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

Lotus-type porous metals, characterized by low densities, large surface areas, and directional properties, are contemporarily utilized as lightweight, catalytic, and energy-damping materials; heat sinks; etc. In this study, the effects of dimensionless working parameters on the morphology of lotus-type pores in metals during unidirectional solidification were extensively investigated via general algebraic expressions. The independent dimensionless parameters include metallurgical, transport, and geometrical parameters such as Sieverts' law constant, a partition coefficient, the solidification rate, a mass transfer coefficient, the imposed mole fraction of a solute gas, the total pressure at the top free surface, hydrostatic pressure, a solute transport parameter, inter-pore spacing, and initial contact angle. This model accounts for transient gas pressure in the pore, affected by the solute transfer, gas, capillary, and hydrostatic pressures, and Sieverts' laws at the bubble cap and top free surface. Solute transport across the cap accounts for solute convection at the cap and the amount of solute rejected by the solidification front into the pore. The shape of lotus-type pores can be described using a proposed fifth-degree polynomial approximation, which captures the major portions between the initial contact angle and the maximum radius at a contact angle of 90 degrees, obtained by conserving the total solute content in the system. The proposed polynomial approximation, along with its working parameters, offers profound insights into the formation and shape of lotus-type pores in metals. It systematically provides deep insights into mechanisms that may not be easily revealed with experimental studies. The prediction of a lotus-type pore shape is thus algebraically achieved in good agreement with the available experimental data and previous analytical results.