Erosion patterns on dissolving and melting bodies

Abstract

The dissolution rate of a solid depends on the concentration of the solution at the interface. It consequently depends on the flow, which takes the dissolved material away. The global shape of dissolving bodies has been studied in water at rest [1] and in a high-speed flow [2]. Here we focus on the pattern formation observed on the wall of a dissolving caramel block and on its geomorphogenetic analogs in nature ( Fig. 1).Caramel is an amorphous material with physicochemical properties similar to the glucose used in [1]. Experiments simply consist in putting blocks of solid caramel tilted from the horizontal in a bath of water at rest [ Fig. 2(a)]. The block dissolves (the interface recedes at a velocity around 1 cm/h) and patterns emerge underneath the block [Figs. 2(c)-2(f)], whereas the top surface remains smooth. First, longitudinal stripes, with a wavelength of 0.5 mm, appear at short times (t = 10 s). Then the stripes cross and form chevrons (t = 10 min). Chevrons open and evolve toward scallops pointing out downward, which are reminiscent of limestone cave holes modeled by phreatic rivers [3]. After 60 min, the caramel scallops are typically 5 mm large and 1 mm deep and travel upward at a velocity of 1 cm/h.To understand why the patterns appear, one must consider the release of dissolved caramel. Because it is denser than water, the dissolution induces a buoyancy-driven flow under the block and the heavy layer of fluid destabilizes into sinking filaments. This phenomenon can be seen as a solutal Rayleigh-Bénard instability, where concentration substitutes for temperature, or, identically, as the Rayleigh-Taylor instability of a thin viscous film, whose thickness is controlled by diffusion [4,5]. This instability of the flow naturally reflects on the field of concentration at the solid interface. The concentration is higher in the filaments than in between, so the dissolution rate of the solid is lower above filaments. This differential dissolution sculpts the surface. The stripes emerge with the same wavelength as the flow instability, which prints onto the dissolving block. Once formed, the stripes interact with the flow: The filaments are channelized by the crests. In return, the concentration field makes the longitudinal stripes unstable and they evolve toward scallops. On the top surface of the block, the buoyancy is stabilizing. The dissolved caramel flows down along the block, which remains smooth.Similar patterns can be observed on immersed walls of icebergs in Greenland [ Fig. 2(g)]. Ice scallops are typically 20 cm large and 4 cm deep and point out upward [Fig. 2(h)]. As the thermodynamic formalism is the same, most dissolution patterns have a melting equivalent [6]. We

Self-sculpting of a dissolvable body due to gravitational convection

“…Our experiments and theoretical estimates indicate that the length scale of the instability is on the order of a millimeter, which is small in comparison to the body sizes studied here. Evidence for fine-scale flows can also be found in previous works of dissolution into fluid below [28][29][30][31]48]. Our visualization studies show that it is these localized flows that carry solute downward and away from the surface and there seems to be little communication or influence among different surface locations.…”

“…The caverns typical of karst are likely carved out by dissolution within a water-filled cavity [3], which we expect to grow primarily by dissolving of the ceiling where unstable density profiles can lead to strong flows. Icebergs and ice shelves represent additional natural analogs, and surface pitting and scallops on their undersides may indicate flow instabilities [30]. Finally, the ever-sharpening regime observed here for dissolution of an upper surface might be applied towards manufacturing structures of extreme fineness.…”

“…Previous research into this problem has focused on the underside of a horizontal surface that dissolves, in which the arrangement of dense solution above the less-dense fluid is gravitationally unstable [28]. This results in buoyancy driven flows that cause roughening of the dissolving surface [29,30], and a theory based on turbulent boundary layers was shown to account for the length scale of the surface patterning [31]. Recent research has also suggested that the upper surface of an upright dissolvable body tends towards a paraboloid [32], and a phenomenological model describes the reduction of its radius with time but does not account for the overall shape.…”

Hydrodynamic-driven morphogenesis of karst draperies: spatio-temporal analysis of the two-dimensional impulse response

“…The astonishing beauty of geological patterns has fascinated humanity for centuries (Hill, Forti & Shaw 1997). Several different geological structures are related to mineral dissolution (Cohen et al 2016) and precipitation (Meakin & Jamtveit 2010) in aqueous systems. A few examples are terraces and steps due to precipitation of dissolved minerals in flowing fluids on the ground, which find a parallel in the structures arising from melting and freezing of ice, usually called icicles and crenulations.…”

Painting fluid motion using convolutional neural networks: An album of fluid motion 2.0

“…Although often categorized as a form of art, photography is arguably the most common technique used in experimental fluid mechanics research. Over the years, many photography methods, such as shadowgraphy [2], schlieren imagining [3], chronophotography [4], long exposures [5], and high-speed frame acquisition [6], have been utilized for flow visualization and as tools to study phenomena that are hidden from the human eye. Now imagine if these visualizations served not just their scientific purpose but became the inspiration of an artistic masterpiece.…”