Numerical Model for Artificial Cilia

Artificial cilia attached to bounding surfaces are highly interesting for transporting and mixing fluids which is an essential task in microfluidics. The chapter introduces a numerical model for artificial cilia based on a bead‐spring chain with bending rigidity whose beads interact hydrodynamically. We explain in detail how one implements the model in its viscous fluid environment using self‐ and cross‐mobilities. In particular, we describe how one treats the bounding surface with its no‐slip boundary condition to which the cilium is attached. The characteristic sperm number compares bending to frictional forces and helps to classify the dynamic behavior of the actuated filament. The second part of the chapter addresses the numerical modeling of a superparamagnetic filament actuated by an external magnetic field which is a very attractive realization of an artificial cilium. The chapter reviews our numerical work, where we explore how the filament can be used for pumping fluid. Our investigations demonstrate that three‐dimensional strokes have a considerably higher pumping performance than their two‐dimensional counterparts. In addition, we mimic metachronal waves in a line of beating cilia by applying actuating fields to each filament separately with a constant phase shift between nearest neighbors. We demonstrate that a specific phase shift enhances the pumping performance strongly and thereby reveal an essential property of metachronal waves in nature.