Singularly sharp pinnacles sculpted by natural convective dissolution

Jinzi Mac Huang, Josh Tong, Michael Shelley and Leif Ristroph

The evolution of landscapes, landforms and other natural structures involves highly interactive physical and chemical processes that often lead to intriguing and recognizable shapes. Particularly intricate and fine-scale features typify the so-called karst morphologies formed by mineral dissolution in flowing 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 its complex, fluctuating and incompletely understood developmental conditions. Here we demonstrate that exceedingly sharp pinnacles 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 initally 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 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 this closed solid-fluid system.

Lab Scale Stone Forest

Formation of Single Tree: Experiment vs Model

Decision-making at a T-junction by gradient-sensing agents

Tanvi Gandhi, Jinzi Mac Huang, Antoine Aubret, Desmond Li, Sophie Ramananarivo, Massimo Vergassola and Jeremie Palacci

Effective navigation relies on adequate information extracted from the surrounding environment. Large organisms, such as larvae or slugs, can faithfully sense the concentration gradients across their bodies -- a strategy that does not lend to smaller organisms with only localized information, often overwhelmed by fluctuations. Instead, bacteria like E.Coli estimate the local concentration and modulate their tumbling rate to direct towards the source of nutrient. The presence of confining boundaries also modifies the global concentration field and raises the challenge of navigation in complex environments. In this Letter, we consider a basic yet essential element of navigation, which is the effect of a single T-junction where incoming agents split into two paths. Here we show that taking the optimal (shortest) path at a junction is a remarkably difficult task for agents that trace the concentration gradient. We study the navigation of colloidal particles by diffusiophoresis and highlight that the statistics of path-taking is primarily set by the geometric criteria. We further use numerical experiments to search for navigation strategies that achieve better selection of optimal paths, including strategies devised by biological organisms: run and tumble or Markovian chemotactic migration. We show that they perform similarly and engineer an alternative "run and whirl" strategy to allow the point particle to navigate with higher accuracy.

Colloids (White) Move towards the Exit of a Maze

SDE Simulation of the same Process

A stable and accurate scheme for solving the Stefan problem with natural convection using Immersed Boundary Smooth Extension

Jinzi Mac Huang, Michael Shelley and David Stein

An important class of physical processes involves the motion of a phase interface whose evolution depends on the gradients of a temperature or concentration field at the boundary. The classical Stefan problem that describes the fluid-solid interface in melting or solidification is one such example, others include the land-forming processes that have sculpted the ``stone forests'' of China and Madagascar. These problems are numerically challenging, requiring the evolution of a free interface whose motion depends on the normal derivatives of an external field which must be evolved in an ever-changing domain. In this contribution we derive a numerical method for the simulation of the Stefan problem coupled to a Navier-Stokes flow, as results when buoyancy or density differences induce convection and mixing. The scheme uses the Immersed Boundary Smooth Extension (IBSE) method to solve the bulk advection-diffusion and fluid equations in the complex, evolving geometry, coupled to a θ-L scheme that provides stable evolution of the boundary. We demonstrate 3rd-order pointwise convergence of the scheme for the classical Stefan problem, and 2nd-order convergence of the scheme when coupled to flow. Examples of dissolution in a high-Reynolds number flow are numerically studied, and qualitatively reproduce the pattern formation observed in recent experiments.

Mullins-Sekerka Instability in Stefan Problems

Dissolution with Natural Convection, Re = 300

Rayleigh-Bénard thermal convection perturbed by horizontal heat flux

Jinzi Mac Huang and Jun Zhang

As an important mechanism of heat transfer by fluids, Rayleigh-Benard thermal convection has been thoroughly investigated in the past. In this study, we examine the effect of heating from one vertical sidewall in an otherwise classical Rayleigh-Benard convection in a cubical domain. Experiments operate at constant top temperature and bottom heating power, side heating to the fluid causes the bulk temperature to increase and hence a higher top-bottom temperature difference. The Rayleigh number thus increases and Nusselt number decreases, rendering a fluid system with reduced heat-passing capability, despite of an enhanced large-scale circulation. Two models explaining our observations are proposed and they lead to equations that collapse the observed data at different side heating powers.

The role of shape-dependent flight stability in the origin of oriented meteorites

Khunsa Amin, Jinzi Mac Huang, Kevin J. Hu., Jun Zhang and Leif Ristroph

The atmospheric ablation of meteoroids is a striking example of the reshaping of a solid object due to its motion through a fluid. Motivated by meteorite samples collected on Earth that suggest fixed orientation during flight—most notably the conical shape of so-called oriented meteorites—we hypothesize that such forms result from an aerodynamic stabilization of posture that may be achieved only by specific shapes. Here, we investigate this issue of flight stability in the parallel context of fluid mechanical erosion of clay bodies in flowing water, which yields shapes resembling oriented meteorites. We conduct laboratory experiments on conical objects freely moving through water and fixed within imposed flows to determine the dependence of orientational stability on shape. During free motion, slender cones undergo postural instabilities, such as inversion and tumbling, and broad or dull forms exhibit oscillatory modes, such as rocking and fluttering. Only intermediate shapes, including the stereotypical form carved by erosion, achieve stable orientation and straight flight with apex leading. We corroborate these findings with systematic measurements of torque and stability potentials across cones of varying apex angle, which furnish a complete map of equilibrium postures and their stability. By showing that the particular conical form carved in unidirectional flows is also posturally stable as a free body in flight, these results suggest a self-consistent picture for the origin of oriented meteorites.

Publication

The role of shape-dependent flight stability in the origin of oriented meteorites
( Link ) Khunsa Amin, Jinzi Mac Huang, Kevin J. Hu.,Jun Zhang and Leif Ristroph
- PNAS (2019)

DFD Gallery of Fluid Motion Video

Media Coverage

Fox News - Earth is littered with mysterious space-cones, and now we know why ( Link )
Phys.org - What gives meteorites their shape? New research uncovers a 'Goldilocks' answer ( Link )
EurekeAlert - What gives meteorites their shape? New research uncovers a 'Goldilocks' answer ( Link )

Stochastic dynamics of fluid–structure interaction in turbulent thermal convection

Jinzi Mac Huang, Jin-Qiang Zhong, Jun Zhang and Laurent Mertz

The motion of a free-moving plate atop turbulent thermal convection exhibits diverse dynamics that displays characteristics of both deterministic and chaotic motions. Early experiments performed by Zhong & Zhang (Phys. Rev. E, vol. 75 (5), 2007, 055301) found an oscillatory and a trapped state existing for a plate floating on convective fluid in a rectangular tank. They proposed a piecewise smooth physical model (ZZ model) that successfully captures this transition of states. However, their model was deterministic and therefore could not describe the stochastic behaviours. In this study, we combine the ZZ model with a novel approach that models the stochastic aspects through a variational inequality structure. With the powerful mathematical tools for stochastic variational inequalities, the properties of the Markov process and corresponding Kolmogorov equations could be studied both numerically and analytically. Moreover, this framework also allows one to compute the transition probabilities. Our present work captures the stochastic aspects of the two aforementioned boundary–fluid coupling states, predicts the stochastic behaviours and shows excellent qualitative and quantitative agreements with the experimental data.

Publication

Stochastic dynamics of fluid–structure interaction in turbulent thermal convection
( Link ) Jinzi Mac Huang, Jin-Qiang Zhong, Jun Zhang and Laurent Mertz
- J. Fluid Mech. (Rapids) (2018)

Self-sculpting of a dissolvable body due to gravitational convection

Megan Davies Wykes, Jinzi Mac Huang, George Hajaar and Leif Ristroph.

Natural sculpting processes such as erosion or dissolution often yield universal shapes that bear no imprint or memory of the initial conditions. Here we conduct laboratory experiments aimed at assessing the shape dynamics and role of memory for the simple case of a dissolvable boundary immersed in a fluid. Though no external flow is imposed, dissolution and consequent density differences lead to gravitational convective flows that in turn strongly affect local dissolving rates and shape changes, and we identify two distinct behaviors. A flat boundary dissolving from its lower surface tends to retain its overall shape (an example of near perfect memory) while bearing small-scale pits that reflect complex near-body flows. A boundary dissolving from its upper surface tends to erase its initial shape and form an upward spike structure that sharpens indefinitely. We propose an explanation for these different outcomes based on observations of the coupled shape dynamics, concentration fields, and flows.

Publication

Self-sculpting of a dissolvable body due to gravitational convection
( Link ) Megan S. Davies Wykes, Jinzi Mac Huang, George A. Hajjar, and Leif Ristroph
- Phys. Rev.Fluids (2018)

Dissolution of a Candy Ball

Concentration Field is Gravitationally Unstable

Dissolution of Candy Coated on a Wire

Media Coverage

Sciences Daily - How landscapes and landforms 'remember' or 'forget' their initial formations ( Link )
Phys.org - How landscapes and landforms 'remember' or 'forget' their initial formations ( Link )
EurekeAlert - How landscapes and landforms 'remember' or 'forget' their initial formations ( Link )

While fluid flows are known to promote dissolution of materials, such processes are poorly understood due to the coupled dynamics of the flow and receding surface. We study this moving boundary problem through experiments in which hard candy bodies dissolve in laminar, high-speed water flows. We find that different initial geometries are sculpted into a similar terminal form before ultimately vanishing, suggesting convergence to a stable shape-flow state. A model linking the flow and solute concentration shows how uniform boundary layer thickness leads to uniform dissolution, allowing us to obtain an analytical expression for the terminal geometry. Newly derived scaling laws predict that the dissolution rate increases with the square root of the flow speed and that the body volume vanishes quadratically in time, both of which are confirmed by experimental measurements.

Publication

Shape dynamics and scaling laws for a body dissolving in fluid flow ( PDF, link ) Jinzi M. Huang, M. Nicholas Moore, Leif Ristroph - J. Fluid Mech. Rapids (2015)

Talks and posters

Breaking Barriers - from Physics to Biology (II), 06/14/2014, Xi'an.
67th APS DFD conference, 11/25/2014, San Francisco.
Poster in room 105, Courant Institute.

Media Coverage

NPR - How Many Licks Does It Take To Get To A Tootsie Pop's Center? ( Link )
NY Post - NYU cracks the question: How many licks to the center of a Tootsie Pop? ( Link )
People - Sweet Science: Study Discovers How Many Licks It Takes to Reach the Center of a Tootsie Pop ( Link )
ABC News - Mathematicians Discover How Many Licks It Takes to Get to the Center of a Tootsie Pop ( Link )
Today - How many licks does it take to get to the center of a Tootsie Pop? ( Link )
NYU - Not candy crush - Scientists identify nature of candy sculpture ( Link )
人民网 - 菠萝科学奖数学奖得主：一颗棒棒糖引发奇妙科研之旅 ( Link)
新浪网 - “菠萝科学奖”数学奖：一根棒棒糖可以舔1000次 ( Link)
文汇报 - 科學研究：一根棒棒糖可以舔1000次 ( Link)
交大新闻网 - 交大毕业生黄金紫凭借“棒棒糖科学”获2015年菠萝科学奖数学奖 ( Link )