  A new type of boundary dynamics is proposed to describe the interface that
sweeps space to collect distributed material. Based upon geometrical
consideration on a simple physical process representing a certain experiment,
the dynamics is formulated as the small diffusion limit of Mullins-Sekerka
problem of crystal growth. It is demonstrated that a steadily extending finger
solution exists for a finite range of propagation speed, but numerical
simulations suggest they are unstable and the interface shows a complex time
development.
