Using Working Parameters to Control Formation and Shape of Lotus-Type Pores

Abstract

The development and final shape of lotus-type pores can be manipulated in advance during unidirectional solidification in this study. Independent parameters considered are solidification rate, ambient pressure, and factor accounting for solute concentration at a selected reference state in liquid deviated from that at the top surface. Lotus-type porous materials have contemporarily been used in heat sinks, energy including shock, vibration, and sound absorption in aircraft engines, etc., which strongly depend on directions, distributions, and pore shapes in solid. This model accounts for transient gas pressure in the pore affected by solute transfer, gas, capillary and hydrostatic pressures, and Sieverts’ law or Henry’s law at the bubble cap and top surface. Solute transport across the cap self-consistently accounts for solute convection at the cap based on a reference concentration deviated from that at the top free surface, the amount of solute rejected by the solidification front into the pore, and the convection-affected concentration at the solidification front. The resulting simultaneous systems of unsteady first-order ordinary differential equations are solved by a MATLAB code. The length of lotus-type pores is also interpreted by the conservation of the solute content in the system. The predicted final shapes of lotus-type pores agree with algebraic results previously confirmed by available experimental data.