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Analytical expression for isolated pore shape in solid

机译：固体分离的孔形状的分析表达

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摘要

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.
机译：在本研究中提供了在固体夹带的气泡之后的孔形状的代数表达。微型或纳米技术中功能材料的性质强烈依赖于固体中的孔形状。该模型基于以前的工作，通过核对孔隙的瞬态气体压力受到不同案例的溶质，以及气体，毛细管和静水压力的平衡，以及气泡帽的物理化学平衡。结果发现，在不同情况下，通过将孔长度划分为大于初始接触角的三个区段，在初始接触角和90度之间，可以通过将孔长度划分为三个区段来实现具有不同情况下的最大孔径半径的精确表达的孔形状的代数预测。小于90度。因此，隔离孔的形状由底部球形帽，半径和长度在初始接触角和最大孔半径和以90度的倾斜角度和顶部球形帽的长度上描绘。控制孔长度的无量纲独立参数包括初始接触角，传质系数，超饱和度，粘合数的产物，液体初始溶液浓度，亨利的法律常数（在1-3例）和分区系数（在3和4例中）。分离孔的三个段和形状的预测长度与由实验数据确认的数值计算同意。

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