“…This is because of increase in solute amount in the boundary layer on the advancing solid-liquid interface at initial time. Predicted result also agrees with that of a single isolated pore and specification of solute concentration in liquid far from the pore [ [10] , [11] , [12] ]. Fig.…”
Section: Resultssupporting
confidence: 78%
“…Lotus-type pores in solid are algebraically predicted for different independent dimensionless working parameters based on selected typical values of = = 34, = 0.11, = 0.035, = 0.0088, = 0.008, = 0.09, = 0.03, = 790, = 7.86, = 1, w = 2.5, = 140° , and = 1 . Instead of solving simultaneous first-order ordinary equations [ 10 ], algebraic equations explicitly gain deep insight into mechanisms of length and maximum radius of lotus-type or single pores. Henry's law constants are allowed to be different at the bubble cap and top free surface, since the latter is higher than the former due to a decrease in surface curvature [ 23 ].…”
Section: Resultsmentioning
confidence: 99%
“…In this study, morphology of lotus-type pores satisfied by Young-Laplace equation and Henry's law at the bubble cap and top free surface during unidirectional solidification are parametrically presented. Instead of solving simultaneous first-order differential equations [ 10 , 11 ], this study extends previous work [ 12 ] to provide a table to get deep insight into understanding of dimensionless working parameters responsible for different shapes of lotus-type pores.…”
Section: Introductionmentioning
confidence: 87%
“…Diameter and inter-pore spacing were found to be inversely proportional product of solidification rate with square root of ambient pressure, agreeing with measurements. Other than proposing a universal phase diagram and simultaneous first-order ordinary differential equations [ 10 ], Wei and Huang [ 11 ] proposed a polynomial with three degrees to predict isolated pore shapes in solid by accounting for either solute transport from the pore across the bubble cap into surrounding liquid or that from the surrounding liquid into the pore in the early stage, denoted by Cases 1 and 2, respectively. Recently, Wei and Lee [ 12 ] combined Cases 1 and 2 interrelated by interaction angle and solute transport parameter to algebraically predict morphology of lotus-type pores.…”
“…This is because of increase in solute amount in the boundary layer on the advancing solid-liquid interface at initial time. Predicted result also agrees with that of a single isolated pore and specification of solute concentration in liquid far from the pore [ [10] , [11] , [12] ]. Fig.…”
Section: Resultssupporting
confidence: 78%
“…Lotus-type pores in solid are algebraically predicted for different independent dimensionless working parameters based on selected typical values of = = 34, = 0.11, = 0.035, = 0.0088, = 0.008, = 0.09, = 0.03, = 790, = 7.86, = 1, w = 2.5, = 140° , and = 1 . Instead of solving simultaneous first-order ordinary equations [ 10 ], algebraic equations explicitly gain deep insight into mechanisms of length and maximum radius of lotus-type or single pores. Henry's law constants are allowed to be different at the bubble cap and top free surface, since the latter is higher than the former due to a decrease in surface curvature [ 23 ].…”
Section: Resultsmentioning
confidence: 99%
“…In this study, morphology of lotus-type pores satisfied by Young-Laplace equation and Henry's law at the bubble cap and top free surface during unidirectional solidification are parametrically presented. Instead of solving simultaneous first-order differential equations [ 10 , 11 ], this study extends previous work [ 12 ] to provide a table to get deep insight into understanding of dimensionless working parameters responsible for different shapes of lotus-type pores.…”
Section: Introductionmentioning
confidence: 87%
“…Diameter and inter-pore spacing were found to be inversely proportional product of solidification rate with square root of ambient pressure, agreeing with measurements. Other than proposing a universal phase diagram and simultaneous first-order ordinary differential equations [ 10 ], Wei and Huang [ 11 ] proposed a polynomial with three degrees to predict isolated pore shapes in solid by accounting for either solute transport from the pore across the bubble cap into surrounding liquid or that from the surrounding liquid into the pore in the early stage, denoted by Cases 1 and 2, respectively. Recently, Wei and Lee [ 12 ] combined Cases 1 and 2 interrelated by interaction angle and solute transport parameter to algebraically predict morphology of lotus-type pores.…”
“…Equations (10)-( 16) stand for time derivatives of advancing liquid-solid interface location, apex radius [19,20], Abel's equation of the first kind [21], pore volume below the advanced liquid-solid interface, pore volume, and liquid layer thickness and cap height [19,20], respectively. Equations (7) or (8) and (10)-( 16) are thus solved using the computer code MATLAB Simulink and Simscape (version R2020b) with the solver ode113, marching from initial condition equation (17) with the maximum time step of 10 , 2 and absolute and relative errors of 1.…”
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.
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