The free boundary model of diffusion-induced grain boundary motion derived in Cahn et
al. [3], Fife et al. [6] and Cahn & Penrose [4] is extended, in the case of thin metallic films, to
account for bidirectional motion, together with the appearance of S-shapes and double seam
configurations. These are often observed in the laboratory. Computer simulations based on
the extended model are given to illustrate these and other features of bidirectional motion.
More generally, the extension accounts for the motion of grain boundaries whose traces on
the film's surface are curved. The new free boundary model is one of forced motion by
curvature, the forcing term possibly changing sign due to the bidirectionality. The thin film
model is derived systematically under explicit assumptions, and an adjustment for grooving
is included.
A free boundary model of epithelial dynamics
