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

Abstract

This study presents a challenging analysis of interfacial equilibrium conditions that control the evolution of lotus-type pores in both metals and nonmetals during solidification. It incorporates Henry’s or Sieverts’ law, affecting solute transfer at the cap and top free surface, and pore evolution. The significance of the directional and lightweight characteristics of lotus-type porous materials makes them vitally important in functional heat sinks, energy absorption, biomedical devices, and other applications. The study extends previous solute transfer models based on solute concentration deviations in the liquid from the top surface and convection-affected segregation at the advancing liquid-solid interface by further considering the effects of interfacial equilibrium conditions on pore development. Typical data selected for the dimensionless Henry’s law constant at the cap and top free surface is 0.175, while the Sieverts’ law constant at the cap and top free surface is 0.03. MATLAB Simulink and Simscape (version R2020b) with the solver ode113 are utilized to solve the resulting simultaneous system of unsteady first-order differential equations. The results show that the size of lotus-type pores increases as the Henry’s law constant at the cap decreases while the Henry's law constant at the top free surface increases. Similar results are observed for Sieverts’ law. Lotus-type pores readily form as the Henry’s law constant at the cap increases while that at the top free surface decreases. The lotus pore length can also be determined and interpreted algebraically using solute content conservation. The model's predictions closely match analytical findings previously validated by experimental data.