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Using as a starting point conservation of momentum, a multiphase mechanicalenergy balance equation is derived that accounts for multiple material phasesand interfaces present within a moving control volume. This balance is appliedto a control volume that is anchored to a three phase contact line as itadvances over the surface of a rough and chemically homogeneous solid. Usingsemi-quantitative models for the material behaviour occurring within thecontrol volume, an order-of-magnitude analysis is performed to find what termswithin the balance are significant, producing an equation that can be used topredict contact angle hysteresis from a knowledge of interface dynamicsoccurring around the three phase contact line. In addition to this equation,the theory also answers several questions that have been discussed within thewetting literature: Namely that (static) contact angle hysteresis is a functionof conditions around the three phase contact line, as opposed to thesurrounding flow system; That contact angle hysteresis results from interface`jumps' that dissipate energy, rather than directly from contact linedeformation; That interfacial dynamics is required to predict contact anglehysteresis, but that these dynamics should be interpreted via energyconservation, and; That dynamic contact angles depend on kinetic energytransport around the three phase contact line, as well as local energydissipation. The framework has been derived using assumptions of incompressibleNewtonian fluids, reversible interface formation and zero-strain solids --future work could relax these assumptions to make the theory more generallyapplicable.

Contact Angle Hysteresis on Rough Surfaces Part I: Mechanical Energy Balance Framework