To overcome this, we have developed a spectral boundary element algorithm for interfacial dynamics of three-dimensional capsules in Stokes flow. Our methodology preserves the main characteristic of the spectral methods, i.e. the exponential convergence in the interfacial accuracy as the number of spectral points increases, but without creating denser systems as spectral methods used in volume discretization do. Owing to its spectral nature, our interfacial algorithm has the significant advantage of the accurate determination of any interfacial property, including geometric derivatives and membrane tensions. We believe that this is an important issue for the correct and accurate determination of very deformed capsule shapes made from membranes obeying non-linear elastic laws such as the Skalak and neo-Hookean (or Mooney-Rivlin) laws.
In contrast to the existing low-order methodologies which are unable to study interfacial dynamics at high flow rates, our spectral algorithm predicts stable transient and steady-state capsule shapes in these flows. The pointed profiles of these shapes are in qualitative agreement with experimental findings. Our results for erythrocytes in strong shear flows are also in excellent agreement with experimental findings from ektacytometry.