Effects of mass transfer coefficient on pore shape in solid

The shape of a pore resulting from a nucleated bubble entrapped by a solidification front for different mass transfer coefficients is predicted in this work. Mass transfer coefficient associated with different reference concentrations is used to determine different characteristics of solute transfer rate across the cap of the pore or bubble responsible for the pore shape in solid. Pore formation and its shape in solid influence 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 self-consistently determined shape of the bubble cap whose surface is satisfied by physico-chemical equilibrium beyond the solidification front, to study different mechanisms for pore formation. Mechanism of pore formation can be Case 1, which is subject to solute transport from the pore across an emerged cap through the concentration boundary layer on the solidification front into surrounding liquid in the early stage. Cases 2a and 2b are referred to opposite directions of solute transport across a submerged cap in the concentration boundary layer. In contrast to the former, the latter exhibits stronger effects of pore volume expansion on solute gas pressure in the pore than solute transport. The results show that an increase in mass transfer coefficient decreases pore radius and time for bubble entrapment in Case 1. An isolated pore cannot be found in Cases 2a and 2b, since solute concentration at the cap increases and decreases rapidly in the late stage, respectively. The predicted pore shape in solid agrees with experimental data. Mass transfer coefficient associated with solidification rate can be used to control the pore shape, which strongly depends on directions and magnitudes of solute transport.