  We extend the geometrical theory presented in [5] for collisional and
frictional particle abrasion to include an independent physical equation for
the evolution of mass and volume. We introduce volume weight functions as
multipliers of the geometric equations and use these mutipliers to enforce
physical volume evolution in the unified equations. The latter predict, in
accordance with Sternberg's Law, exponential decay for volume evolution. We
describe both the PDE versions, which are generalisations of Bloore's equations
and their heuristic ODE approximations, called the box equations. The latter
are suitable for tracking the collective abrasion of large particle
populations. The mutual abrasion of identical particles, called the self-dual
ows, play a key role in explaining geological scenarios. We give stability
criteria for the self-dual ows in terms of the parameters of the physical
volume evolution models and show that under reasonable assumptions these
criteria can be met by physical systems. We also study a natural
generalisation, the unidirectional Bloore equation, covering the case of
unidirectional abrasion. We have previously shown that his equation admits
travelling front solutions with circular profiles. More generally, in three
dimensions, they are so-called linear or special Weingarten surfaces.
