Kinetic theory of coupled binary-fluid-surfactant systems
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917289740206080 |
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| author | Hardy, Alexandra J. Cameron, Samuel McDonald, Steven Daddi-Moussa-Ider, Abdallah Tjhung, Elsen |
| author_facet | Hardy, Alexandra J. Cameron, Samuel McDonald, Steven Daddi-Moussa-Ider, Abdallah Tjhung, Elsen |
| contents | We derive a self-consistent hydrodynamic theory of coupled binary-fluid-surfactant systems from the underlying microscopic physics using Rayleigh's variational principle. At the microscopic level, surfactant molecules are modelled as dumbbells that exert forces and torques on the fluid and interface while undergoing Brownian motion. We obtain the overdamped stochastic dynamics of these particles from a Rayleighian dissipation functional, which we then coarse-grain to derive a set of continuum equations governing the surfactant concentration, orientation, and the fluid density and velocity. This approach introduces a polarization field, representing the average orientation of surfactants, and yields a mesoscopic free energy functional from which all governing equations are consistently derived. The resulting model accurately captures key surfactant phenomena, including surface tension reduction and droplet stabilization, as confirmed by both perturbation theory and numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kinetic theory of coupled binary-fluid-surfactant systems Hardy, Alexandra J. Cameron, Samuel McDonald, Steven Daddi-Moussa-Ider, Abdallah Tjhung, Elsen Soft Condensed Matter Statistical Mechanics We derive a self-consistent hydrodynamic theory of coupled binary-fluid-surfactant systems from the underlying microscopic physics using Rayleigh's variational principle. At the microscopic level, surfactant molecules are modelled as dumbbells that exert forces and torques on the fluid and interface while undergoing Brownian motion. We obtain the overdamped stochastic dynamics of these particles from a Rayleighian dissipation functional, which we then coarse-grain to derive a set of continuum equations governing the surfactant concentration, orientation, and the fluid density and velocity. This approach introduces a polarization field, representing the average orientation of surfactants, and yields a mesoscopic free energy functional from which all governing equations are consistently derived. The resulting model accurately captures key surfactant phenomena, including surface tension reduction and droplet stabilization, as confirmed by both perturbation theory and numerical simulations. |
| title | Kinetic theory of coupled binary-fluid-surfactant systems |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2506.12955 |