Kamel Mohammed H, Eldesoky Islam M, Maher Bilal M, Abumandour Ramzy M
Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, Egypt.
Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Shebin El-Kom, Egypt.
Appl Bionics Biomech. 2015;2015:703574. doi: 10.1155/2015/703574. Epub 2015 Jun 2.
Peristaltic pumping induced by a sinusoidal traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid mixed with rigid spherical particles is investigated theoretically taking the slip effect on the wall into account. A perturbation solution is obtained which satisfies the momentum equations for the case in which amplitude ratio (wave amplitude/channel half width) is small. The analysis has been carried out by duly accounting for the nonlinear convective acceleration terms and the slip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth-order terms yield the Poiseuille flow and the first-order terms give the Orr-Sommerfeld equation. The results show that the slip conditions have significant effect within certain range of concentration. The phenomenon of reflux (the mean flow reversal) is discussed under slip conditions. It is found that the critical reflux pressure is lower for the particle-fluid suspension than for the particle-free fluid and is affected by slip condition. A motivation of the present analysis has been the hope that such theory of two-phase flow process under slip condition is very useful in understanding the role of peristaltic muscular contraction in transporting biofluid behaving like a particle-fluid mixture. Also the theory is important to the engineering applications of pumping solid-fluid mixture by peristalsis.
研究了在充满粘性不可压缩流体与刚性球形颗粒混合物的二维通道壁中，由正弦行波引起的蠕动泵送，并考虑了壁面的滑移效应。得到了一个微扰解，该解满足振幅比（波幅/通道半宽）较小时的动量方程。通过适当考虑非线性对流加速度项和波浪壁上流体部分的滑移条件进行了分析。控制方程推导到了振幅比的二阶项。零阶项给出泊肃叶流，一阶项给出奥尔-索末菲方程。结果表明，在一定浓度范围内，滑移条件有显著影响。讨论了滑移条件下的回流现象（平均流反转）。发现颗粒-流体悬浮液的临界回流压力比无颗粒流体的临界回流压力低，且受滑移条件影响。本分析的一个动机是希望这种滑移条件下的两相流过程理论在理解蠕动肌肉收缩在输送行为类似颗粒-流体混合物的生物流体中的作用方面非常有用。此外，该理论对于蠕动泵送固-液混合物的工程应用也很重要。
