The current study deals the theoretical investigation of a viscous fluid due to metachronal waves of cilia through the curved channel with porous medium effects. Due to the complex nature of flow regime, curvilinear coordinates are used to develop constitutive equations for two-dimensional flow. Firstly, the whole system is transformed from fixed frame to wave frame of reference. Secondly, the scaling factors are used to convert the system of EOM ( equation of motion ) into the dimensionless form. To analyse the flow phenomena due to metachronal waves ( a sequence of beating of cilia from row to row ), we employed long wavelength and creeping flow approximation. Finally, the components of fluid velocity are replaced by the derivatives of stream function. Analytical solution of stream function is calculated. The influence of key physical parameters i.e. curvature parameter, porosity parameter and two distinct amplitude ratios of metachronal wave patterns on fluid transp...

中文翻译：

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弯曲通道中纤毛驱动的流体流动：复杂波和多孔介质的影响

目前的研究对粘性流体进行了理论研究，该粘性流体是由于纤毛的历时性波通过弯曲通道而产生的，具有多孔介质效应。由于流动状态的复杂性，曲线坐标被用于开发二维流动的本构方程。首先，将整个系统从固定参考帧转换为参考波形帧。其次，比例因子用于将EOM（运动方程）系统转换为无量纲形式。为了分析由次同步波（一排又一排的纤毛跳动）引起的流动现象，我们采用了长波长和蠕变流动近似法。最后，流速函数由流函数的导数代替。计算了流函数的解析解。