Research concentrates mainly on electrochemical digital simulation;
that is, the solution of Fick's diffusion equation, with the special
boundary conditions given by the electrochemical context. In recent
times, some of the major problems have been solved, such as that of
fast homogeneous reactions, coupled reactions, and stability in this
context has been examined. We now have a handle on most of these
problems and the publications list reflects activity on these fronts.
The above holds for one-dimensional systems, and the thrust is now in 2-D systems, in particular that for the microelectrodes, that are now ubiquitous. We must be able to simulate these systems efficiently, in order to, for example, measure reaction rates. Some preliminary work indicates that there may be unexpected stability problems here, and these need examination. "Brute force" has been tried but now abandoned in favour of sparse matrix solvers such as MA28. Crank-Nicolson's oscillations have been tamed, and the BDF method investigated. Higher-order derivative approximations have been developed, increasing efficiency, and reference values computed for current at an ultramicrodisk and -band electrodes.
ADI methods are often used for convenience, rather than sparse matrices, to solve these 2D systems, and the most commonly used method, that of Peaceman and Rachford, is prone to the same oscillations as Crank-Nicolson. We have worked on this and a paper has been published in which we show how to eliminate the oscillations, by five different approaches. We have also recently provided accurate reference values of the current at the ultramicrodisk and ultramicroband electrodes. Recent work includes simulation of the conical well electrode, the conical-tip electrode and accurate values of fluxes at cylindrical and capped cylindrical electrodes. Presently work is in progress on the use of the Saul'yev method for these two-dimensional systems.
Papers of the last 5 years, in reverse order:
Du kan downloade bogen som pdf-fil