  Spiky coatings (also known as nanoforests or Fakir-like surfaces) have found
many applications in chemical physics, material sciences and biotechnology,
such as superhydrophobic materials, filtration and sensing systems, selective
protein separation, to name but a few. In this paper, we provide a systematic
study of steady-state diffusion towards a periodic array of absorbing
cylindrical pillars protruding from a flat base. We approximate a periodic cell
of this system by a circular tube containing a single pillar, derive an exact
solution of the underlying Laplace equation, and deduce a simple yet exact
representation for the total flux of particles onto the pillar. The dependence
of this flux on the geometric parameters of the model is thoroughly analyzed.
In particular, we investigate several asymptotic regimes such as a thin pillar
limit, a disk-like pillar, and an infinitely long pillar. Our study sheds a
light onto the trapping efficiency of spiky coatings and reveals the roles of
pillar anisotropy and diffusional screening.
