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Two bodies, e.g. grains with a certain surface contour, are assumed to be in contact at a plane interface, e.g. a common grain boundary with an arbitrary inclination relatively to the surface and with zero mobility and diffusivity. A groove appears due to surface diffusion along the triple line, i.e. the intersection line of the two surfaces and the grain boundary. The thermodynamic extremum principle is applied to derive the evolution equations for the surfaces of both bodies as well as the contact conditions at the triple line. Applications to grooving and wetting are demonstrated and compared with the results from the literature. The simulations indicate that the groove root angle can be significantly different from the value of the dihedral angle calculated from the equilibrium condition for the specific grain boundary and surface energies. Moreover, it is demonstrated that the groove angle is dependent on the kinetic parameters, e.g. surface diffusion coefficients of individual grains. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.