1997
DOI: 10.1557/proc-481-59
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Effects of Finite Rate Phase Transformation Kinetics on The Steady-State Solidification Front Propagation Speed in Undercooled Pure Liquids

Abstract: This novel approach to modeling the steady-state solidification of undercooled pure liquids is based upon first principles. Continuum equations are used to describe a volumetrically averaged, coexisting mixture of solid and liquid in the thin phase transformation zone between regions of pure liquid and pure solid. These equations are coupled with a dynamic equilibrium based rate law that describes temperature dependent phase transformation kinetics. The time scale associated with finite rate phase transformati… Show more

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“…whereH =h/kT M represents the ratio of phase-change enthalpy for an atom to the average thermal energy of an atom at temperature T M , and = kT M /E F represents the ratio of average thermal energy to the activation energy for freezing. Estimates of E F from the literature (Jackson & Chalmers 1956), as well as calculations using the mesoscale model to match Willnecker's front speed data (Norris 1993), indicate that the magnitude of is approximately 10 −3 , hence it will be considered a small parameter.…”
Section: (D ) Source-term Developmentmentioning
confidence: 99%
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“…whereH =h/kT M represents the ratio of phase-change enthalpy for an atom to the average thermal energy of an atom at temperature T M , and = kT M /E F represents the ratio of average thermal energy to the activation energy for freezing. Estimates of E F from the literature (Jackson & Chalmers 1956), as well as calculations using the mesoscale model to match Willnecker's front speed data (Norris 1993), indicate that the magnitude of is approximately 10 −3 , hence it will be considered a small parameter.…”
Section: (D ) Source-term Developmentmentioning
confidence: 99%
“…For example, the specific total energy at any given point is the average of the specific total energy distributed in both the liquid and solid within δV. Similar definitions are developed for the specific internal energy, specific enthalpy and all other variables and parameters (Norris 1993). The characteristic length scale of δV, denoted O(δV 1/3 ), must be much smaller than the conduction length scale, yet only slightly larger than the length scale for which the addition or removal of a small portion of solid material within δV will not significantly alter the values of the averaged variables.…”
Section: Mesoscale Model Formulation (A) Volumetric Averagingmentioning
confidence: 99%
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