Diffusion towards a nanoforest of absorbing pillars
arXiv:2210.15378 · doi:10.1063/5.0132197
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.
References in corpus (26)
- Anomalous transport in the crowded world of biological cells
- Geometrical structure of Laplacian eigenfunctions
- Hydrodynamic friction of fakir-like super-hydrophobic surfaces
- Paradigm shift in diffusion-mediated surface phenomena
- Mortality, Redundancy, and Diversity in Stochastic Search
- Universal formula for the mean first passage time in planar domains
- Exploration and Trapping of Mortal Random Walkers
- Mean first-passage time of surface-mediated diffusion in spherical domains
- Transfer across Random versus Deterministic Fractal Interfaces
- The escape problem for mortal walkers
- Exact solutions and physical analogies for unidirectional flows
- Fluctuations and correlations in chemical reaction kinetics and population dynamics
- Imperfect Diffusion-Controlled Reactions
- How winding is the coast of Britain ? Conformal invariance of rocky shorelines
- Conformal Mapping on Rough Boundaries I: Applications to harmonic problems
- Heat Transport through Rough Channels
- Homogenized boundary conditions and resonance effects in Faraday cages
- Mean first-passage time to a small absorbing target in an elongated planar domain
- First-passage times to anisotropic partially reactive targets
- Applications of electrostatic capacitance and charging
- Resonance scattering in a waveguide with identical thick barriers
- A physicist's guide to explicit summation formulas involving zeros of Bessel functions and related spectral sums
- Steady-state reaction rate of diffusion-controlled reactions in sheets
- Screening effects in flow through rough channels
- Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?
- Mode matching methods for spectral and scattering problems