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Full-Text Articles in Condensed Matter Physics
Nonlocal Diffusion Models: Application To Rapid Solidification Of Binary Mixtures, Sergey Sobolev
Nonlocal Diffusion Models: Application To Rapid Solidification Of Binary Mixtures, Sergey Sobolev
Sergey Sobolev
Various theoretical treatments and models for nonlocal diffusion are briefly reviewed and discussed. The nonlocal effects arise in far from equilibrium processes, which involve extremely fast heat and mass transfer at very small time and length scales. With only diffusive dynamics, the nonlocal models result in a set of transfer equations of parabolic type with an infinite velocity of diffusive disturbances. With the wavelike dynamics, the models lead to a set of transfer equations of hyperbolic type with a finite velocity of diffusive disturbances. Rapid solidification of binary alloys has been used to illustrate the influence of the nonlocal diffusion …
Diffusion-Stress Coupling In Liquid Phase During Rapid Solidification Of Binary Mixtures, Sergey Sobolev
Diffusion-Stress Coupling In Liquid Phase During Rapid Solidification Of Binary Mixtures, Sergey Sobolev
Sergey Sobolev
An analytical model has been developed to describe the diffusion-viscous stress coupling in the liquid phase during rapid solidification of binary mixtures. The model starts with a set of evolution equations for diffusion flux and viscous pressure tensor, based on extended irreversible thermodynamics. It has been demonstrated that the diffusion-stress coupling leads to non-Fickian diffusion effects in the liquid phase. With only diffusive dynamics, the model results in the nonlocal diffusion equations of parabolic type, which imply the transition to complete solute trapping only asymptotically at an infinite interface velocity. With the wavelike dynamics, the model leads to the nonlocal …