In this paper, the simultaneous effect of Hall current and ion slip on an infinite-length model of ciliary propulsion of a microscopic organism through porous medium has been investigated. We have considered a symplectic metachronal wave of extensible envelope over the organism. The partial differential equations of creeping flow are transformed into an ordinary differential equation with the help of stream function. The series solution of velocity distribution and pressure distribution are obtained in the presence of a magnetic field and porous medium. Also, the trapping phenomena has been discussed with the help of stream lines. The effects of Hartmann number, ion slip, Hall current, and the porosity parameter on the velocity field and stream function are observed by graphical results.

中文翻译：

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霍尔电流和离子滑移作用下多孔介质中CILIA诱导的MHD流动的级数解

在本文中，研究了霍尔电流和离子滑移对通过多孔介质的微生物机体纤毛推进的无限长模型的同时影响。我们已经考虑了在生物体上可扩展包膜的辛的变时波。借助流函数，将蠕变流的偏微分方程转换为常微分方程。在磁场和多孔介质的存在下获得速度分布和压力分布的级数解。另外，已经在流线的帮助下讨论了捕集现象。通过图形结果观察到哈特曼数，离子滑移，霍尔电流和孔隙率参数对速度场和流函数的影响。