For applications where droplet breakup and surfactant adsorption are strongly coupled, a diffuse interface model is developed. The model is based on a free energy functional, partly adapted from the sharp interface model of [Diamant and Andelman 34(8):575-580, (1996)]. The model is implemented as a 2D Lattice Boltzmann scheme, similar to existing microemulsion models, which are coupled to hydrodynamics. Contrary to these microemulsion models, we can describe realistic adsorption isotherms, such as the Langmuir isotherm. From the free energy, functional analytical expressions of equilibrium properties are derived, which compare reasonably with numerical results. Interfacial tension lowering scales with the logarithm of the area fraction of the interface unloaded with a surfactant:, Delta sigma similar to ln(1 - psi(0)). Furthermore, we show that adsorption kinetics are close to the classical relations of Ward and Tordai. Prelimary simulations of droplets in shear flow show promising results, with surfactants migrating to interfacial regions with highest curvature. We conclude that our diffuse interface model is very promising for apprehending the above-mentioned applications as membrane emulsification.
- simple shear-flow
- of-fluid method
- membrane emulsification
van der Sman, R. G. M., & van der Graaf, S. (2006). Diffuse interface model of surfactant adsorption onto flat and droplet interfaces. Rheologica Acta, 46(1), 3-11. https://doi.org/10.1007/s00397-005-0081-z