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 ∆p, sphere radius a, gap thickness h 0 , and viscosity η as Q ∼ η −1 a 1/2 h 5/2 0 (∆p c − ∆p) 5/2 ∆p, where the critical pressure ∆p c scales with the spring constant k and sphere radius a as ∆p c ∼ ka −2 . These predictions compared favorably to the results of our experiments with no free parameters.
The glymphatic system of cerebrospinal fluid transport through the perivascular spaces of the brain has been implicated in metabolic waste clearance, neurodegenerative diseases and in acute neurological disorders such as stroke and cardiac arrest. In other biological low-pressure fluid pathways such as in veins and the peripheral lymphatic system, valves play an important role in ensuring the flow direction. Though fluid pressure is low in the glymphatic system and directed bulk flow has been measured in pial and penetrating perivascular spaces, no valves have yet been identified. Valves, which asymmetrically favour forward flow to backward flow, would imply that the considerable oscillations in blood and ventricle volumes seen in magnetic resonance imaging could cause directed bulk flow. Here, we propose that astrocyte endfeet may act as such valves using a simple elastic mechanism. We combine a recent fluid mechanical model of viscous flow between elastic plates with recent measurements of in vivo elasticity of the brain to predict order of magnitude flow-characteristics of the valve. The modelled endfeet are effective at allowing forward while preventing backward flow.
Pulsating flows are common in many industrial, scientific, and natural fluidic systems. However, because the oscillatory flow component disturbs, e.g., optical measurements, deposition, or industrial processes, it is rarely desired. Moreover, in physiological conditions, pulsation control is desired. We explore the effect of using a plant-inspired nonlinear resistor to smooth the output of a peristaltic pump. Incorporating a 3D printed millifluidic biomimetic device reduces the oscillation amplitudes by 3 orders of magnitude, from 100% to 0.1% of the output flow rate. This represents a tenfold improvement relative to a purely linear resistive-capacitive approach. The observed flow kinetics compare well to a predictive model of peristaltic transport, allowing the further development of optimized fluid-handling systems driven by pulsatile flow. Applications to particle tracking and jetting are considered.
Soft plates immersed in fluids appear in many biological processes, including swimming, flying, and breathing. The plate deforms in response to fluid flows, yet fluid stresses are in turn influenced by the plate's deformation. We present a mathematical model examining the flow of a viscous fluid in a narrow slit formed by two rectangular elastic plates, and demonstrate a strongly nonlinear flow response. The volumetric flow rate first increases linearly with pressure; however, the bending of the plates causes the corners to approach. This in turn reduces the flow rate. In some cases, the corners meet and the slit no longer permits flow. Our model, which is based on low-Reynolds-number hydrodynamics and linear plate theory, yields insights into two competing effects: While the plate bending generally reduces the slit aperture, it also causes the two plates to move apart, thus increasing the gap. Relations to biomedical flows are outlined and potential applications to flow control in man-made systems are considered.
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