The evolution of landscapes, landforms, and other natural structures involves highly interactive physical and chemical processes that often lead to intriguing shapes and recurring motifs. Particularly intricate and fine-scale features characterize the so-called karst morphologies formed by mineral dissolution into water. An archetypal form is the tall, slender, and sharply tipped karst pinnacle or rock spire that appears in multitudes in striking landforms called stone forests, but whose formative mechanisms remain unclear due to complex, fluctuating, and incompletely understood developmental conditions. Here, we demonstrate that exceedingly sharp spires also form under the far-simpler conditions of a solid dissolving into a surrounding liquid. Laboratory experiments on solidified sugars in water show that needlelike pinnacles, as well as bed-of-nails-like arrays of pinnacles, emerge robustly from the dissolution of solids with smooth initial shapes. Although the liquid is initially quiescent and no external flow is imposed, persistent flows are generated along the solid boundary as dense, solute-laden fluid descends under gravity. We use these observations to motivate a mathematical model that links such boundary-layer flows to the shape evolution of the solid. Dissolution induces these natural convective flows that, in turn, enhance dissolution rates, and simulations show that this feedback drives the shape toward a finite-time singularity or blow-up of apex curvature that is cut off once the pinnacle tip reaches microscales. This autogenic mechanism produces ultra-fine structures as an attracting state or natural consequence of the coupled processes at work in the closed solid-fluid system.

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Tracheal displacement is thought to be the primary mechanism by which changes in lung volume influence upper airway patency. Caudal tracheal displacement during inspiration may help preserve the integrity of the upper airway in response to increasing negative airway pressure by stretching and stiffening pharyngeal tissues. However, tracheal displacement has not been previously quantified in obstructive sleep apnea (OSA). Accordingly, we aimed to measure tracheal displacements in awake individuals with and without OSA. The upper head and neck of 34 participants [apnea-hypopnea index (AHI) = 2–74 events/h] were imaged in the midsagittal plane using dynamic magnetic resonance imaging (MRI) during supine awake quiet breathing. MRI data were analyzed to identify peak tracheal displacement and its timing relative to inspiration. Epiglottic pressure was measured separately for a subset of participants ( n = 30) during similar experimental conditions. Nadir epiglottic pressure and its timing relative to inspiration were quantified. Peak tracheal displacement ranged from 1.0–9.6 mm, with a median (25th–75th percentile) of 2.3 (1.7–3.5) mm, and occurred at 89 (78–99)% of inspiratory time. Peak tracheal displacement increased with increasing OSA severity (AHI) ( R2 = 0.28, P = 0.013) and increasing negative nadir epiglottic pressure ( R2 = 0.47, P = 0.023). Relative inspiratory timing of peak tracheal displacement also correlated with OSA severity, with peak displacement occurring earlier in inspiration with increasing AHI ( R2 = 0.36, P = 0.002). Tracheal displacements during quiet breathing are larger in individuals with more severe OSA and tend to reach peak displacement earlier in the inspiratory cycle. Increased tracheal displacement may contribute to maintenance of upper airway patency during wakefulness in OSA, particularly in those with severe disease. NEW & NOTEWORTHY Tracheal displacement is thought to play an important role in stabilizing the upper airway by stretching/stiffening the pharyngeal musculature. Using dynamic magnetic resonance imaging, this study shows that caudal tracheal displacement is more pronounced during inspiration in obstructive sleep apnea (OSA) compared with healthy individuals. Softer pharyngeal muscles and greater inspiratory forces in OSA may underpin greater tracheal excursion. These findings suggest that tracheal displacement may contribute to maintenance of pharyngeal patency during wakefulness in OSA.