## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### 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.

**KEYWORDS**

PAPER SUBMITTED: 2019-12-12

PAPER REVISED: 2020-06-12

PAPER ACCEPTED: 2020-06-12

PUBLISHED ONLINE: 2021-01-31

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