A hybrid Volume of Fluid Phase-Field method for Direct Numerical Simulations of soluble surfactant-laden interfacial flows
Résumé
We present a hybrid Volume-of-Fluid (VoF) and Phase-Field method for general soluble surfactant-laden interfacial flows. The scheme retains the VoF method for interface tracking and momentum solution, while a diffused Phase-Field serves as a smooth carrier for surfactant transport enabling consistent coupling between the bulk and interfacial concentration fields without the computation of surface derivatives. Adsorption and desorption kinetics are incorporated through regularized source terms localized at the interface, and the dependence of surface tension on surfactant concentration can be specified for general equation of states. The method is fully adaptive via quadtree/octree Adaptive Mesh Refinement (AMR), enabling accurate and efficient simulations in planar, axisymmetric, and three-dimensional domains with high parallel scalability. Rigorous validation against analytical solutions for surfactant transport on deforming interfaces and for diffusion-driven adsorption in the no-flow limit confirms the accuracy and convergence of the approach. To demonstrate the coupled capabilities of the framework, we investigate the buoyancy-driven rise of a bubble in the presence of soluble surfactants, in both axisymmetric and three-dimensional configurations. By independently varying the Biot number and the Damk\"ohler number, we recover the correct asymptotic limits corresponding to clean-interface and insoluble-surfactant dynamics, and characterize the intermediate soluble regime. The resulting Marangoni stresses, induced by non-uniform interfacial surfactant concentrations, significantly reduce interfacial mobility, leading to measurable reductions in terminal velocity and pronounced modifications of the bubble trajectory. These results demonstrate the robustness of the method in capturing the complex interplay between hydrodynamics, bulk and interfacial surfactant transport, and Marangoni stresses in realistic three-dimensional geometries.
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