Bond number effects on pore shape in solid

The pore shape affected by Bond number, indicating the ratio between hydrostatic pressure and capillary pressure, of a bubble entrapped by a solidification front is predicted. Bond number is responsible for bubble nucleation, surface area and shape of the bubble or pore cap beyond the solidification front. Surface area determines solute transport across the cap, whereas contact angle of the cap delineates pore shape in solid. The critical velocity for entrapment of a bubble is also related to Bond number. Pore formation in solid influence not only microstructure of materials, but also contemporary issues of biology, engineering, foods, geophysics and climate change, etc. This work extends previous models accounting for mass and momentum transport of solute across a coupled shape of the bubble cap to predict the pore shape in solid. The study also accounts for different directions and magnitudes of solute transport across the cap in different cases. Case 1 is subject to solute transport from the pore across an emerged cap in a concentration boundary layer on the solidification front to surrounding liquid in the early stage. Case 2 indicates solute transport across a submerged cap in a concentration boundary layer to the pore. In contrast to Case 2a, pore value expansion in Case 2b exhibits a more important role in solute concentration at the cap than solute transport across the cap in the late stage. The results show that an increase in Bond number decreases pore radius and time for bubble entrapment in Case 1. An isolated pore cannot be formed in Cases 2a and 2b. The predicted growth and entrapment of a tiny bubble as a pore in solid are found to agree with experimental data. A realistic prediction and control of the pore shape in solid via Bond number has therefore been obtained.