Helices in the wake of precipitation fronts

TL;DR

This paper presents a theoretical analysis of how helical patterns form behind precipitation fronts on cylindrical surfaces, using the Cahn-Hilliard equation and pulled-front formalism, revealing a critical radius condition for helix emergence.

Contribution

It introduces a novel theoretical framework combining the Cahn-Hilliard equation and pulled-front formalism to explain helix formation on cylinders, aligning with recent experimental findings.

Findings

Helical structures form behind precipitation fronts on cylinders.

Helices only appear when the cylinder radius exceeds a critical value.

Analytical solutions predict the conditions for helix emergence.

Abstract

A theoretical study of the emergence of helices in the wake of precipitation fronts is presented. The precipitation dynamics is described by the Cahn-Hilliard equation and the fronts are obtained by quenching the system into a linearly unstable state. Confining the process onto the surface of a cylinder and using the pulled-front formalism, our analytical calculations show that there are front solutions that propagate into the unstable state and leave behind a helical structure. We find that helical patterns emerge only if the radius of the cylinder R is larger than a critical value R>R_c, in agreement with recent experiments.