Crystalline Motion of discrete interfaces in the Blume-Emery-Griffiths Model: partial wetting

TL;DR

This paper extends the variational analysis of lattice systems modeling two phases with surfactant to the partial wetting regime, revealing complex interface dynamics and metastable states, bridging microscopic models and experimental phenomena.

Contribution

It provides the first discrete-to-continuum variational description of partially wetted crystalline interfaces, incorporating complex coupling effects.

Findings

Partial wetting introduces coexistence of moving and pinned facets.

Long-lived metastable states emerge in the evolution.

The model captures surfactant-induced pinning phenomena.

Abstract

We continue the variational study of the discrete-to-continuum evolution of lattice systems of Blume-Emery-Griffith type which model two immiscible phases in the presence of a surfactant. In our previous work \cite{CFS}, we analyzed the case of a completely wetted crystal and described how the interplay between surfactant evaporation and mass conservation leads to a transition between crystalline mean curvature flow and pinned evolutions. In the present paper, we extend the analysis to the regime of partial wetting, where the surfactant occupies only a portion of the interface. Within the minimizing-movements scheme, we rigorously derive the continuum evolution and show how partial wetting introduces a complex coupling between interfacial motion and redistribution of surfactant. The resulting evolution exhibits new features absent in the fully wetted case, including the coexistence of moving and pinned facets or the emergence and long-lived metastable states. This provides, to our knowledge, the first discrete-to-continuum variational description of partially wetted crystalline interfaces, bridging the gap between microscopic lattice models and experimentally observed surfactant-induced pinning phenomena in immiscible systems.