Diffusion towards a nanoforest of absorbing pillars

TL;DR

This paper provides an exact analytical study of steady-state diffusion towards a periodic array of absorbing nanostructured pillars, analyzing how geometric parameters influence particle flux and trapping efficiency.

Contribution

It introduces a simplified model using a circular tube with a single pillar to derive exact solutions for diffusion flux, revealing effects of pillar shape and spacing.

Findings

Exact flux formulas for various pillar geometries

Analysis of asymptotic regimes like thin and long pillars

Insights into trapping efficiency and diffusional screening

Abstract

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.