Analytical Considerations for Hydraulic Resistance Models of the Flow in Electrochemical Cells

The distributed resistance analogy combines local volume-averaging with computational fluid dynamics. It has previously been used to perform three-dimensional calculations for fluid flow (and heat/species/charge transfer) in electrochemical devices such as fuel cell and electrolyzer stacks. These may employ arbitrary-shaped passages, non-uniform local current density, and variable fluid properties. In this paper, the foundation of the distributed resistance methodology is expounded, considering macroscopic and microscopic force and mass balances for plane ducts. Results are presented for the example of the cathode channel of a polymer electrolyte fuel cell. Comparisons are made with analytical and numerical solutions for constant and variable current density along the channel. Distributed resistance analogy and detailed computational fluid dynamics calculations are also compared. Mass transfer through the channel wall leads to additional boundary and inertial effects which alter the value of the distributed resistance. However these effects are shown to be minor for the geometries and current densities encountered in polymer electrolyte fuel cells today. It is concluded that the method forms a sound basis for performance calculations. The work contains information relevant to numerous applications based on hydraulic resistance networks, whenever mass transfer is present.