Found this interesting (synopsis of a) paper on those beautiful curls we all see when our prints have gone wrong… Most printers don’t just drop the filament from the nozzle, of course, but squash it onto the build surface, so this may not have an immediate application. Might be useful to look at for tackier materials that don’t need to be pushed down to stick to the build plate, however.
http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.114.174501