AI 中文总结
研究偏心环形管道中流动，考虑多孔阻力与流固相互作用，通过微扰法简化问题为轴向压力的非线性偏微分方程，建立降阶模型，助于理解多孔穿透PAS的流动，小振幅蠕动波时有解析解。
AI 中文摘要
Coenen等人（《流体力学杂志》，第921卷，2021年，第R2页）在动脉周围空间（PAS）流动的背景下，建立了刚性壁非轴对称环形管道中蠕动泵的降阶模型。体内研究表明，PAS的外壁会因内部流动而发生显著位移，且穿透性PAS形成多孔通道。为考虑这些生物力学因素，我们重新审视偏心环形管道中的流动问题，纳入多孔阻力以及顺应性外壁与脑脊髓液流动之间的双向耦合流固相互作用。轴向动量方程中的达西 - 布林克曼项考虑了多孔介质的阻力。我们通过微扰法考虑蠕动和顺应壁位移引起的水力阻力变化，将问题简化为轴向压力的单个非线性偏微分方程。该降阶模型有助于我们对通过多孔穿透PAS的流动建立机理理解，并能进行参数研究。对于小振幅蠕动波，可得到解析解。
英文摘要
Coenen \textit{et al.}\ (\textit{J. Fluid Mech.}, vol.~921, 2021, p.~R2) developed a reduced-order model of peristaltic pumping in non-axisymmetric annular conduits with rigid walls, in the context of periarterial space (PAS) flows. \textit{In vivo} studies show that the PAS's outer wall undergoes significant displacement due to flow within and that the penetrating PASs form a porous pathway. To account for these biomechanical aspects, we revisit the problem of flow in an eccentric annular conduit and incorporate porous drag and two-way-coupled fluid--structure interaction between the compliant outer wall and the cerebrospinal fluid flow within. A Darcy--Brinkman term in the axial momentum equation accounts for drag due to the porous medium. We account for changes in hydraulic resistance due to peristalsis and compliant-wall displacements perturbatively, thereby reducing the problem to a single nonlinear partial differential equation for the axial pressure. This reduced-order model allows us to build a mechanistic understanding of flow through a porous penetrating PAS and enables parametric studies. For small-amplitude peristaltic waves, analytical solutions are possible.
Comments18 pages, 6 figures
