The optimal electrode thickness

Most electrodes used in commercial applications like batteries and fuel cells contain electrodes that are porous to increase the reactive surface area. Strangely, a hitherto largely unanswered but important question is how thick such electrodes should ideally be. Thick electrodes will gives a high resistance while thin electrodes less surface area. Unsurprisingly there is an optimum, graphically shown in the below graph.

The dimensionless electrode overpotential versus electrode thickness. For the notation used see:

The seminal 1962 paper of Newman and Tobias provided exact but implicit analytical solutions. Introducing a generalization of the effectiveness factor concept, I obtained approximate explicit current-potential relations that are insightful and easy to use. Using these, analytical expressions could be derived for both the optimal electrode thickness and porosity of catalyst layers as well as battery electrodes.

A theoretical analysis of the optimal electrode thickness and porosity” can be freely accessed through:

A poster summarizing the paper presented at Modval 2019poster

A short presentation adapted from a talk at the ISE 2018 conference in Bologna or at the ECCM Conference in The Hague in 2019.

An excellent first introduction to the modeling porous electrodes can be found at:


Magnetic drug targeting possible even in large arteries


By attaching drugs to magnetic nanoparticles, magnetic fields can concentrate them at the location in the body where they are needed. Pre-clinical trials have shown some potential for treatment of superficial cancer tumors. More applications could be envisioned when targets deeper in the body can be reached.

Our 2009 publication was perhaps the first three-dimensional simulation showing that it is possible to capture particles from the bloodstream of large arteries like the coronary and carotid artery. This opens up the possibility of applying the technique to combat also cardiovascular diseases.

Because of an old theorem, the drugs can only be held in a stable position deep inside the body using a dynamic magnetic field configuration or in a quasi-stable position using carefully tailored magnetic fields. Despite this fundamental complication, progress remains to be made today, particularly from the perspective of computational modeling.

Computational Simulations of Magnetic Particle Capture in Arterial Flows
J. W. Haverkort, S. Kenjeres, and C. R. Kleijn