We consider the stability of flux-driven flow through a long planar rigid channel, where a segment of one wall is replaced by a pre-tensioned hyperelastic (neo-Hookean) solid of finite thickness and subject to a uniform external pressure. We construct the steady configuration of the nonlinear system using Newton's method with spectral collocation and high-order finite differences. In agreement with previous studies, which use an asymptotically thin wall, we show that the thick-walled system always has at least one stable steady configuration, while for large Reynolds numbers the system exhibits three co-existing steady states for a range of external pressures. Two of these steady configurations are stable to non-oscillatory perturbations, one where the flexible wall is inflated (the upper branch) and one where the flexible wall is collapsed (the lower branch), connected by an unstable intermediate branch. We test the stability of these steady configurations to oscillatory perturbations using both a global eigensolver (constructed based on an analytical domain mapping technique) and also fully nonlinear simulations. We find that both the lower and upper branches of steady solutions can become unstable to self-excited oscillations, where the oscillating wall profile has two extrema. In the absence of wall inertia, increasing wall thickness partially stabilises the onset of oscillations, but the effect remains weak until the wall thickness becomes comparable to the width of the undeformed channel. However, with finite wall inertia and a relatively thick wall, higher-frequency modes of oscillation dominate the primary global instability for large Reynolds numbers.
Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of topological fractal analysis for 2D binary digital images by using a graph-based topological model of them, called Homological Spanning Forest (HSF, for short). Defined at interpixel level, this set of two trees allows to topologically describe the (black and white) connected component distribution within the image with regards to the relationship "to be surrounded by". This distribution is condensed into a rooted tree, such that its nodes are connected components determined by some special sub-trees of the previous HSF and the levels of the tree specify the degree of nesting of each connected component. We ask for topological auto-similarity by comparing this topological description of the whole image with a regular rooted tree pattern. Such an analysis can be used to directly quantify some characteristics of biomedical images (e.g. cells samples or clinical images) that are not so noticeable when using geometrical approaches.
Among the different polymers (proteins, polysaccharides, etc.) that make up natural fibers, fibroin is a protein produced by silk spinning animals, which have developed an optimized system for the conversion of a highly concentrated solution of this protein into high-performance solid fibers. This protein undergoes a self-assembly process in the silk glands that result from chemical gradients and by the application of mechanical stresses during the last step of the process. In the quest for a process that could mimic natural spinning at massive scales, we have discovered that turbulence offers a novel and promising solution: a turbulent liquid jet can be formed by a chemically green and simple coagulating liquid (a diluted solution of acetic acid in etanol) co-flowing with a concentrated solution of fibroin in water by the use of a Flow Blurring nebulizer. In this system, (a) the co-flowing coagulant liquid extracts water from the original protein solution and, simultaneously, (b) the self-assembled proteins are subjected to mechanical actions, including splitting and stretching. Given the non-negligible produced content with the size and appearance of natural silk, the stochastic distribution of those effects in our process should contain the range of natural ones found in animals. The resulting easily functionalizable and tunable one-step material is 100% biocompatible, and our method a perfect candidate to large-scale, low-cost, green and sustainable processing of fibroin for fibres and textiles.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.