Solute convection effects on a bubble entrapped as a pore during unidirectional upward solidification

•Strong horizontal flow deflects the pore shape toward the downstream direction.•Upward flow near the bubble cap is dominated by pressure difference across the cap.•Vertical velocity component at the bubble cap is responsible for time for bubble entrapment.•Time for bubble entrapment is scaled to reflect dominant effects of solute transport.•There exist local maximum concentration regions in triangle shapes near the triple- phase line. A transport model is proposed to predict entrapment of a bubble during unidirectional upward solidification. Pore formation and its shape in solid influence not only microstructure of materials, but also contemporary issues of various sciences of biology, engineering, foods, geophysics and climate change, etc. In this study, COMSOL computer code is used to solve conservation equations of mass, momentum, energy and solute concentration in liquid, gas and solid phases satisfied by their interfacial conditions. It shows that strong convection deflects the pore growth toward the downstream direction. Time for bubble entrapment, however, depends on the ratio between square of concentration boundary layer thickness and solute diffusivity. Concentration boundary layer thickness is proportional to solute diffusivity divided by difference in bubble growth rate and vertical component of fluid velocity at the bubble cap. The latter is almost independent of incoming horizontal flow. Solute diffusion is therefore the mechanism responsible for bubble entrapment, where the bubble growth rate and vertical velocity component of fluid at the bubble cap are of the same order of magnitude. A triangle region with local high concentration is also found to occur in solid region near the triple-phase line. Predicted contact angle agrees with that obtained from the Abel’s equation of the first kind during solidification. This work provides a general model for a fundamental and systematical understanding of mechanisms of a bubble entrapped as a pore in solid.