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Full-Text Articles in Condensed Matter Physics

Nonlocal Diffusion Models: Application To Rapid Solidification Of Binary Mixtures, Sergey Sobolev Jan 2014

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 Jan 2014

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 …


On The Transition From Diffusion-Limited To Kinetic-Limited Regimes Of Alloy Solidification, Sergey Sobolev Oct 2013

On The Transition From Diffusion-Limited To Kinetic-Limited Regimes Of Alloy Solidification, Sergey Sobolev

Sergey Sobolev

An abrupt transition from diffusion-limited solidification to diffusionless, kinetic-limited solidification with complete solute trapping is explained as a critical phenomenon which arises due to local non-equilibrium diffusion effects in the bulk liquid. The transition occurs when the interface velocityVpasses through the critical pointV=VD, where V=VDis the bulk liquid diffusive velocity. Analytical expressions are developed for velocity–temperature and velocity–undercooling functions, using local non-equilibrium partition coeffi-cient based on the Jackson et al. kinetic model and the local non-equilibrium diffusion model of Sobolev. The calculated functions dem-onstrate a sharp break in the velocity–undercooling and velocity–temperature relationships at the critical pointV=VD. At this point …


Local Nonequilibrium Solute Trapping Model For Non-Planar Interface, Sergey Sobolev Jan 2013

Local Nonequilibrium Solute Trapping Model For Non-Planar Interface, Sergey Sobolev

Sergey Sobolev

A generalized solute trapping model was proposed incorporating the dependency on interfacial normal velocity along the dendrite side, as an extension of the continuous growth model modified by Sobolev with the local nonequilibrium diffusion model (LNDM). The present model predicts that the transition to diffusionless solidification is not sharp, but occurs in a range of velocities. Analysis indicates that for local nonequilibrium solute diffusion in bulk liquid the effect of the interfacial normal velocity dependency on solute partitioning is considerable.


Rapid Colloidal Solidifications Under Local Nonequilibrium Diffusion Conditions, Sergey Sobolev Jan 2012

Rapid Colloidal Solidifications Under Local Nonequilibrium Diffusion Conditions, Sergey Sobolev

Sergey Sobolev

Partition coefficient for rapid solidification of colloidal suspensions has been calculated under local nonequilibrium diffusion conditions typically used when processing advanced materials. It has been demonstrated that the local nonequilibrium diffusion effects stabilize the planar solid liquid interface and lead to an abrupt transition to diffusionless solidification with complete particle trapping. The effective diffusion coefficient, which depends on interface velocity and particle size, has been introduced. It explains the strong dependences of the partition coefficient and the velocity leading to absolute stability of a planar solid–liquid interface on particle size.


An Analytical Model For Complete Solute Trapping During Rapid Solidification Of Binary Alloys, Sergey Sobolev Dec 2011

An Analytical Model For Complete Solute Trapping During Rapid Solidification Of Binary Alloys, Sergey Sobolev

Sergey Sobolev

An analytical model has been developed to describe solute partitioning during rapid solidification of binary alloys under local nonequilibrium conditions. The model takes into account the deviations from equilibrium both at the solid–liquid interface according to the kinetic approach of Jackson et al. based on Monte Carlo simulations and in the bulk liquid using local nonequilibrium diffusion model (LNDM). The dimensionless growth parameter b found in the Monte Carlo simulations as the important parameter for solute trapping has been modified for the local nonequilibrium diffusion case. An analytical expression has been developed for the velocity-dependent partition coefficient K which predicts …


Local Non-Equilibrium Diffusion Effects On The Kinetic Phase Boundaries In Solidification, Sergey Sobolev Jan 1997

Local Non-Equilibrium Diffusion Effects On The Kinetic Phase Boundaries In Solidification, Sergey Sobolev

Sergey Sobolev

No abstract provided.


Effects Of Local Non-Equilibrium Solute Diffusion On Rapid Solidification Of Alloys, Sergey Sobolev Jan 1996

Effects Of Local Non-Equilibrium Solute Diffusion On Rapid Solidification Of Alloys, Sergey Sobolev

Sergey Sobolev

A conceptual foundation for the study of local non-equilibrium solute diffusion under rapid solidifica- tion conditions is proposed. The model takes into account the relaxation to local equilibrium of the solute flux and incorporates two diffusion speeds, VDb, the bulk liquid diffusion speed, and VDi, the interface diffusive speed, as the most important parameters governing the solute concentration in the liquid phase and solute partitioning. The analysis of the model predicts complete solute trapping and the transition to a purely thermally controlled solidification, which occur abruptly when the interface velocity V equals the bulk liquid diffusion speed VDb. The abrupt …


Local Non-Equilibrium Model For Rapid Solidification Of Undercooled Melts, Sergey Sobolev Jan 1995

Local Non-Equilibrium Model For Rapid Solidification Of Undercooled Melts, Sergey Sobolev

Sergey Sobolev

No abstract provided.