  Using as a starting point conservation of momentum, a multiphase mechanical
energy balance equation is derived that accounts for multiple material phases
and interfaces present within a moving control volume. This balance is applied
to a control volume that is anchored to a three phase contact line as it
advances over the surface of a rough and chemically homogeneous solid. Using
semi-quantitative models for the material behaviour occurring within the
control volume, an order-of-magnitude analysis is performed to find what terms
within the balance are significant, producing an equation that can be used to
predict contact angle hysteresis from a knowledge of interface dynamics
occurring around the three phase contact line. In addition to this equation,
the theory also answers several questions that have been discussed within the
wetting literature: Namely that (static) contact angle hysteresis is a function
of conditions around the three phase contact line, as opposed to the
surrounding flow system; That contact angle hysteresis results from interface
`jumps' that dissipate energy, rather than directly from contact line
deformation; That interfacial dynamics is required to predict contact angle
hysteresis, but that these dynamics should be interpreted via energy
conservation, and; That dynamic contact angles depend on kinetic energy
transport around the three phase contact line, as well as local energy
dissipation. The framework has been derived using assumptions of incompressible
Newtonian fluids, reversible interface formation and zero-strain solids --
future work could relax these assumptions to make the theory more generally
applicable.
