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

Abstract

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.