Geometric Control of Lotus-Type Pore Formation in Solids

This study explores the manipulation of formation and shape of the lotus-type pores during unidirectional solidification, considering various geometrical parameters such as initial liquid layer thickness and contact angle, Bond number, and interpore spacing. Lotus porous materials are valued for their lightweight, air permeability, and anisotropic physical, thermal, and mechanical properties, making them useful in micro- or nano-technologies such as heat sinks, filters, energy absorption, and biomedical devices. In this model, unsteady solute gas pressure in the pore is balanced by capillary and hydrostatic pressures, as well as interfacial physicochemical equilibrium and appropriate evaluation of solute transfer through the cap. Henry’s law and Sieverts’ law for interfacial physicochemical equilibrium apply to nonmetals and metals, respectively. The resulting simultaneous unsteady ordinary differential equations are solved using the MATLAB/Simulink - Simscape toolbox (version R2020b). Typical data selected include a dimensionless initial liquid layer thickness of 6,000, an initial contact angle of \(120^{0}\) ${120}^0$ , a Bond number of \(7 \times 10^{ - 5}\) $7\times {10}^{-5}$ , and an interpore spacing of 3. Regardless of whether Henry’s or Sieverts’ law applies at the liquid-gas interfaces, the computed results show that lotus pores readily form as the initial liquid layer thickness, Bond number, and interpore spacing decrease, while the length of lotus pores increases with increasing initial liquid layer thickness, initial contact angle, Bond number, and decreasing interpore spacing. Conservation of solute within the system aids in interpreting pore shapes, which align well with previous algebraic and experimental results.