  We investigate the evolution of axis ratios, roundness (isoperimetric ratio)
and the number of static balance points under distance-driven flows. The latter
have already been proposed by Aristotle as models of particle shape evolution
and recent studies indicate that they may serve as models for frictional
abrasion. We show exact conditions under which Aristotle's original claims are
true. For several geophysical shape descriptors we prove monotonic or
quasiconcave time evolution and compare these results with results from the
literature on curvature-driven flows as models of collisional abrasion.
