A hybrid Volume of Fluid Phase-Field method for Direct Numerical Simulations of soluble surfactant-laden interfacial flows

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We present a hybrid Volume-of-Fluid (VoF) 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 bulk and interfacial concentration fields without computing surface derivatives. Adsorption/desorption kinetics are incorporated through regularized source terms localized at the interface, and surface tension can be specified for general equations of state. The method is fully adaptive via quadtree/octree Adaptive Mesh Refinement, enabling 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 accuracy and convergence. We then investigate the buoyancy-driven rise of a bubble in the presence of soluble surfactants, in axisymmetric and three-dimensional configurations. By independently varying the Biot and Damköhler numbers, 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 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 interplay between hydrodynamics, bulk and interfacial transport, and Marangoni stresses in realistic three-dimensional geometries.

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