An integral equation method for closely interacting surfactant‐covered droplets in wall‐confined Stokes flow

• Published in: International journal for numerical methods in fluids 2020-12, Vol.92 (12), p.1975-2008
• Main Authors: Pålsson, Sara, Tornberg, Anna‐Karin
• Format: Article
• Language: English
• Subjects: Accuracy; Boundary integral method; Boundary integral methods; Channel flow; Computational fluid dynamics; Convergence of numerical methods; drop deformation; Droplets; Drops; fast Ewald summation; Handles; Implicit-explicit; insoluble surfactants; Integral equation methods; Integral equations; Interacting droplets; Mathematical models; microfluidics; Numerical methods; Periodic channels; periodic flow; Quadratures; special quadrature; Stationary solids; Stokes equations; Stokes flow; Surface active agents; Surfactants; Time-stepping schemes; two-phase flow; wall-bounded flow
• ISSN: 0271-2091; 1097-0363; 1097-0363
• DOI: 10.1002/fld.4857

Summary A highly accurate method for simulating surfactant‐covered droplets in two‐dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions. A boundary integral method together with a special quadrature scheme is applied to solve the Stokes equations to high accuracy, also for closely interacting droplets. The problem is considered in a periodic setting and Ewald decompositions for the Stokeslet and stresslet are derived. Computations are accelerated using the spectral Ewald method. The time evolution is handled with a fourth‐order, adaptive, implicit‐explicit time‐stepping scheme. The numerical method is tested through several convergence studies and other challenging examples and is shown to handle drops in close proximity both to other drops and solid objects to high accuracy. A highly accurate boundary integral method for simulating surfactant‐covered droplets in two‐dimensional Stokes flow with solid objects and walls. A spectrally accurate Ewald summation method is used for efficient computation of periodic solutions, together with a new symmetric Ewald decomposition of the 2D stresslet and truncation error estimates. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions, as well as droplets in close interaction with both other drops and the solids.