Abstract

We present two problems in which complex variable techniques provide an essential component of the analysis. First, a model of a superhydrophobic cylinder rotating in a viscous liquid is considered. The boundary of the cylinder is assumed to contain alternating no-slip and no-shear surfaces oriented transverse to the flow. The main interest is in computing the hydrodynamic torque on the cylinder. An explicit solution to the flow problem is obtained by combining complex variable techniques with asymptotic analysis. This work is joint with Ehud Yariv (Technion). Second, we present a new boundary integral method for computing the evolution of multiple surfactant covered drops in 2D Stokes flow. The method maintains high accuracy when drops are in very close proximity, which is a challenging situation for numerical computation. Complex variable techniques are critical in both the design and validation of the method. This is joint work with Sara Palsson and Anna-Karin Tornberg (KTH Stockholm).