流体-结构相互作用在自然界和技术中无处不在。然而，系统往往是如此复杂，数值模拟或特设的假设，必须用来深入了解流体和固体力学之间的复杂相互作用的细节。在本文中，我们提出了一个简单的仿生软阀，说明在低雷诺数的流体动力和弹性力之间的相互作用的基本特征的粘性流的实验和理论。该装置包括连接到位于锥形圆柱形通道内的弹簧的球体。弹簧与通道的中心轴线对齐，并且在球体上施加压降，从而迫使液体通过球体和通道壁之间的狭窄间隙。球体的平衡位置由弹簧力和流体动力之间的平衡决定。由于间隙厚度随球体位置而变化，因此系统具有压力相关的液压阻力。这导致施加的压力和流速之间的非线性关系：流量最初随压力增加，但当压力超过某个临界值时随着间隙关闭而减小。为了使这些观察合理化，我们提出了一个数学模型，将流动的复杂性降低到二维润滑近似。得到了压降/流速的封闭式表达式，该表达式揭示了流速$Q$取决于压降$Δp$、球体半径$a$、间隙厚度$h_0$和粘度$η$，公式为$Q\sim η^{-1} a^{1/2}h_0^{5/2}\left(Δp_c-Δp\right)^{5/2}Δp$，其中临界压力$Δp_c$与弹性常数$k$和球体半径$a$成比例，公式为$Δp_c\sim k a^{-2}$。这些预测与我们没有自由参数的实验结果相比是有利的。
英文摘要：
Fluid-structure interactions are ubiquitous in nature and technology. However, the systems are often so complex that numerical simulations or ad hoc assumptions must be used to gain insight into the details of the complex interactions between the fluid and solid mechanics. In this paper, we present experiments and theory on viscous flow in a simple bioinspired soft valve which illustrate essential features of interactions between hydrodynamic and elastic forces at low Reynolds numbers. The setup comprises a sphere connected to a spring located inside a tapering cylindrical channel. The spring is aligned with the central axis of the channel and a pressure drop is applied across the sphere, thus forcing the liquid through the narrow gap between the sphere and the channel walls. The sphere's equilibrium position is determined by a balance between spring and hydrodynamic forces. Since the gap thickness changes with the sphere's position, the system has a pressure-dependent hydraulic resistance. This leads to a non-linear relation between applied pressure and flow rate: flow initially increases with pressure, but decreases when the pressure exceeds a certain critical value as the gap closes. To rationalize these observations, we propose a mathematical model that reduced the complexity of the flow to a two-dimensional lubrication approximation. A closed-form expression for the pressure-drop/flow rate is obtained which reveals that the flow rate $Q$ depends on the pressure drop $Δp$, sphere radius $a$, gap thickness $h_0$, and viscosity $η$ as $Q\sim η^{-1} a^{1/2}h_0^{5/2}\left(Δp_c-Δp\right)^{5/2}Δp$, where the critical pressure $Δp_c$ scales with the spring constant $k$ and sphere radius $a$ as $Δp_c\sim k a^{-2}$. These predictions compared favorably to the results of our experiments with no free parameters.
Viscous streaming is an efficient mechanism to exploit inertia at the microscale for flow control. While streaming from rigid features has been thoroughly investigated, when body compliance is involved, as in biological settings, little is known. Here, we investigate body elasticity effects on streaming in the minimal case of an immersed soft cylinder. Our study reveals an additional streaming process, available even in Stokes flows. Paving the way for advanced forms of flow manipulation, we illustrate how gained insights may translate to complex geometries beyond circular cylinders.
Rotation of an immersed cylinder sliding near a thin elastic coating
已知的是，在粘性流体中平行于软壁平移的物体产生使壁变形的流体动力应力，这进而导致物体上的升力。最近在软斜面附近进行的圆柱体在重力作用下滑动的实验证实了升力的理论论据，也报告了圆柱体的无法解释的稳态旋转[Saintyves et al. PNAS 113（21），2016]。出于这些观察结果，我们表明，在润滑极限，一个无限的圆柱体，在一个粘性流体平行于一个软壁，以恒定的速度和分离距离平移也必须旋转，以保持免费的扭矩。利用洛伦兹互等定理，我们分析表明，对于小变形的弹性层，角速度的圆柱尺度与滑动速度的立方。这些预测在数字上得到了证实。然后，我们将该理论应用到重力驱动的运动的一个圆柱体附近的软倾斜，并找到定性的协议与实验观察，即较软的弹性层的结果在一个更大的角速度的圆柱体。
A circular Hele-Shaw cell bounded by a volumetrically confined elastic solid can act as a fluidic fuse: during radially outward fluid flow, the solid deforms in response to the viscous pressure field such that the gap expands near the inlet (at the centre) and contracts near the outlet (around the rim). If the flow rate exceeds a critical value, the gap at the outlet can close completely, interrupting/choking the flow. Here, we consider the injection of gas into such a soft-walled Hele-Shaw cell filled with viscous liquid. Our theoretical model and numerical simulations for axisymmetric flow d…
Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Weierstrass-Institute for Applied Analysis and Stochastics（魏尔斯特拉斯应用分析与随机学研究所）；Leibniz-Institut für Verbundwerkstoffe GmbH（莱布尼茨复合材料有限公司研究所）
