From nonlinear reaction-diffusion processes to permanent microscale structures

Abstract

Biomorphs are polycrystalline aggregates that self-assemble during inorganic precipitation reactions. The shape repertoire of these microstructures include hemispherical objects with complicated internal features such as radial spikes and cones as well as folded sheets reminiscent of corals. We propose that at the microscale, some of these patterns are caused by nonlinear reaction-diffusion processes and present a simple model for this unconventional type of precipitation. The model consists of three reaction steps that convert a reactant species autocatalytically into an intermediate and eventually into a solid, immobile product. Numerical simulations of the model in three space dimensions reveal product structures that are similar to the experimentally observed biomorphs.

Geometrical dynamics of edge-driven accretive surface growth

“…Here, by deploying a self-consistent covariant formulation, we provide a geometrical theory that describes a range of precipitating structures and captures their complex morphologies independent of absolute scale. Since our theory is properly covariant, it is not limited to prescribed geometries and thus complements previous work in this area [18,21,24,25].…”

“…Under the smooth surface assumption, these unifying characteristics imply universal mathematical constraints (due to geometric compatibility) imposed on the growth dynamics and final form of infinitesimally thin surfaces. To quantify the growth and form of these effectively 2D systems, current theoretical approaches usually limit the analysis to prescribed geometries or single-valued surface height functions [18,21,24,25]. Here, by deploying a self-consistent covariant formulation, we provide a geometrical theory that describes a range of precipitating structures and captures their complex morphologies independent of absolute scale.…”

Fibrous Bundles in Biomorph Systems: Surface‐Specific Growth and Interaction with Microposts

“…These structures form spontaneously when a basic solution containing silicate and Ba 2+ (or Sr 2+ or Ca 2+ ) [12–14] ions is exposed to a carbonate source (e. g. air). Recent studies strongly suggest that biomorph shapes result from dynamic instabilities of an underlying nonlinear reaction‐diffusion system [15–17] that is possibly related to a self‐propagating band of decreased pH ahead of the active growth zone [18,19] . Based on this assumption, our group successfully simulated a variety of experimentally observed sheet shapes [15,17] as well as three‐dimensional coral‐type biomorphs [16] …”

Geometrical dynamics of edge-driven surface growth

“…Under the smooth surface assumption, these unifying characteristics imply universal mathematical constraints (due to geometric compatibility) imposed on the growth dynamics and final form of infinitesimally thin surfaces. To quantify the growth and form of these effectively 2D systems, current theoretical approaches often limit the analysis to prescribed geometries or single-valued surface height functions [18,21,24,25]. Here, by deploying a self-consistent covariant theory, we provide a geometrical theory that is capable of describing a range of precipitating patterned structures and capturing their complex, absolute-scale-free morphologies.…”