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In order to counter adverse effects resulting from the impingement of high energy plasmas on solid material surfaces, especially as this relates to fusion reactor high heat flux components, the idea of protecting the material surface with a thin film of liquid metal has been advanced. In principle, this film would protect the underlying substrate from physical sputtering and reduce thermal stresses in the structure. However, serious concerns related to establishing such a liquid metal flow and its performance in a fusion environment need to be addressed. In particular, the interaction of the conducting metal film with the complicated magnetic fields typical of a diverted reactor plasma may lead to retardation of the film resulting in channel flooding, velocity profiles not conducive to effective heat transfer, and possibly even detachment of the film from the substrate. In addition, the momentum carried by the plasma particles may deform the film shape to a significant extent, possibly disrupting the flow or leaving sections on the substrate inadequately protected. Proposed here are several mathematical and experimental models intended to address these specific questions. Mathematical models will be derived from the basic set of incompressible magnetohydrodynamic equations for the cases of fully developed and developing film flow. The fully developed flow model allows simplification of the governing equations to two dimensions, facilitating their solution. The data obtained from this formulation will yield the velocity, induced magnetic field, and height of the film as a function of space and flow parameters. From this data the effect of the plasma momentum on the shape of the surface will be seen, as will the velocity structure across the channel, a structure that is only assumed in previous modeling attempts. The developing film model, based on simplifying assumptions for the height and velocity profiles determined from the previous model for the fully developed case, will account for spatial and temporal varying magnetic fields. In this way it will be possible to model more fusion relevant field distributions and establish their effect on the evolution of the film and its possible flooding or detachment as it flows along the substrate

MHD modelling of liquid metal films for fusion divertor surface protection