Direct numerical simulations for surfactant-laden interfacial flows with moving contact lines and above the critical micelle concentration

High fidelity numerical simulations of complex fluids are the next frontier in advancing computational modelling for multiphase flows. A highly robust, parallelised, and accurate representation of surfactant-laden interfacial flows enable a wide scope of its applications in cleaning, mixing, agriculture, microfluidics, etc. In this work, we focus on extending our code BLUE [1] to inherit several new features to simulate surfactant-laden flows that are inevitable in the real world. We consider a comprehensive model that accounts for Marangoni stresses (arising from interfacial tension gradients), sorption kinetics (including adsorption/desorption associated with the deformable and liquid-solid interfaces), interfacial and bulk diffusion, and moving contact lines. This model also accounts for situations wherein the surfactant bulk concentration exceeds the critical micelle concentration above which micellar aggregates are expected to form. As an exemplar problem, we use surfactant-laden drop impact on a solid surface to showcase the rich physics of surfactant-laden transport phenomena. The surfactant species interact via adsorption at and desorption from the interfaces, and via micelle breakup to release monomers and re-formation via monomer aggregation; importantly, adsorption and desorption at the contact line is also taken into consideration. Such a highly coupled transport process involves a large number of dimensionless parameters (over 20). The Weber number in the problem is kept relatively low, and the contact angle sufficiently large to account for substrate hydrophobicity. We elucidate the rich mechanisms underlying surfactant-laden flows with micelles and contact lines through a parametric study within the above framework.

References:

[1] S. Shin, J. Chergui, D. Juric, L. Kahouadji, O. K. Matar, and R. V. Craster, “A hybrid interface tracking–level set technique for multiphase flow with soluble surfactant,” Journal of Computational Physics, vol. 359, pp. 409–435, 2018