标题： 收缩诱导流的几何学 显示英文标题

标题： The Geometry of Contraction-Induced Flows

摘要： 蠕动是许多生物和工程流动背后的驱动机制。 在蠕动泵送中，管壁的波状收缩会产生局部体积变化，从而引发流动。 净流量是由于动量方程中的几何非线性引起的，必须正确捕捉这些非线性以准确计算流动。 虽然大多数先前的模型关注于半径约束的蠕动，但它们常常忽略了纵向长度的变化——这是弹性材料径向收缩的自然结果。 在本文中，为了更准确地描述蠕动泵送，我们计算了弹性血管在横向和纵向方向同时发生收缩时的流动，并保持应变中出现的几何非线性。 仔细分析要求我们使用弹性管的拉格朗日坐标来研究我们的流体。 我们通过研究具有随时间变化的度量的固定边界内的流体来对流动特性进行解析计算。 这种数学处理甚至适用于大振幅的收缩，我们通过将解析结果与COMSOL仿真进行比较来验证这一点。 我们证明横向和纵向收缩在壁面应变的同一阶次上引起瞬时流动，但方向相反。 我们研究了壁面泊松比对流动轮廓的影响。 不可压缩的壁面通过最小化局部体积变化来抑制流动，而 auxetic 壁面则增强流动。 对于半径约束的蠕动波，壁面不可压缩性会减少反流和粒子捕获。 相比之下，长度约束的波通常会产生回流，尽管对于某些泊松比，在大振幅下仍可能发生捕获。 这些结果提供了对弹性介质中蠕动更完整的描述，并为研究由收缩引起的流动提供了一个框架。 显示英文摘要

摘要： Peristalsis is the driving mechanism behind a broad array of biological and engineered flows. In peristaltic pumping, a wave-like contraction of the tube wall produces local changes in volume which induce flow. Net flow arises due to geometric nonlinearities in the momentum equation, which must be properly captured to compute the flow accurately. While most previous models focus on radius-imposed peristalsis, they often neglect longitudinal length changes - a natural consequence of radial contraction in elastic materials. In this paper, to capture a more accurate picture of peristaltic pumping, we calculate the flow in an elastic vessel undergoing contractions in the transverse and longitudinal directions simultaneously, keeping the geometric nonlinearities arising in the strain. A careful analysis requires us to study our fluid using the Lagrangian coordinates of the elastic tube. We perform analytic calculations of the flow characteristics by studying the fluid inside a fixed boundary with time-dependent metric. This mathematical manipulation works even for large-amplitude contractions, as we confirm by comparing our analytical results to COMSOL simulations. We demonstrate that transverse and longitudinal contractions induce instantaneous flows at the same order in wall strain, but in opposite directions. We investigate the influence of the wall's Poisson ratio on the flow profile. Incompressible walls suppress flow by minimizing local volume changes, whereas auxetic walls enhance flow. For radius-imposed peristaltic waves, wall incompressibility reduces both reflux and particle trapping. In contrast, length-imposed waves typically generate backflow, although trapping can still occur at large amplitudes for some Poisson ratios. These results yield a more complete description of peristalsis in elastic media and offer a framework for studying contraction-induced flows more broadly.