of a viscous compressible liquid mixed with rigid spherical particles of the same size in a channel is theoretically investigated. The momentum equations for the compressible flow are solved with a perturbation analysis. The analysis is carried out by duly accounting for the nonlinear convective acceleration terms for the fluid part on the wavy wall. The zeroth-order terms yield the Poiseuille flow, and the first-order terms give the Orr-Sommerfeld equation. The explicit expression for the net axial velocity is derived. The effects of the embedded parameters on the axial fluid velocity are studied through different engineering applications. The features of the flow characteristics are analyzed and discussed in detail. The obtained results are evaluated for various parameters associated with the blood flow in the blood vessels with diameters less than 5 500 μm, whereas the particle diameter has been taken to be 8 μm. This study provides a scope to evaluate the effect of the theory of two-phase flow characteristics with compressible fluid problems, and is helpful for understanding the role of engineering applications of pumping solid-fluid mixture by peristaltically driven motion.

关键词: compressible liquid, two-phase flow, peristaltic transport, perturbation method

Abstract:

The peristaltic pumping of a viscous compressible liquid mixed with rigid spherical particles of the same size in a channel is theoretically investigated. The momentum equations for the compressible flow are solved with a perturbation analysis. The analysis is carried out by duly accounting for the nonlinear convective acceleration terms for the fluid part on the wavy wall. The zeroth-order terms yield the Poiseuille flow, and the first-order terms give the Orr-Sommerfeld equation. The explicit expression for the net axial velocity is derived. The effects of the embedded parameters on the axial fluid velocity are studied through different engineering applications. The features of the flow characteristics are analyzed and discussed in detail. The obtained results are evaluated for various parameters associated with the blood flow in the blood vessels with diameters less than 5 500 μm, whereas the particle diameter has been taken to be 8 μm. This study provides a scope to evaluate the effect of the theory of two-phase flow characteristics with compressible fluid problems, and is helpful for understanding the role of engineering applications of pumping solid-fluid mixture by peristaltically driven motion.

Key words: two-phase flow, peristaltic transport, compressible liquid, perturbation method

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