Abstract
Mechanisms of the length and maximum radius of lotus-type or single pores in ice or nonmetals satisfied by Henry's law at gas-liquid interfaces dissolved by a gas during unidirectional solidification are rigorously investigated and supported by a Table from algebraic predictions involving different dimensionless working parameters. Lotus-type porous materials characterized by directional properties have been often used as functional materials in food, biomedical, and micro- and nano-technologies. Following previous work taking into account solute amount and transport within the pore, and concentration boundary layers on the advancing solid-liquid interface and bubble cap, and the Young-Laplace equation and Henry's law at liquid-gas interfaces, the algebraic study further provides a Table for a quantitative and extensive understanding of different mechanisms of length and maximum radius. Dimensionless parameters include solute transport parameters of Henry's law constant, mass transfer coefficient, partition coefficient, solute gas amount in imposed ambient, and solute transport parameter, and fluid and thermal parameters of solidification rate, imposed gas pressure, hydrostatic pressure, and geometrical parameter of inter-pore spacing. The controlling of the shapes of lotus-type pores is achieved by a good comparison between predicted maximum diameter and inter-pore spacing during freezing of water dissolved by oxygen gas.