# Influence of surface tension in the surfactant-driven fracture of closely-packed particulate monolayers

## TL;DR

This paper presents a phase-field model to study how surface tension influences fracture patterns in closely-packed particulate monolayers, validated by experiments showing high sensitivity to surface tension differences.

## Contribution

The study introduces a new phase-field model for surfactant-driven fracture in particulate monolayers, incorporating surface tension effects and validated by experimental data.

## Key findings

- Model qualitatively matches experimental fracture patterns
- Surface tension differences critically affect fracture regimes
- Thresholds identified for different fracture behaviors

## Abstract

A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer as the surfactant concentration increases through the evolution of a damage field. Initial-boundary value problems are constructed and spatially discretized with finite element approximations to the displacement and surfactant damage fields. A comparison between model-based simulations and existing experimental observations indicates a qualitative match in both the fracture patterns and temporal scaling of the fracture process. The importance of surface tension differences is quantified by means of a dimensionless parameter, revealing thresholds that separate different regimes of fracture. These findings are supported by newly performed experiments that validate the model and demonstrate the strong sensitivity of the fracture pattern to differences in surface tension.