TY - JOUR
T1 - Ultra-sharp pinnacles sculpted by natural convective dissolution
AU - Huanga, Jinzi Mac
AU - Tonga, Joshua
AU - Shelley, Michael
AU - Ristroph, Leif
N1 - Funding Information:
ACKNOWLEDGMENTS. We thank M. Davies Wykes, S. Childress, and J. Zhang for useful discussions. We acknowledge support from the NSF through the grant CBET-1805506 and from the Lilian and George Lyttle Chair of Applied Mathematics.
Publisher Copyright:
© 2020 National Academy of Sciences. All rights reserved.
PY - 2020/9/22
Y1 - 2020/9/22
N2 - 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.
AB - 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.
KW - Dissolution
KW - Fluid-structure interaction
KW - Geomorphology
KW - Natural convection
KW - Stone forest
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U2 - 10.1073/pnas.2001524117
DO - 10.1073/pnas.2001524117
M3 - Article
C2 - 32900954
AN - SCOPUS:85091593378
VL - 117
SP - 23339
EP - 23344
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
SN - 0027-8424
IS - 38
ER -