Alcove formation in dissolving cliffs driven by density inversion instability

Sharma, Ram Sudhir; Berhanu, Michaël; Kudrolli, Arshad

doi:10.1063/5.0092331

Cited by 4 publications

(8 citation statements)

References 24 publications

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“…The presence of the buoy screens part of the slab, resulting in the area of the bottom surface being nearly two times larger than the top surface. Thus, while part of the greater contribution of the bottom surface is due to its larger surface area, bottom-facing surfaces dissolve faster than top-facing surfaces ( 41 ).…”

Section: Resultsmentioning

confidence: 99%

“…The recession rate

can be calculated based on material properties and the inclination of the dissolving surface. In the presence of solutal convection ( 41 ),

, where

is the density of the dissolving solid,

is the saturation density of the solute,

is the saturation concentration,

is the diffusion coefficient, and

is the concentrated solute boundary layer thickness ( SI Appendix , section 7 ). When the surface is oriented downward, the boundary layer is subject to a Rayleigh–Bénard instability.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Dissolution-driven propulsion of floating solids

Chaigne,

Berhanu,

Kudrolli

2023

Proc. Natl. Acad. Sci. U.S.A.

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We show that unconstrained asymmetric dissolving solids floating in a fluid can move rectilinearly as a result of attached density currents which occur along their inclined surfaces. Solids in the form of boats composed of centimeter-scale sugar and salt slabs attached to a buoy are observed to move rapidly in water with speeds up to 5 mm/s determined by the inclination angle and orientation of the dissolving surfaces. While symmetric boats drift slowly, asymmetric boats are observed to accelerate rapidly along a line before reaching a terminal velocity when their drag matches the thrust generated by dissolution. By visualizing the flow around the body, we show that the boat velocity is always directed opposite to the horizontal component of the density current. We derive the thrust acting on the body from its measured kinematics and show that the propulsion mechanism is consistent with the unbalanced momentum generated by the attached density current. We obtain an analytical formula for the body speed depending on geometry and material properties and show that it captures the observed trends reasonably. Our analysis shows that the gravity current sets the scale of the body speed consistent with our observations, and we estimate that speeds can grow slowly as the cube root of the length of the inclined dissolving surface. The dynamics of dissolving solids demonstrated here applies equally well to solids undergoing phase change and may enhance the drift of melting icebergs, besides unraveling a primal strategy by which to achieve locomotion in active matter.

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Section: Resultsmentioning

confidence: 99%

“…The recession rate

can be calculated based on material properties and the inclination of the dissolving surface. In the presence of solutal convection ( 41 ),

, where

is the density of the dissolving solid,

is the saturation density of the solute,

is the saturation concentration,

is the diffusion coefficient, and

is the concentrated solute boundary layer thickness ( SI Appendix , section 7 ). When the surface is oriented downward, the boundary layer is subject to a Rayleigh–Bénard instability.…”

Section: Resultsmentioning

confidence: 99%

Dissolution-driven propulsion of floating solids

Chaigne,

Berhanu,

Kudrolli

2023

Proc. Natl. Acad. Sci. U.S.A.

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“…It then destabilizes into plumes sinking in the bottom of the tank. The characteristic distance between plumes scales like

, which is given by a constant Rayleigh number criterion ( 23 , 25 , 32 , 34 ):

…”

Section: Comparison To Scallop Patterns In Solutal Convection Experim...mentioning

confidence: 99%

Emergence of tip singularities in dissolution patterns

Chaigne,

Carpy,

Massé

et al. 2023

Proc. Natl. Acad. Sci. U.S.A.

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Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock-like salt, gypsum, or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the mass transfer, and the flow leads to the formation of remarkable patterns, like scallop patterns in caves. We emphasize the common presence of very sharp shapes and spikes, despite the diversity of hydrodynamic conditions and the nature of the soluble materials. We explain the generic emergence of such spikes in dissolution processes by a geometrical approach. Singularities at the interface emerge as a consequence of the erosion directed in the normal direction, when the surface displays curvature variations, like those associated with a dissolution pattern. First, we demonstrate the presence of singular structures in natural interfaces shaped by dissolution. Then, we propose simple surface evolution models of increasing complexity demonstrating the emergence of spikes and allowing us to explain at long term by coarsening the formation of cellular structures. Finally, we perform a dissolution pattern experiment driven by solutal convection, and we report the emergence of a cellular pattern following well the model predictions. Although the precise prediction of dissolution shapes necessitates performing a complete hydrodynamic study, we show that the characteristic spikes which are reported ultimately for dissolution shapes are explained generically by geometrical arguments due to the surface evolution. These findings can be applied to other ablation patterns, reported for example in melting ice.

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“…Projecting (30) onto the horizontal direction e 1 , using (32), and rearranging gives the exact relationship…”

Section: Relationship To Dragmentioning

confidence: 99%

“…Flow-induced erosion acts across a range of scales in the natural world, from massive geological structures sculpted by wind or water [1,28,20,32,19], to mesoscopic patterns formed by surface or internal flows [6,7,36], and down to granular and porous networks slowly disintegrating in groundwater flows [10,34,22,15,8,11,37]. The associated nonlinear feedback between changing shapes and the surrounding flows can imprint across all of these scales, affecting large-scale features as well as small-scale ones, such as the microstructure of porous materials.…”

Section: Introductionmentioning

confidence: 99%

How fluid-mechanical erosion creates anisotropic porous media

Moore¹,

Cherry²,

Chiu³

et al. 2022

Preprint

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Using a Cauchy integral formulation of the boundary integral equations, we simulate the erosion a porous medium comprised of up to 100 solid bodies embedded in a Stokes flow. The grains of the medium are resolved individually and erode under the action of surface shear stress. Through nonlinear feedback with the surrounding flow fields, microscopic changes in grain morphology give way to larger-scale features in the medium such as channelization. The Cauchy-integral formulation and associated quadrature formulas enable us to resolve dense configurations of nearly contacting bodies. We observe substantial anisotropy to develop over the course of erosion; that is, the configurations that result from erosion generally permit flow in the longitudinal direction more easily than in the transverse direction by up to a factor of six. These results suggest that the erosion of solid material from groundwater flows may contribute to previously observed anisotropy of natural porous media.

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Alcove formation in dissolving cliffs driven by density inversion instability

Cited by 4 publications

References 24 publications

Dissolution-driven propulsion of floating solids

Dissolution-driven propulsion of floating solids

Emergence of tip singularities in dissolution patterns

How fluid-mechanical erosion creates anisotropic porous media

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