Unified algebraic expression of lotus-type pore shape in solid

Abstract

Algebraic expressions for the shapes of lotus-type or isolated pores after bubbles completely entrapped in solid during unidirectional solidification are provided in this study. Functional materials of lotus-type porous metals are fabricated by unidirectional solidification of molten metals dissolving gasses such as hydrogen, oxygen or nitrogen. In view of superior and anisotropic features of mechanical, thermal and electrical properties, unidirectional lotus-type pore materials have been widely used in bio-, micro- and nano-technologies. The present model is based on a previous work by accounting for transient gas pressure in the pore affected by solute transfer and balance of gas, capillary and hydrostatic pressures, and physico-chemical equilibrium at the bubble cap. Solute transport across the bubble cap during solidification can be in different directions as previously denoted by Cases 1 and 2 due to relative magnitude between height of bubble cap and thickness of the concentration boundary layer on the solidification front. Proposing the self-consistently unified model combining Cases 1 and 2 and introducing a solute transport parameter, algebraic expressions of lotus-type pores and isolated pore can be obtained. Predicted and measured maximum radius, total length, inter-pore spacing, aspect ratio and porosity of lotus-type pores subject to Henry's law and Sievert's law as well as shape of an isolated pore during unidirectional solidification of water containing oxygen gas, liquid copper containing hydrogen, and water containing carbon dioxide, respectively, agree quite well.