Numerical calculation of the limiting current for a cylindrical thin layer flow cell

A cylindrical thin layer flow cell for the investigation of electrochemical reactions is described. Due to the geometry of the cell, known approaches to a quantitative interpretation of the measurements based on high flow rate asymptotics fail. Instead, a numerical method is introduced which models coupled fluid flow and reactant transport. Due to the use of a pointwise divergence-free finite element method, coupled to a finite volume method, the obtained approximate reactant distribution is guaranteed to remain in physically relevant bounds. The method is used to interpret limiting current measurements in the flow cell. The comparison to the measured values shows that a quantitative interpretation of the limiting current measurements depends on the ability to obtain sufficiently exact information about cell geometry, diffusion coefficient and inlet concentration. At the same time, for higher flow rates, the scaling of the limiting current with the flow rate seems to be well described by the Leveque asymptotic law for channel type cells.