Using the universal phase diagrams to describe pore shape development in solid for different solidification rates

• Published in: International journal of heat and mass transfer Vol. 158; p. 119977
• Main Authors: Wei, P.S., Wu, C.M., Huang, Y.K., Chang, C.C.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.09.2020; Elsevier BV
• Subjects: Boundary conditions; Bubble capture; Bubble entrapment; Bubbles; Contact angle; Contact pressure; Coordinates; Equations of state; Functional materials; Gas pressure; Geophysics; Laplace equation; Liquid-solid interfaces; Mass transfer; Phase change; Phase diagram; Phase diagrams; Pore formation; Pore shape; Porosity; Solidification; Solidification defect; Solids; Temperature gradients; Phase diagram; Phase change; Pore shape; Bubble entrapment; Porosity; Bubble capture; Pore formation; Solidification defect
• DOI: 10.1016/j.ijheatmasstransfer.2020.119977
• ISSN: 0017-9310

•The general shapes of a pore resulted from a tiny bubble captured by a solidification front can be self-consistently described by the universal and unique three phase diagrams.•Phase diagrams account for solidification rate and apex radius determined by Stefan boundary condition and Young-Laplace equation, respectively.•Phase diagrams can predict pore shapes for Cases 1 and 2 subject to solute transport across the cap in different directions in early stage.•Phase diagrams confirm that the bubble can be completely entrapped in Cases 1 and 2a. In contrast to Case 2b, Case 2a represents a stronger effect of solute transport from the surrounding liquid into pore on solute gas pressure than volume expansion of the pore in the early stage.•Case 2b is the only case which cannot be entrapped as an isolated pore in solid. This study shows that there exist the universal three phase diagrams to describe general development of the pore shape in solid, resulting from a bubble captured by a solidification front with different solidification rates. Pore formation and its shape strongly determine microstructural quality of materials, functional materials encountered in biology, chemistry, engineering, foods, and phenomena of geophysics and climate change, and so on. The solidification rate plays an important role in solute transport and gas pressure, contact angle of the bubble cap, and pore shape in solid. Three universal phase diagrams are under dimensionless coordinate systems of (1) solidification rate, temperature gradients in solid and liquid at the solidification front, (2) solidification rate, contact angle and growth rate of base radius of the cap, and (3) apex radius, contact angle and base radius of the cap. Solidification rate is determined by temperature gradients in liquid and solid at the solid-liquid interface governed by the Stefan boundary condition, whereas apex radius is determined by solute gas pressure in the pore governed by the Young-Laplace equation, equation of state, and different cases governing directions of mass transfer in the pore. Extending previous analysis, phase diagrams in this study confirm that the bubble cannot be completely entrapped in Case 2b, which represents a stronger effect of pore volume expansion on solute gas pressure than solute transport from the surrounding liquid to pore in the early stage. The computed and measured results of development of the pore shape are in good agreement.