Deriving Flow Velocity and Initial Concentration From Liesegang‐Like Patterns.

Zebra rocks, characterized by their striking reddish‐brown stripes, rods, and spots of hematite (Fe‐oxide), showcase complex self‐organized patterns formed under far‐from‐equilibrium conditions. Despite their ease of recognition, the underlying mechanisms of pattern‐forming processes remain elusive. We introduce a novel advection‐dominated phase‐field model that effectively replicates the Liesegang‐like patterns observed in Zebra rocks. This numerical model leverages the concept of phase separation, a well‐established principle governing Liesegang phenomena in a two‐dimensional setting. Our findings reveal that initial solute concentration and fluid flow velocity are critical determinants in pattern morphologies. We quantitatively explain the spacing and width of a specific Liesegang‐like pattern category. Furthermore, the model demonstrates that vanishingly low initial concentrations promote the formation of oblique patterns, with inclination angles influenced by rock heterogeneity. Additionally, we establish a quantitative relationship between band thickness and geological parameters for orthogonal bands. This enables the characterization of critical geological parameters based solely on static patterns observed in Zebra rocks, providing valuable insights into their formation environments. The diverse patterns in Zebra rocks share similarities with morphologies observed on early Earth and Mars, such as banded iron formations and hematite spherules. Our model, therefore, offers a plausible explanation for the formation mechanisms of these patterns and presents a powerful tool for deciphering the geochemical environments of their origin. Plain Language Summary: Zebra rocks, known for their unique red and brown stripes and spots, hold clues to how similar patterns formed on early Earth and Mars. We have developed a new model to explain how these intriguing patterns form. The model suggests that the flow of fluids and the initial amount and location of dissolved iron‐oxide (rust) in water plays a big role in shaping the final Zebra rock design. The speed of the flow and the initial amount of rust can create different stripe and spot patterns, just like the ones in Zebra rocks. By studying these rocks, we can potentially decipher fluid flow scenarios of ancient environments on both Earth and Mars. Key Points: Patterns enable identification of flow velocity and concentration when observedFive Liesegang‐like patterns are replicated by varying flow velocities and initial concentrationsOne class of inclined patterns is identified in a very narrow flow velocity and low concentration regime [ABSTRACT FROM AUTHOR]