Coefficients of Reaction‐Diffusion Processes Derived From Patterns in Rocks

Abstract

Self-organization develops autonomously in reaction-diffusion systems and is observed in many rock textures in geology (

Dendritic Growth Patterns in Rocks: Inverting the Driving and Triggering Mechanisms

“…This finding supports that a common formation mechanism for Liesegang rings is stemming from a driving force for the solute transport (like Mnor Fe-bearing acidic fluid) which is either an extremely slow flux induced by an (electro-)chemical potential difference or a slow mechanically forced fluid flow caused by a stress gradient, for example, compaction from overburden stress or tectonic forces (Liu et al, 2023a), or a combination thereof. Liesegang rings consequently can form independent of the primary high permeability interbed layers or secondary crack interfaces that control dendrites.…”

“…Scaled parameters for both simulations are $$\bar{a}=100$$, a 0 = 0, m 0 = −1.5, D b = 1.0, κ = 1.0, ɛ = 1.0, γ = 0.15, σ = 0.2, and η c = 0, except b 0 = 1.0 and D a = 2 for the local bands A while b 0 = 0.75 and D a = 3 for the local bands (b) For parameter definitions refer to Liu et al. (2023a).…”

“…The inversion of the ratio of solid over fluid diffusivity follows from a conversion of the approach in our earlier work (Liu et al., 2023a) from a Cartesian‐to a cylindrical coordinate system. The observed rings in Figure 1 are irregular suggesting heterogeneities that affected their growth.…”

“…Their formation mechanism has been a special focus of interest for the early philosophers, artists and the scientific community. Examples are many and varied, ranging from spiral waves in the Belousov–Zhabotinsky redox reaction (Yamaguchi et al., 1991) to disordered‐branching patterns in electrochemical deposition systems (Arguello et al., 2022), from the formation of Liesegang stripes (Liesegang, 1906; Liu et al., 2023a) to dendritic growth in reaction‐diffusion systems (Chopard et al., 1991; Z. Xu & Meakin, 2008), from oil recovery by fluid injection (Furui et al., 2022) to mineral precipitation during geologic sequestration (T. Xu et al., 2003). Understanding the underlying physical mechanism of pattern‐forming processes is of significant interest in science and technology.…”

“…Second, the dynamic transition of rhythmic bands toward more complex and irregular exists, like spotted patterns or combined stripes and spots, such as Mississippi Valley Type deposits (Wang et al., 2015). For more detailed information, see our recent work that decoded important coefficients governing the time scales of the formation of Liesegang patterns in rocks from a thermodynamic perspective (Liu et al., 2023a).…”