Fractal diffusion-reaction model for a porous electrode

Abstract

Fractal modifications of Fick?s laws are discussed by taking into account the electrode?s porous structure, and a fractal derivative model for diffusion-reaction process in a thin film of an amperometric enzymatic reaction is established. Particular attention is paid to giving an intuitive grasp for its fractal variational principle and its solution procedure. Extremely fast or extremely slow diffusion process can be achieved by suitable control of the electrode?s surface morphology, a sponge-like surface leads to an extremely fast diffusion, while a lotus-leaf-like uneven surface predicts an extremely slow process. This paper sheds a bright light on an optimal design of an electrode?s surface morphology.

The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus

“…Another example is the motion of the Moon, which is naturally periodic; however, if we measure its motion at an extremely far distance, its motion becomes stochastic, and the Heisenberg-like uncertainty principle works for the Moon [9]. He and Qian showed that the fractal diffusion process in water depends on the fractal dimensions [10], and other scientists also discussed the fractional advection-reaction-diffusion process [11] and the fractal diffusion-reaction process [12]. A cocoon's air/moisture permeability and its thermal property can best be revealed by the fractal-fractional model [13,14], and the fractal microelectromechanical systems show even more amazing properties [15][16][17][18].…”