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 that of a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer with increasing surfactant concentration 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.
Highlights
When a densely packed monolayer of hydrophobic particles is placed on the surface of a liquid, the particles interact through capillary bridges,[1] leading to the formation of particle rafts
Through model-based simulations and accompanying experiments, we demonstrate that surface tension differences play a vital role in the overall fracture response of particle rafts
We study whether the dimensionless parameter w can be used to construct a phase diagram for the fracture patterns that are produced
Summary
When a densely packed monolayer of hydrophobic particles is placed on the surface of a liquid, the particles interact through capillary bridges,[1] leading to the formation of particle rafts. The macroscopic properties of these rafts reflect an interplay between fluid and solid mechanics,[2,3,4] giving rise to novel physics. This interplay is relevant to a wide range of applications, from the synthesis of ‘‘liquid marbles’’5 to the design of drug delivery systems[6] to the stabilization of drops.[7]. Through model-based simulations and accompanying experiments, we demonstrate that surface tension differences play a vital role in the overall fracture response of particle rafts
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