The Fate of Molecular Species in Water Layers in the Light of Power-Law Time-Dependent Diffusion Coefficient

Abstract

In the present paper, we propose two methods for tracking molecular species in water layers via two approaches of the diffusion equation with a power-law time-dependent diffusion coefficient. The first approach shows the species densities and the growth of different species via numerical simulation. At the same time, the second approach is built on the fractional diffusion equation with a time-dependent diffusion coefficient in the sense of regularised Caputo fractional derivative. As an illustration, we present here the species densities profiles and track the normal and anomalous growth of five molecular species OH, H2O2, HO2, NO3-, and NO2- via the calculation of the mean square displacement using the two methods.

Keywords

• molecular dynamics
• time-dependent diffusion coefficient
• anomalous diffusion
• fractional calculus
• plasma medicine