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Soft intertwined channel systems are frequently found in fluid flow networks in nature. The passage geometry of these systems can deform due to fluid flow, which can cause the relationship between flow rate and pressure drop to deviate from the Hagen–Poiseuille linear law. Although fluid–structure interactions in single deformable channels have been extensively studied, such as in Starling’s resistor and its variations, the flow transport capacity of an intertwined channel with multiple self-intersections (a ‘hydraulic knot’), is still an open question. We present experiments and theory on soft hydraulic knots formed by interlinked microfluidic devices comprising two intersecting channels separated by a thin elastomeric membrane. Our experiments show flow–pressure relationships similar to flow limitation, where the limiting flow rate depends on the knot configuration. To explain our observations, we develop a mathematical model based on lubrication theory coupled with tension-dominated membrane deflections that compares favourably with our experimental data. Finally, we present two potential hydraulic knot applications for microfluidic flow rectification and attenuation.

Molecular diffusion in bulk liquids proceeds according to Fick's law, which stipulates that the particle current is proportional to the conductive area. This constrains the efficiency of filtration systems in which both selectivity and permeability are valued. Previous studies have demonstrated that interactions between the diffusing species and solid boundaries can enhance or reduce particle transport relative to bulk conditions. However, only cases that preserve the monotonic relationship between particle current and conductive area are known. In this paper, we expose a system in which the diffusive current increases when the conductive area diminishes. These examples are based on the century-old theory of a charged particle interacting with an electrical double layer. This surprising discovery could improve the efficiency of filtration and may advance our understanding of biological pore structures.

Controlling fluid flow from an unsteady source is a challenging problem that is relevant in both living and man-made systems. Animals have evolved various autoregulatory mechanisms to maintain homeostasis in vital organs. This keeps the influx of nutrients essentially constant and independent of the perfusion pressure. Up to this point, the autoregulation processes have primarily been ascribed to active mechanisms that regulate vessel size, thereby adjusting the hydraulic conductance in response to, e.g., sensing of wall shear stress. We propose an alternative elastohydrodynamic mechanism based on contacting soft vessels. Inspired by Starling's resistor, we combine experiments and theory to study the flow of a viscous liquid through a self-intersecting soft conduit. In the overlapping region, the pressure difference between the two channel segments can cause one pipe segment to dilate while the other is compressed. If the tissue is sufficiently soft, this mode of fluid-structure interactions can lead to flow autoregulation. Our experimental observations compare well to a predictive model based on low-Reynolds-number fluid flow and linear elasticity. Implications for conduit arrangement and passive autoregulation in organs and limbs are discussed.

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., 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.

The economics, environmental impact, and mechanical properties of paper-based storage containers have been widely studied. However, knowledge of the physical processes relevant to the end-user experience is unavailable. This paper outlines the main effects associated with the closing and opening of telescoping boxes, which are used, for instance, to store and transport board games, footwear, mobile phones, and tablet computers. The sliding motion of the lid is controlled by the flow in a thin film of air in the gap separating the lid and the base of the box. Based on a broad comparison between theory and experiments on real and synthetic boxes, we find that the process is primarily controlled by the shape of the gap between the base and the lid. We derive a master equation for the lid motion and identify the origin of three distinct experimental regimes. Finally, an optimal design for a rapidly closing box is identified.

In most plant tissues, threads of cytoplasm, or plasmodesmata, connect the protoplasts via pores in the cell walls. This enables symplasmic transport, for instance in phloem loading, transport and unloading. Importantly, the geometry of the wall pore limits the size of the particles that may be transported, and also (co-)defines plasmodesmal resistance to diffusion and convective flow. However, quantitative information on transport through plasmodesmata in non-cylindrical cell wall pores is scarce. We have found conical, funnel-shaped cell wall pores in the phloem-unloading zone in growing root tips of five eudicot and two monocot species, specifically between protophloem sieve elements and phloem pole pericycle cells. 3D reconstructions by electron tomography suggested that funnel plasmodesmata possess a desmotubule but lack tethers to fix it in a central position. Model calculations showed that both diffusive and hydraulic resistance decrease drastically in conical and trumpet-shaped cell wall pores compared with cylindrical channels, even at very small opening angles. Notably, the effect on hydraulic resistance was relatively larger. We conclude that funnel plasmodesmata generally are present in specific cell–cell interfaces in angiosperm roots, where they appear to facilitate symplasmic phloem unloading. Interestingly, cytosolic sleeves of most plasmodesmata reported in the literature do not resemble annuli of constant diameter but possess variously shaped widenings. Our evaluations suggest that widenings too small for unambiguous identification on electron micrographs may drastically reduce the hydraulic and diffusional resistance of these pores. Consequently, theoretical models assuming cylindrical symmetries will underestimate plasmodesmal conductivities.

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.

Droplet microarray technology is of great interest in biology and chemistry as it allows for significant reactant savings and massive parallelization of experiments. Upon scaling down the footprint of each droplet in an array, it becomes increasingly challenging to produce the array drop-by-drop. Therefore, techniques for parallelized droplet production are developed, e.g., dip-coating of biphilic substrates. However, it is in general difficult to tailor the characteristics of individual droplets, such as size and content, without updating the substrate. Here, the method of dip-coating of uniformly patterned biphilic substrates in so-called “acceleration-mode” to produce droplet arrays featuring gradients in droplet height for fixed droplet footprint is developed. The results herein present this method applied to produce drops with base diameters varying over orders of magnitude, from as high as 6 mm to as small as 50 µm; importantly, the experimentally measured power-law-dependency of volume on capillary-number matches analytical theory for droplet formation on heterogenous substrates though the precise quantitative values likely differ due to 2D substrate patterning. Gradient characteristics, including average droplet volume, steepness of the gradient, and its monotonicity, can all be tuned by changing the dip-coating parameters, thus providing a robust method for high-throughput screening applications and experiments.

Water-absorbing materials consisting of hydrogel particles are widely used for agricultural substrates, hygienic products, drug delivery systems, and microfluidic devices. Hydrogel particles absorb water with expansion, leading to dynamics involving complicated interactions of intergranular liquid flow and hydrogel deformation. It is thus difficult to predict the water absorption rate of these materials. Water flow in hydrogel-coated capillary tubes also occurs with the deformation of flow passages, so it can be analogous to capillary flow through porous structures made of hydrogels. Here we report a combined experimental and theoretical investigation of water flow through capillaries whose inner surface is covered with a hydrogel layer. We experimentally measured the flow rate of water through hydrogel-coated capillary tubes and the volume of water absorbed by the hydrogel layer. We developed a mathematical model for capillary flow including the effects of the water absorption and swelling of the hydrogel layer. Our model is in good agreement with the measurements of the water flow rate and elucidates how the absorption and swelling of hydrogel regulate capillary flow. This study provides a theoretical framework for understanding the dynamics of capillary flow through porous structures composed of hydrogels, leading to insights into the engineering applications of porous hydrogel materials.

Plant tissues exhibit a symplasmic organization; the individual protoplasts are connected to their neighbors via cytoplasmic bridges that extend through pores in the cell walls. These bridges may have diameters of a micrometer or more, as in the sieve pores of the phloem, but in most cell types they are smaller. Historically, botanists referred to cytoplasmic bridges of all sizes as plasmodesmata. The meaning of the term began to shift when the transmission electron microscope (TEM) became the preferred tool for studying these structures. Today, a plasmodesma is widely understood to be a ‘nano-scale’ pore. Unfortunately, our understanding of these nanoscopic channels suffers from methodological limitations. This is exemplified by the fact that state-of-the-art EM techniques appear to reveal plasmodesmal pore structures that are much smaller than the tracer molecules known to diffuse through these pores. In general, transport processes in pores that have dimensions in the size range of the transported molecules are governed by different physical parameters than transport process in the macroscopic realm. This can lead to unexpected effects, as experience in nanofluidic technologies demonstrates. Our discussion of problems of size in plasmodesma research leads us to conclude that the field will benefit from technomimetic reasoning – the utilization of concepts developed in applied nanofluidics for the interpretation of biological systems.