Sufficient conditions using liquid concentration profile to control formation and shape of lotus-type pores in solid

Sufficient conditions to control solute transport across the cap responsible for the formation, development, and final shape of the lotus-type pores for different spatial variations of the partition coefficient, and the ratio between concentration in solid at the solidification front and concentration at a reference state near the top free surface during unidirectional solidification are presented in this study. Lotus-type porous material contemporarily used in micro-or nano-technologies strongly depend on distributions, orientations, and shapes of pores in solid. The model accounts for solute pressure in the pore affected by solute transport and balance of gas, capillary and hydrostatic pressures, and Sieverts' law or Henry's law at the bubble cap and top free surface. Solute transport across the cap accounts for rejection and convection-affected concentration at solidification front, and convection based on the reference state deviated from that at the top free surface. The resulting simultaneous systems of unsteady first-order ordinary differential equations are solved by MATLAB code. Changing rate of solute pressure in the pore responsible for entrapment and final length of lotus-type pores affected by volume expansion, and solute transport due to diffusion and rejection by the solidification front at the cap is also analyzed. The predicted shapes of lotus-type pores agree with algebraic expression confirmed by available experimental data.