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Interaction of vacancies with grain boundaries (GBs) is involved in many processes occurring in materials, including radiation damage healing, diffusional creep, and solid-state sintering. We analyze a model describing a set of processes occurring at a GB in the presence of a non-equilibrium, non-homogeneous vacancy concentration. Such processes include vacancy diffusion toward, away from, and across the GB, vacancy generation and absorption at the GB, and GB migration. Numerical calculations within this model reveal that the coupling among the different processes gives rise to interesting phenomena, such as vacancy-driven GB motion and accelerated vacancy generation/absorption due to GB motion. The key combinations of the model parameters that control the kinetic regimes of the vacancy-GB interactions are identified via a linear stability analysis. Possible applications and extensions of the model are discussed.e's comments, Comment: 35 pages, 9 figures. Minor revisions per referee's comments. Published in Acta Materialia. Supplementary file containing additional figures is available from first author (mcfadden@nist.gov)