Influence of variable diffusion coefficient on solid-liquid interface migration kinetics during transient liquid phase bonding

Ghanbar, A.; Michael, D. E.; Ojo, O.A.

doi:10.1080/14786435.2019.1615149

Cited by 9 publications

(5 citation statements)

References 15 publications

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“…Instead, the diffusion coefficients vary with temperature based on the Arrhenius equation [6]. Moreover, the diffusion coefficient in the solid also varies with solute concentration, so it will be modeled with the concentration-dependent relation used by Ghanbar et al, [13] as shown in Eq. [7].…”

Section: A Governing Equationsmentioning

confidence: 99%

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Numerical Simulation Study of Temperature Gradient Transient Liquid Phase Bonding with Concentration-Dependent Diffusivity

Bamidele

Ojo

2021

Metall Mater Trans A

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A new numerical model is developed to study the kinetics of temperature gradient transient liquid phase (TG-TLP) bonding under concentration-dependent diffusivity by using a first-order implicit-explicit finite-difference numerical method and Landau coordinate transformation with adaptable spatial discretization. The model is validated with experimental data reported in the literature. The results of computational analysis by the new model show that the presence of solute concentration gradient in the liquid is the major factor that enables shorter solidification completion time in TG-TLP bonding compared to the conventional transient liquid phase bonding (C-TLP bonding). In contrast to the common assumption that solid-state diffusion can be ignored during the modeling of TG-TLP bonding, this work shows that solid-state diffusion plays a significant role, not only in controlling the transition in solidification behavior from bidirectional to unidirectional, but also affects the kinetics of the bonding process. Moreover, it is found that the anomalous increase in solidification completion time with increase in temperature that occurs during C-TLP bonding can be avoided by TG-TLP bonding. This is possible if the solute concentration gradient in the liquid is sufficiently high to enable adequate solidification kinetics to overcome increased volume of liquid that accompanies increase in bonding temperature.

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Section: A Governing Equationsmentioning

confidence: 99%

“…The future interface positions s1 nþ1 and s2 nþ1 are determined by using the interface solutions calculated with Eqs. [13] and [14], respectively. 4.…”

Section: Moving Boundary Equationsmentioning

confidence: 99%

Numerical Simulation Study of Temperature Gradient Transient Liquid Phase Bonding with Concentration-Dependent Diffusivity

Bamidele

Ojo

2021

Metall Mater Trans A

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“…The diffusion and moving boundary equations used to model the TLP processing in planar and non-planar systems are shown as follows [18]; …”

Section: Development Of the Numerical Modelmentioning

confidence: 99%

“…This method enables the model to adequately converge and improves its flexibility to analyse several boundary conditions in planar and non-planar systems, even in cases where the diffusion coefficient is not constant. A similar hybrid approach has been recently used by the present authors to study the influence of concentration and time dependency of diffusivity on the kinetics of solid–liquid interface migration in planar systems [18]. The hybrid approach allows the use of explicit finite difference method for the solid-state diffusion without sacrificing computational efficiency by enabling the solutions to be stable at relatively larger time steps.…”

Section: Development Of the Numerical Modelmentioning

confidence: 99%

Effect of non-planar geometry on diffusion kinetics during brazing repair process

Ghanbar

Ojo

2020

Materials Science and Technology

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A new finite difference numerical model is used to study the influence of non-planar (cylindrical and spherical) solid–liquid interface geometry on the kinetics of isothermal solidification during diffusion brazing or transient liquid phase repair process. Notwithstanding that limited work had been reported on non-planar systems, this study shows that non-planarity of the solid–liquid interface can have significant effects on the kinetics of solid–liquid phase transformation during the repair process, which are crucial to the understanding and optimisation of the repair process in non-planar systems.

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“…It is important to state that, in many works related to Langmuir’s model, the authors considered constant mass diffusivity [ 22 , 23 , 24 , 25 , 26 ]. However, this assumption is not completely consistent with the real process behavior, since the moisture migration rates are higher at the shorter process times and decrease for longer times; therefore, mass diffusivity varies with the water concentration inside the material [ 27 ]. Even among the works that consider variable mass diffusivity (with the general Fick´s model), there are still few studies that established the mass diffusion coefficient as a function of the average moisture content [ 28 , 29 , 30 , 31 , 32 ], and almost none that consider mass diffusion coefficient as a function of the local moisture content inside the material.…”

Section: Introductionmentioning

confidence: 99%

Non-Fickian Moisture Absorption in Vegetable Fiber Reinforced Polymer Composites: The Effect of the Mass Diffusivity

2021

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This article aims to study the non-Fickian water absorption process in vegetable fiber-reinforced polymer composite using the Langmuir-type model, evaluating the influence of mass diffusivity on the process. The numerical solutions of the governing equations were obtained using the finite-volume method. Transient results of the local and average moisture content, free and entrapped water molecules concentration considering the constant diffusivity and as a function of the average and local moisture content were presented and analyzed. It was observed that the mass diffusivity effectively influences the water absorption behavior, especially in the initial time of the process, where higher differences in the water migration rates into the material are found. The largest free and entrapped water molecule concentration gradients were found close to the composite surface, especially when considering constant mass diffusivity.

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Influence of variable diffusion coefficient on solid-liquid interface migration kinetics during transient liquid phase bonding

Cited by 9 publications

References 15 publications

Numerical Simulation Study of Temperature Gradient Transient Liquid Phase Bonding with Concentration-Dependent Diffusivity

Numerical Simulation Study of Temperature Gradient Transient Liquid Phase Bonding with Concentration-Dependent Diffusivity

Effect of non-planar geometry on diffusion kinetics during brazing repair process

Non-Fickian Moisture Absorption in Vegetable Fiber Reinforced Polymer Composites: The Effect of the Mass Diffusivity

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