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This is the case because we consider a locally flat interface. For a curved interface, the integral which involves the Laplacian of leads to the classical Gibbs-Thomson curvature correction which is proportional to the interface free energy. Moreover we do not discuss surface diffusion and interface stretching (see, for example,) which are generically smaller than interface kinetic effects in the macroscopic limit.
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This is the case because we consider a locally flat interface. For a curved interface, the integral which involves the Laplacian of leads to the classical Gibbs-Thomson curvature correction which is proportional to the interface free energy. Moreover we do not discuss surface diffusion and interface stretching (see, for example,) which are generically smaller than interface kinetic effects in the macroscopic limit.
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