In science as in everyday life, we take electricity for granted in the developed world. It's hard to imagine doing basic experiments without plugging in a power supply or using instruments that work on conveniently packaged off-the-shelf batteries. I was recently re-reading my copy of Cassell's Popular Educator, a mid-1850s weekly that offers a glimpse into a different and messy world of electric cells, now mostly defunct. The copper-zinc Daniell cell and the zinc-carbon Leclanché cell are well known - the latter as the ancestor of the classic 'dry battery'. Other types, such as the Bunsen, Callan, and Maynooth cells, are best forgotten; their nitric acid electrolyte gave off toxic nitrous acid fumes. The Popular Educator refers to the Maynooth especially as 'very unpleasant to use'. In such scary company, it's easy to miss Grove's Gas Battery: 'Interesting, though rarely if ever used in practice'. It was an obscure beginning for what's now one of the most actively-researched power technologies: the fuel cell.
Exploring an effect discovered in 1838 by his friend and correspondent Christian Friedrich Schoenbein, Sir William Robert Grove developed a cell that made electricity by reversing the electrolysis of water. The apparatus involved hydrogen and oxygen tubes, each with a platinum electrode, inverted in a shared sulphuric acid electrolyte. Grove found that a current flowed between the electrodes, the gases being consumed in a 2:1 ratio, showing that they were recombining into water. There was a deal of dispute over how it worked, until Ostwald's explanation in the 1890s: the electrical energy came from catalysed oxidation of hydrogen at the anode, and reduction of oxygen at the cathode.
Grove had hopes for the Gas Battery as a power source for driving telegraph systems and 'experiments of slow crystallisation' (something of a Victorian vogue, the kind of experiment that led Babbage's contemporary Andrew Crosse to his strange observations of mites, Acarus crossii, supposedly created by the electricity). Grove never got the Gas Battery to commercial form. In hindsight, it was doomed in the 19th century by various factors. The platinum kept the cost high, as is still the case. In addition, it proved unworkable with gas from industrial sources, whose carbon monoxide content poisoned the catalyst. This was the problem with the coal-derived 'Mond gas' tried by Ludwig Mond and Carl Langer, sometimes credited for coining the term 'fuel cell'. Another failure of Victorian fuel-cell experimentation was William Jacques' attempt to make electricity direct from coal. His furnace-heated battery appeared to work - until it was shown to be producing its output by thermoelectricity rather than an electrochemical reaction. But in any case, this was 'blue sky research' in the face of the runaway success of alternating current distribution and fossil fuel engines.
After slow development in the early 20th century, fuel cells eventually came to prominence with the US space programme in the 1960s. Despite the cost and early technical hitches, a power source that ran on propellant fuels and produced drinking water as a by-product was highly attractive for spacecraft. The Gemini missions used the PEM (Proton Exchange Membrane - a polymer electrolyte) system invented by General Electric; while the Apollo missions and Space Shuttle used the alkali (KOH electrolyte) cells invented in the 1930s by Francis Thomas Bacon.
In the late 20th century interest in fuel cells grew, initially for their potential as non-polluting heavy-duty power plants and automotive applications, but later for the scope in consumer electronics, being compact and up to 80 per cent efficient in converting chemical energy to electricity. The field has diversified, with decades-old ideas for alternative electrolytes being reinvestigated - for instance, molten carbonate and solid-oxide cells with a megawatt capacity. For a detailed history of the many types, I recommend the Smithsonian Institution's online Fuel Cell History Project.
Basic fuel cell. The ionic current varies with type: in solid oxide cells, for instance, oxygen ions travel from cathode to anode. Courtesy of US Department of Energy, Energy Efficiency and Renewable Energy.
History is one thing; the modelling and design of practical devices is another. A single fuel cell develops less than a volt, so practical cells consist of 'stacks'. Typically, each component cell has a multilayer structure to optimise reaction and transport conditions. For example, in a Proton Exchange Membrane fuel cell, the hydrogen passes 1) through 'serpentine' channels that maximise its contact with 2) a porous medium, through which it diffuses to 3) the catalyst layer (platinum on nano-sized carbon particles) where it loses electrons then conducts as protons through 4) the polymer membrane to meet oxygen arriving through similar layers on the other side (layers which also conduct away water and heat, while keeping the membrane wet).
There are also many different requirements to be tailored to the application. As a recent Comsol News noted, the needs for a car fuel cell - rapid start-up and low weight - aren't an issue for a static power plant. Or a cell running at 1000C with a large air compressor, however efficient, won't cut it in a mobile phone.
Juggling such factors is a difficult 'multiphysics' problem of partial differential equations - in electrochemistry, electrostatics, fluid dynamics, ion transport, and thermal effects - with highly non-linear coupling. Fortunately, many of the regions of a cell can be also modelled in isolation, and although the cell specifics vary, there are also generic problems. For instance, Grove noticed that his Gas Battery worked better when the electrodes were roughened with a deposit of platinum grains: maximising catalyst area is just as important with modern fuel cells. The Butler-Volmer equation for activation controlled reactions (i.e. the reaction rate being controlled by an electrochemical charge transfer process) is widely applicable.
Another generic model is the succession of flow regimes as gas enters the cell: incompressible Navier-Stokes fluid flow in the serpentine channels; Darcy's Law (viscous flow proportional to pressure gradient) in the porous boundary layer; and Maxwell-Stefan diffusion (driven by concentration gradient) in the catalyst. The diagram opposite shows a similar model, one of the several examples in the Electrochemical Engineering module of Comsol's Femlab, a general-purpose multi-physics finite-element package that has been used for many academic studies of fuel cell operation.
3D model in Femlab 3.1 analysing gas flow in an air-fed cathode of a PEM fuel cell. Left from top: the model divides into two subdomains, the serpentine gas channel governed by the Navier-Stokes equations; and the underlying reactive boundary layer where the flow is described by Maxwell-Stefan diffusion and convection. A scripted two-stage solution with a static non-linear solver can be photoprocessed to graph parameters such as (right from top) the pressure in a channel, and the mass fraction of water in the channel and substrate. Controlling water output is important: if it is too high, droplets form and clog the channel.
Many high-end finite-element packages offer more specific support in the form of dedicated toolkits for fuel-cell designers. These tend to focus on PEM and solid-oxide fuel cells (a gauge of their importance in the field). Fluent Inc., for instance, offers tools for its Fluent CFD package for designers of solid oxide and PEM fuel cells, covering electrochemistry and potential field for both types, and membrane-electrode assembly and water flow in the diffusion layers and flow channels in the latter. Another, the CD-adapco group, has corresponding specialist tools, expert system pre-processing modules for its Star-CD: es-pemfc for PEM cells, designed to be used with University of South Carolina electrochemistry subroutines; and es-sofc, developed in collaboration with Pacific Northwest National Laboratory, for solid oxide cells. The ESI Group's CFD-ACE+ has an optional fuel cell module covering the same pair, along with Direct Methanol cells. This newer type, whose overall reaction is oxidising methanol to carbon dioxide at temperatures as low as 50°C, has strong prospects in portable applications, as Felix Grant describes in the accompanying section.
The strongest focus for modelling, however, appears to be PEM fuel cells. In 2003, the introductory paper to the Computational Fuel Cell Dynamics II conference commented how the 'historic race' among the world's major automotive manufactures to develop PEM cells as clean, high-efficiency alternatives to internal combustion had added impetus to their modelling. Of course, fuel cells shouldn't be seen as a Holy Grail: the arguments and counterarguments are well known. Hydrogen fuel cells, in the worst scenario, may only shift pollution and carbon dioxide generation upstream to the power station that generates the electricity that produces the hydrogen. Many fuel cell types, such as direct methanol, generate carbon dioxide. On the other hand, centralised generation can be better managed, and the sheer conversion efficiency pollutes less although burning the same amount of fuel.
As a piece of historical closure, it's interesting to see the growth of 'clean coal' technologies such as the Lawrence Livermore National Laboratory's new Direct Carbon Conversion fuel cell (based on carbon particles in a bed of molten alkali metal carbonate) and the (so far horribly inefficient) iron/coal low-temperature fuel cell of Douglas Weibel and Roman Boulatov at Harvard University. Even William Jacques' coal fuel cell is no longer so far-fetched.
