Models and simulations of surfactant-driven fracture in particle rafts

Abstract

A continuum-based model for the surfactant-driven fracture of closely-packed particle rafts is extended to examine the influence of micro-scale density variability. The model treats the particle monolayer as an elastic sheet endowed with a critical fracture energy that can be reduced through interaction with a flowing surfactant. In addition to the displacement of the monolayer, the model employs a surfactant damage field that serves as both an indicator function for the surfactant concentration as well as the damage to the monolayer. Spatial variability in the particle packing is incorporated in the model through a continuum mapping approach. The formulation gives rise to a coupled system of nonlinear partial differential equations with an irreversibility constraint. The evolution equations are recast in variational form and discretized with an adaptive finite element method. Simulations are provided to demonstrate convergence of the model, illustrate the sensitivity of the fracture process to variations in the initial packing fraction field, and make comparisons with experimental observations. The results indicate that crack bifurcations can occur in regions with spatially uniform packing as well as spatially variable packing, suggesting that both the macro-scale mechanics and the random aspects of the packing contribute to these instabilities. The model is also used to predict the response of these systems to multiple injection sources and obstacles in the domains. Finally, the model is extended to non-planar surfaces as a means to study systems in which confinement and jamming can only occur due to multiple injection sites.