Existence of an isolated pore in solid during unidirectional solidification

Abstract This study provides the universal curves for exact predictions of the existence or effective or maximum radius of an isolated pore resulting from a bubble entrapped by a solidification front. Formation and size of an isolated pore in solid plays an important role in predicting and controlling microstructural defects in products, manufacturing functional materials, devices or detectors in nanotechnology and bioengineering and understanding atmospheric phenomena, and so on. The study extends previous work accounting for time-dependent solute gas pressure in the pore due to solute transport across the bubble cap on which balance of pressures and physico-chemical equilibrium are satisfied. Four cases are referred to different evaluations of solute transport rate across the bubble cap in different directions in the literature. The results find that the maximum radius at contact angle of 90 degrees of an isolated pore can be exactly and universally calculated under dimensionless parameters of supersaturation ratio, solidification rate-to-mass transfer coefficient ratio, Henry’s law constant, product of Bond number with initial liquid concentration and partition coefficient in different solute transport models at contact angle of 90 degrees. Regardless of how the bubble initiates, existence and maximum radius of the isolated pore only depend on dimensionless parameters at contact angle of 90 degrees. Predicting and controlling of existence of an isolated pore in solid are thus provided. Predicted pore radii for different models agree quite well with experimental data in the literature.