Ou Y T, Wei P S
Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan.
Heliyon. 2024 Feb 14;10(5):e26224. doi: 10.1016/j.heliyon.2024.e26224. eCollection 2024 Mar 15.
Sufficient conditions to control solute transport across the cap responsible for the formation, development, and final shape of the lotus-type pores for different spatial variations of the partition coefficient, and the ratio between concentration in solid at the solidification front and concentration at a reference state near the top free surface during unidirectional solidification are presented in this study. Lotus-type porous material contemporarily used in micro-or nano-technologies strongly depend on distributions, orientations, and shapes of pores in solid. The model accounts for solute pressure in the pore affected by solute transport and balance of gas, capillary and hydrostatic pressures, and Sieverts' law or Henry's law at the bubble cap and top free surface. Solute transport across the cap accounts for rejection and convection-affected concentration at solidification front, and convection based on the reference state deviated from that at the top free surface. The resulting simultaneous systems of unsteady first-order ordinary differential equations are solved by MATLAB code. Changing rate of solute pressure in the pore responsible for entrapment and final length of lotus-type pores affected by volume expansion, and solute transport due to diffusion and rejection by the solidification front at the cap is also analyzed. The predicted shapes of lotus-type pores agree with algebraic expression confirmed by available experimental data.
本研究给出了在单向凝固过程中，针对不同分配系数空间变化以及凝固前沿固体中浓度与顶部自由表面附近参考状态下浓度之比，控制溶质通过帽状物传输的充分条件，而帽状物负责莲花型气孔的形成、发展及最终形状。当代用于微纳技术的莲花型多孔材料强烈依赖于固体中气孔的分布、取向和形状。该模型考虑了溶质传输对气孔中溶质压力的影响，以及气体、毛细管压力和静水压力的平衡，还有气泡帽和顶部自由表面处的西韦茨定律或亨利定律。溶质通过帽状物的传输考虑了凝固前沿的排斥和对流影响浓度，以及基于偏离顶部自由表面参考状态的对流。通过MATLAB代码求解由此产生的非稳态一阶常微分方程组。还分析了气孔中溶质压力的变化率，其负责截留和受体积膨胀影响的莲花型气孔的最终长度，以及由于扩散和凝固前沿在帽状物处的排斥导致的溶质传输。莲花型气孔的预测形状与现有实验数据证实的代数表达式相符。
