Sorgentone, Chiara; Tornberg, Anna-Karin A highly accurate boundary integral equation method for surfactant-laden drops in 3D. (English) Zbl 1391.76456 J. Comput. Phys. 360, 167-191 (2018). Summary: The presence of surfactants alters the dynamics of viscous drops immersed in an ambient viscous fluid. This is specifically true at small scales, such as in applications of droplet based microfluidics, where the interface dynamics become of increased importance. At such small scales, viscous forces dominate and inertial effects are often negligible. Considering Stokes flow, a numerical method based on a boundary integral formulation is presented for simulating 3D drops covered by an insoluble surfactant. The method is able to simulate drops with different viscosities and close interactions, automatically controlling the time step size and maintaining high accuracy also when substantial drop deformation appears. To achieve this, the drop surfaces as well as the surfactant concentration on each surface are represented by spherical harmonics expansions. A novel reparameterization method is introduced to ensure a high-quality representation of the drops also under deformation, specialized quadrature methods for singular and nearly singular integrals that appear in the formulation are evoked and the adaptive time stepping scheme for the coupled drop and surfactant evolution is designed with a preconditioned implicit treatment of the surfactant diffusion. Cited in 20 Documents MSC: 76M15 Boundary element methods applied to problems in fluid mechanics 76D07 Stokes and related (Oseen, etc.) flows 76D45 Capillarity (surface tension) for incompressible viscous fluids Keywords:boundary integral method; Stokes flow; surfactant; spherical harmonics Software:SHTns PDFBibTeX XMLCite \textit{C. Sorgentone} and \textit{A.-K. Tornberg}, J. Comput. 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