Unified algebraic expression of lotus-type pore shape in solid

Wei, P. S.; Lee, B.Y.

doi:10.1016/j.ijheatmasstransfer.2021.122269

Cited by 6 publications

(30 citation statements)

References 36 publications

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“…´-m K m mol 9.68 10 4 3 from equation (2). The Henrys' law constant was chosen to increase with the pressure [27]. The maximum radius of the lotus-type pores was usually found to decrease as the imposed solute gas pressure at the top free surface increases [13][14][15].…”

Section: Resultsmentioning

confidence: 99%

“…It evidently shows that the free energy barrier decreases as the difference between the solute gas pressure and the liquid pressure on the cap increases, whereas the surface tension and the contact angle of the cap decrease. Substituting the solute gas pressure in the pore determined by the Henry's law or the Sieverts' law [27], equation (21) indicates that the lotus-type pores readily occur in the supersaturated liquid ahead of a localized concave region of the solidification front.…”

Section: Discussionmentioning

confidence: 99%

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Scaling of inter-pore spacing of lotus-type pores

2023

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The present study is to scale the inter-pore spacing and bubble radius required for controlling the porosity of the lotus-type pores in the solid during a unidirectional solidification. The porosity in solid degrade properties of material in welding, casting and additive manufacturing, etc. On the other hand, the ordered cylindrical pores in the material are often used to improve the functional properties, such as the tensile and compression stresses, the impact and acoustic energy absorption, the permeability, and the thermal and electrical conductivity, etc. Different from the traditional minimum undercooling criterion to estimate the porosity and size of lotus-type pores, this study relevantly combines the Gibbs-Thomson equation, the Young-Laplace equation, the nucleation theory, and the Henry’s law or Sieverts’ law to scale the inter-pore spacing and the critical radius of the lotus-type pores, which are considered as the same order of the wavelength and the amplitude of the morphological instability of the solidification front, respectively. This work revises the minimum undercooling criterion which ignores the nucleating bubble on the solidification front, and conducts irrelevant evaluation of the curvature of the solidification front. The present work finds the revised scaling results and available experimental data to be in good agreement. The sizes of the pores and the porosity in the solid can be successfully controlled in advance.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Scaling of inter-pore spacing of lotus-type pores

2023

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“…In this study, morphology of lotus-type pores satisfied by Young-Laplace equation and Henry's law at the bubble cap and top free surface during unidirectional solidification are parametrically presented. Instead of solving simultaneous first-order differential equations [ 10 , 11 ], this study extends previous work [ 12 ] to provide a table to get deep insight into understanding of dimensionless working parameters responsible for different shapes of lotus-type pores.…”

Section: Introductionmentioning

confidence: 86%

“…With the above assumption, the entrapped bubble in solid is divided into three segments, defined by initial contact angle, and inclination angle or contact angle of 90°, as sketched by Fig. 2 [ 12 ]. The pore shape is closely related and described by the second segment.…”

Section: System Model and Analysismentioning

confidence: 99%

“…Other than proposing a universal phase diagram and simultaneous first-order ordinary differential equations [ 10 ], Wei and Huang [ 11 ] proposed a polynomial with three degrees to predict isolated pore shapes in solid by accounting for either solute transport from the pore across the bubble cap into surrounding liquid or that from the surrounding liquid into the pore in the early stage, denoted by Cases 1 and 2, respectively. Recently, Wei and Lee [ 12 ] combined Cases 1 and 2 interrelated by interaction angle and solute transport parameter to algebraically predict morphology of lotus-type pores. The predicted pore shapes were in good agreements with available experimental results during freezing of water filled with oxygen gas and carbon dioxide, and liquid copper imposed by hydrogen gas.…”

Section: Introductionmentioning

confidence: 99%

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