Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Poster: Statistical Physics

DY 22.2: Poster

Wednesday, March 19, 2025, 10:00–12:00, P3

A novel mathematical model for the coupled binary-fluid surfactant system — •Alexandra Hardy, Steven McDonald, Abdallah Daddi-Moussa-Ider, and Elsen Tjhung — The Open University, Milton Keynes, UK

We propose a new binary-fluid surfactant mathematical model derived from modeling the surfactant molecules as dumbbells. By explicitly taking into account the molecules alignment, we gain new field variable p(r,t); the average orientation of surfactants. Combined with standard phase-field theory for binary fluids gives the system equations, which we both solve numerically and analytically. We employ a hybrid finite difference (FDM) and spectral method for the simulations. Whereas regular perturbation theory is used for the equilibrium solutions, facilitated by assuming weak coupling between surfactant and fluid. Three investigations are presented, firstly we demonstrate excellent agreement between simulation and the analytical solutions for a planar water-oil interface. Second, we prove that our model accurately predicts the decrease in surface tension with increasing surfactant concentration, in line with experiments and related theory. Finally, we show that our model is capable of preventing surfactant-laden droplet coalescence due to the added polarization field p(r,t).

Keywords: Surfactants; Diffuse Interfaces; Numerical Modeling; Surface Tension; Coalescence