Solute segregation due to a bubble entrapped as a pore in solid during unidirectional solidification

Abstract

Solute segregation of carbon dioxide in water during entrapment of a bubble by a solidification front is numerically investigated. The bubble can be initiated by supersaturation ahead of the solidification front. Porosity influences not only microstructure of materials, but also formation of functional materials in biology, engineering, foods, and geophysics, and so on. The model was proposed in a previous work accounting for conservation equations with interfacial balances of mass, momentum, energy and concentration. Using commercial COMSOL computer code, this study further finds that different solute distributions in liquid and solid in the presence of an entrapping bubble can be attributed to solute diffusivity of liquid and partition coefficient. A high solute diffusivity of liquid enhances solute diffusion away from the pore along the solidification front, leading to negligible solute transport from liquid to solidification front, whereas a low solute diffusivity of liquid gives rise to significant solute transport from the solidification front to liquid. A decrease in solute diffusivity of liquid or partition coefficient therefore results in high solute accumulation and a high concentration region covering liquid and solid in a triangle shape near the triple-phase line. In contrast to exponential decrease for a high solute diffusivity of liquid, radial variation of solute concentration in solid in the vicinity of pore jumps to high value through the high concentration region and maintains relative constant for a low diffusivity of liquid. Solute concentration in solid significantly decreases as solute diffusivity of liquid or partition coefficient increases. Predicted contact angle agree with solutions of Abel's equation of the first or second kind. This work is critical to understand solute segregation induced by formation of a pore in solid.