Andrei Kulikovsky

The current voltage plot of PEM fuel cell with long feed channels

Abstract The formula for voltage loss on the cathode side of the polymer electrolyte membrane fuel cell (PEMFC) is derived, taking into account oxygen consumption in the feed channel. Limiting current density due to the oxygen exhaustion along the channel is obtained. Theory predictions are in line with experiments that were performed to test the theory. The results reveal new reserves for the optimization of the cell performance. They also show new in situ electroanalytical options: the study of electrochemical reaction in the catalyst layer via the cell voltage–current plots and via detecting of the feed gas consumption or local current distribution along channel.

Fuel cell basics

In this Chapter, the basic principles of fuel cells are discussed. A fuel cell at an open circuit is represented as a sum of two charged capacitors. Thermodynamics relates the cell open-circuit voltage (OCV) to the change of the Gibb’s free energy of the overall fuel cell reaction. The dependence of the OCV on the reagent concentration (Nernst equation) and on the temperature is discussed.

Direct Methanol–Hydrogen Fuel Cell

We report a regime of direct methanol fuel cell (DMFC) operation. Measurements of local current show that with a lack of oxygen, the cell splits into three domains. Close to the inlet of the oxygen channel, the cell generates current in a normal DMFC mode (galvanic domain, GD). Close to the outlet of this channel, it works in an electrolysis mode and produces hydrogen (electrolytic domain). At a high rate of hydrogen production, H 2 permeates to the GD and contributes to current production, i.e., part of the GD operates as a hydrogen cell. Performance of the cell in this regime is discussed.

Chapter 3 – One-dimensional model of a fuel cell

Publisher Summary This chapter focuses on the one-dimensional model of a fuel cell that includes the losses in the GDL and membrane. A one-dimensional curve ignores losses due to reactant transport in the feed channels and when these losses are negligible, the equations derived form a model for cell performance. The model provides a method for calculating transport losses in other situations, and these losses are of particular interest for low-temperature fuel cells, in which they usually limit the cell current. The oxygen flux through the GDL by Ficks equation with the effective diffusion coefficient Db is described where Db corresponds to the oxygen binary diffusion coefficient corrected for GDL porosity. In case of a one-dimensional model of DMFC, the DMFC is fed with the liquid methanol-water solution where the diffusivity of methanol in water is low and the respective voltage loss cannot be neglected. Another source of voltage loss specific to DMFC is methanol crossover through the polymer electrolyte membranes, which offer a high resistance to crossover of gases. But the mechanism of proton transport in these membranes is inherently related to water molecules, and PEM membranes are highly permeable to water. Since methanol and water molecules are similar, methanol easily permeates these membranes. The exact analytical solutions to the heat transport equations in the catalyst layers and membrane of a PEFC are derived, and the results are illustrated by two cases, first when the temperature on the outer sides of the MEA is kept fixed and second, when the cathode side of the MEA is thermally insulated.

Chapter 2 – Catalyst layer performance

Publisher Summary This chapter focuses on catalyst layer (CL) performance and discusses various functional models that predict the distribution of local currents, reaction rate, and species concentration in the CL. The numerical effect of the oxygen diffusion coefficient D on the CCL polarization voltage ŋ0 for the general case of the Butler–Volmer conversion function is also discussed. The nonuniform catalyst loading can be beneficial for CL performance, and under uniform loading, the peak of current production is located at the membrane interface. Thus catalyst loading close to the membrane at the cost of lower loading at the GDL interface, where the rate of electrochemical conversion is anyway low, should be increased. One of the key problems in DMFC technology is sluggish kinetics of methanol oxidation, which in DMFC modeling is often described by the Tafel or Butler–Volmer relations. The heat production and transport in the catalyst layer is studied and the expressions for temperature shape across the CL and for the heat flux emitted by the CL are also derived. The process of reducing the heat balance equation in the CL to the boundary condition for the external problem of heat transport in the other fuel cell components, which also gives the exact expressions and makes it possible to establish their limits of validity, is also presented.

Chapter 4 – Quasi-2D model of a fuel cell

Publisher Summary This chapter constructs quasi-2D models of fuel cells that take into account the variation of local parameters such as reactant and product concentration, current density, and overpotentials along the feed channel. The cell with meander channels can always be cut and transformed into an equivalent cell and this transformation implies that we neglect reactant crossover through the gas-diffusion layer between the two adjacent turns of the meander. Feed gas consumption affects the hydrodynamics of channel flow, and the electro-osmotic effect causes the transfer of water from the anode channel to the cathode channel, due to which the mass of the flow changes, which may ultimately affect flow density and velocity. The features of single-phase flow in the cathode channel of a PEFC or DMFC are discussed, and for this a model that takes into account mass and momentum transfer through the channel/GDL interface is presented. The model gives exact solutions and helps in clarifying how the electrochemical reactions and electro-osmotic effect affect the flow in the fuel cell channels. A model of PEFC that couples transport of water and oxygen across the cell with oxygen depletion and water accumulation along the air channel is constructed, to understand the effect of water on cell performance without time-consuming CFD calculations. The model equations for the case of constant oxygen stoichiometry are also formulated. The quasi-2D model makes it possible to predict general scenarios of the degradation process, without specifying its microscopic origin.

Chapter 5 – Modelling of fuel cell stacks

Publisher Summary This chapter focuses on the modeling of fuel cell stacks. To increase the power of the FC system and to achieve high volumetric power density, fuel cells are assembled in stacks, which are layered structures consisting of membrane-electrode assemblies (fuel cells) clamped between metal or graphite bipolar plates (BPs) with channels for feed gas supply. Fuel cell stacks are devices of tremendous complexity and the overall thermal effect of electrochemical reactions in cells is heat production. The functioning of an individual fuel cell requires a continuous supply of feed gases or liquids and the removal of excess water and heat. There are three approaches to stack modeling, and the first one is fully 3D modeling, which takes into account the hydrodynamics of flows in channels, heat transport, and potential distribution over the stack volume. The second approach, which is widely used in SOFC modeling, is to model a single cell in a stack that takes into account the stack environment by using periodic or adiabatic boundary conditions for the temperature of cell surfaces. The process of splitting a fully 3D Laplace equation, for voltage and temperature distribution over the stack volume into a number of 2D Poisson equations for the voltages and temperatures of individual bipolar plates, is also presented. The cells (MEAs) can be represented as thin interfaces with prescribed equations for voltage–current characteristics and for heat fluxes. A physical 2D model for a single element that can be replicated to the number of processors equal to the number of elements in a stack is also presented.