Scaling of inter-pore spacing of lotus-type pores

Abstract

The present study is to scale the inter-pore spacing and bubble radius required for controlling the porosity of the lotus-type pores in the solid during a unidirectional solidification. The porosity in solid degrade properties of material in welding, casting and additive manufacturing, etc. On the other hand, the ordered cylindrical pores in the material are often used to improve the functional properties, such as the tensile and compression stresses, the impact and acoustic energy absorption, the permeability, and the thermal and electrical conductivity, etc. Different from the traditional minimum undercooling criterion to estimate the porosity and size of lotus-type pores, this study relevantly combines the Gibbs-Thomson equation, the Young-Laplace equation, the nucleation theory, and the Henry’s law or Sieverts’ law to scale the inter-pore spacing and the critical radius of the lotus-type pores, which are considered as the same order of the wavelength and the amplitude of the morphological instability of the solidification front, respectively. This work revises the minimum undercooling criterion which ignores the nucleating bubble on the solidification front, and conducts irrelevant evaluation of the curvature of the solidification front. The present work finds the revised scaling results and available experimental data to be in good agreement. The sizes of the pores and the porosity in the solid can be successfully controlled in advance.


Interfacial physico-chemical equilibrium control of lotus-type pore formation in solid

“…The key assumptions underlying this phenomenon are that lotus pores with a spherical cap emerge from distributed spherical bubbles within a static liquid and grow symmetrically along their axis. The interpore spacing w is a consequence of morphological instability [18]. Furthermore, the pores exclusively contain solute gas, with any vaporized gas from the solvent being negligible.…”

Parametric Control via the Algebraic Expression of Lotus-Type Pore Shapes in Metals

“…Based on the analytical solute concentration in liquids and the minimum undercooling criterion provided by the Jackson–Hunt model during eutectic solidification, Liu et al [ 10 ] predicted and experimentally confirmed decreases in porosity, pore radius, and inter-pore spacing as solidification speed, total gas pressure, and partial pressure of hydrogen and argon increased during the gasarite solidification of copper. The Jackson–Hunt theory and analytical solutions of solute concentration were, however, criticized by Lee et al [ 11 ], Drenchev et al [ 12 ], and Wei et al [ 13 ]. Lu et al [ 14 ] also provided a simple thermodynamic model to describe the relationship between processing variables and the pore structure for the ordered porosity copper fabricated via directional solidification.…”