Transient growth of second phases during solution treatment

Heckel, R. W.; Hickl, Anthony J.; Zaehring, Richard J.; Tanzilli, R. A.

doi:10.1007/bf02644230

Cited by 28 publications

(10 citation statements)

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“…This is a reality because the dissolution and exsolution of CO 2 cause the volume changes of both water and oil phases. Moving boundary problems have been discussed widely in different areas, such as oxidation of alloys, 46 spontaneous emulsification, 47 absorption by the liquid of a single component from a mixture of gas, 48 and brass diffusion couples with multilayers, 49 among others. Danckwerts 48 presented a general solution for the moving interface problem in unsteady-state heat conduction or in diffusion within two-phase regions.…”

Section: Theorymentioning

confidence: 99%

Mass Transfer of CO₂ in a Carbonated Water–Oil System at High Pressures

Shu

Dong

Chen

2016

Ind. Eng. Chem. Res.

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In this paper, CO2 diffusion coefficients in a carbonate water–oil system are determined by measuring the pressure buildup in the closed water–oil system experimentally and modeling the pressure change mathematically. The mathematical method of investigating one-dimensional, time-dependent heat conduction in a composite medium is adopted to solve the mass transfer problem between two liquid phases. The model is combined with well-designed trial-and-error method to determine diffusion coefficients of CO2 in both water and oil phases at the same time. The model considers a moving interface between carbonated water and oil as well as variations of interface concentrations of CO2 in these two phases, which more effectively conforms to reality. Results show that the pressure buildup during the diffusion process resulted from the increased density and swelling of the oil phase. The diffusion coefficient of CO2 in the water phase plays a major role in the interphase mass transfer process.

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Section: Theorymentioning

confidence: 99%

Mass Transfer of CO₂ in a Carbonated Water–Oil System at High Pressures

Shu

Dong

Chen

2016

Ind. Eng. Chem. Res.

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“…Therefore, to prevent the accumulation (or depletion) of matter, the interface must move. This effect has been observed experimentally in numerous systems, notably by Tanzilli and co-workers [2,3]. An important application of such phenomena concerns the particular case in which one of the phases is a liquid.…”

Section: Introductionmentioning

confidence: 95%

Modelling of transient liquid phase bonding in binary systems—A new parametric study

Illingworth

Golosnoy

Clyne

2007

Materials Science and Engineering: A

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An established mathematical model, describing the rate at which transient liquid phase bonding (TLP bonding) progresses in binary alloy systems, is subjected to careful scrutiny. It is shown that the process can be characterised using just two dimensionless parameters. An advantage of such dimensionless characterisation is demonstrated by analysis of the solution for solidification of semi-infinite systems. It is known that analytical formulae for the rate at which the liquid region solidifies are valid only for certain restricted cases. This is investigated by numerical modelling, and the requirements for the formulae to be applicable are rationalised. Maps presented here can be used to determine whether the semi-infinite solution would provide an acceptable approximation for any given system. Information is also presented concerning optimal combinations of phase diagram characteristics, diffusivities and system dimensions required for rapid TLP solidification, which can be used to identify the best melting point depressant (MPD) materials to use for particular TLP requirements. The analysis reveals that, as a consequence of their higher solubilities, elements forming substitutional solutes in the parent plates may often allow faster TLP solidification than those forming interstitial solutes, despite the fact that the latter group normally exhibits much higher diffusivities.

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“…Therefore, the quantification of the kinetics of the process has been attempted by mathematical models that track the moving boundaries of the phases in the metallic systems of interest. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] The mathematics of the moving boundary diffusion problem assumes complexity if an implicit formulation is attempted because the position of the interface is not known a priori. Analytical solutions exist only for simplified situations; typically involving boundary motion in one dimension in an infinite medium.…”

Section: Introductionmentioning

confidence: 99%

“…Solid state diffusion using two main finite difference techniques, namely, variable grid spacing and fixed grid methods developed by Murray and Landis 30 had been widely employed. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] In the variable grid spacing method, the interface boundary is fixed at a mesh point that moves with the boundary. The node size in each phase is contracted or expanded, while their number remains constant.…”

Section: Introductionmentioning

confidence: 99%

Numerical treatment of diffusional phase transformation through fully implicit control volume method

Verma¹,

Chandra²,

Dhindaw³

2005

Materials Science and Technology

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Solid state, diffusion controlled phase transformation kinetics with a moving boundary has been quantified using a fully implicit, fixed grid, finite difference method based on the control volume approach. In a departure from the usual modeling techniques for phase change problems, the region undergoing phase change has also been considered as a control volume. A new equation for the interface flux balance has been obtained that minimises the mass balance error that normally plagues the numerical solution of moving boundary problems. The model has been validated with the calculated phase thickness based on binary equilibrium diagram and available experimental data in the literature for the Cu-Zn system and a good match has been obtained. The results obtained by the present formulation are compared with those obtained from the other models. In addition to the improved accuracy of the prediction because of elimination of the mass balance error, the proposed method has the usual advantages of a fully implicit scheme.

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Transient growth of second phases during solution treatment

Cited by 28 publications

References 1 publication

Mass Transfer of CO₂ in a Carbonated Water–Oil System at High Pressures

Mass Transfer of CO₂ in a Carbonated Water–Oil System at High Pressures

Modelling of transient liquid phase bonding in binary systems—A new parametric study

Numerical treatment of diffusional phase transformation through fully implicit control volume method

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Transient growth of second phases during solution treatment

Cited by 28 publications

References 1 publication

Mass Transfer of CO2 in a Carbonated Water–Oil System at High Pressures

Mass Transfer of CO2 in a Carbonated Water–Oil System at High Pressures

Modelling of transient liquid phase bonding in binary systems—A new parametric study

Numerical treatment of diffusional phase transformation through fully implicit control volume method

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Product

Resources

About

Mass Transfer of CO₂ in a Carbonated Water–Oil System at High Pressures

Mass Transfer of CO₂ in a Carbonated Water–Oil System at High Pressures