This instructable is based on work done by Bruce Logan and his team at Penn State University and on the microbial fuel cells built by Abbie Groff, a student at Conestoga Valley High School in Lancaster, PA. The research she performed with her MFCs helped her win the Grand Champion Award at the 2005 Lancaster County Science Fair.
Now to be completely honest the fuel cell we will build is not "purely" an algae fuel cell, it is a microbial fuel cell that uses anaerobic bacteria to decompose organic matter, in our case dead algae.
The fuel cell will consume the algae (or other organic material) with two significant by-products, electricity (always useful) and methane gas. In a production system the methane must be captured for further use for instance as fuel for a steam powered generator which processes its exhaust plume through an algae based (or other) exhaust gas scrubber.
In this design its very cleverly captured in the sealed anode and if you come up with some clever way to do something with it, I'd be very pleased to hear it.