The shapes of a pore resulting from an entrapped bubble by a solidification front for different locations of the bubble below the free surface are predicted in this work. Bubble location is an important factor affecting temperature gradient in liquid, solute gas dissipated into the ambient, heterogeneous nucleation of the bubble and shape of the bubble cap, and subsequent entrapment and the pore shape in solid. The shapes of pores in solid influence not only material properties, but also contemporary issues of engineering, biology, medical technology and science, etc. This study takes into account solute transport across a coupling shape of the pore cap determined by the Young-Laplace equation governing balance of liquid, gas and capillary pressures. The results find that increases in depthwise location of a bubble increase pore radius and time for bubble entrapment as solute transport is from the pore across cap emerged through a concentration boundary layer along the solidification front into surrounding liquid in the early stage. On the other hand, the bubble cannot be entrapped, provided that solute transport in opposite directions across the cap submerged in a concentration boundary layer along the solidification front. The predicted growth and entrapment of a tiny bubble as a pore in solid agree with experimental data. Understanding and controlling of the pore shape via controlling bubble location is of interest and challenging.

The shapes of a growing or decaying bubble entrapped by a solidification front are predicted in this work. The bubble results from supersaturation of a dissolved gas in the liquid ahead of the solidification front. Pore formation and its shape in solid are one of the most critical factors affecting properties, microstructure, and stresses in materials. In this study, the bubble and pore shapes entrapped in solid can be described by a three-dimensional phase diagram, obtained from perturbation solutions of Young-Laplace equation governing the tiny bubble shape in the literature. The predicted growth and entrapment of a microbubble as a pore in solid are found to agree with experimental data. This work thus provides a realistic prediction of the general growth of the pore shape as a function of different working parameters.