J. Fransaer et al., VARIATIONS IN THE FLOW OF CURRENT TO DISK ELECTRODES CAUSED BY PARTICLES, Journal of electroanalytical chemistry [1992], 391(1-2), 1995, pp. 11-28
The first exact solution of the flow of current in a semi-infinite ele
ctrolyte bounded by an insulating plane to a finite number of disk ele
ctrodes embedded in the plane, when the electrolyte contains a number
of spherical or prolate particles, is presented. The method is based o
n the addition of fundamental solutions of the Laplace equation which
conform to the particular geometry of the electrodes and particles. A
solution is obtained through the boundary collocation technique. The a
ccuracy and convergence of the method were tested by a detailed analys
is of the flow of current in the case of a spherical particle located
in front of a disk electrode. The model was used to study the resistan
ce variations of the flow of current to a single electrode induced by
particles and, in the absence of particles, the ohmic and concentratio
n interactions of multiple electrodes. Through the solution of the bou
ndary value problem governing the flow of current to a set of electrod
es in the presence of particles, the inverse problem is also solved, i
.e. an algorithm is developed which finds the position of a particle b
ased on the currents flowing to a set of electrodes. The performance a
nd robustness of this algorithm are illustrated using synthetic data.
The algorithm allows the tracking of individual particles, enabling in
formation on the presence, velocity and residence time of particles in
the vicinity of surfaces to be obtained from recordings of fluctuatio
ns of the electrolyte resistance with time.