  We investigate the ability of a multi-order parameter phase field model with
obstacle potentials to describe grain boundary premelting in equilibrium
situations. In agreement with an energetic picture we find that the transition
between dry and wet grain boundaries at the bulk melting point is given by the
threshold $2\sigma_{sl}=\sigma_{gb}$, with $\sigma_{sl}$ being the solid-melt
interfacial energy and $\sigma_{gb}$ the energy of a dry grain boundary. The
predictions for premelting are confirmed by simulations using the phase field
package OpenPhase. For the prediction of the kinetics of melting along grain
boundaries in pure materials, taking into account the short ranged interactions
which are responsible for the grain boundary premelting, a sharp interface
theory is developed. It confirms that for overheated grain boundaries the
melting velocity is reduced (increased) for non-wetting (wetting) grain
boundaries. Numerical steady state predictions are in agreement with a fully
analytical solution in a subset of the parameter space. Phase field simulations
confirm the predictions of the sharp interface theory.
