Analytical expression for isolated pore shape in solid

Abstract

Algebraic expressions for the pore shape after a bubble completely entrapped in solid are provided in this study. Properties of functional materials in micro-or nano-technologies strongly depend on pore shapes in solid. The model is based on a previous work by accounting for transient gas pressure in the pore affected by solute transfer for different cases, and balance of gas, capillary and hydrostatic pressures, and physico-chemical equilibrium at the bubble cap. The results find that algebraic prediction of the pore shapes with exact expressions of the maximum pore radii in different cases can be accomplished by dividing the pore length into three segments with inclination angles greater than initial contact angle, between initial contact angle and 90 degrees, and less than 90 degrees. The shape of an isolated pore is thus delineated by the bottom spherical cap, radius and length at the initial contact angle and maximum pore radius and length at inclination angle of 90 degrees, and top spherical cap. Dimensionless independent parameters controlling the pore length include initial contact angle, mass transfer coefficient, supersaturation ratio, product of Bond number with initial solute concentration in liquid, Henry's law constant (in Cases 1-3), and partition coefficient (in Cases 3 and 4). The predicted lengths in three segments and shapes of the isolated pore agree with numerical computations confirmed by experimental data.