Uncertainty Quantification of Phase Transition Problems with an Injection Boundary

We develop an enthalpy-based modeling and computational framework to quantify uncertainty in Stefan problems with an injection boundary. Inspired by airfoil icing studies, we consider a system featuring an injection boundary inducing domain changes and a free boundary separating phases, resulting in two types of moving boundaries. Our proposed enthalpy-based formulation seamlessly integrates thermal diffusion across the domain with energy fluxes at the boundaries, addressing a modified injection condition for boundary movement. Uncertainty then stems from random variations in the injection boundary. The primary focus of our Uncertainty Quantification (UQ) centers on investigating the effects of uncertainty on free boundary propagation. Through mapping to a reference domain, we derive an enthalpy-based numerical scheme tailored to the transformed coordinate system, facilitating a simple and efficient simulation. Numerical and UQ studies in one and two dimensions validate the proposed model and the extended enthalpy method. They offer intriguing insights into ice accretion and other multiphysics processes involving phase transitions

Constructing the Lyapunov Function through Solving Positive Dimensional Polynomial System

We propose an approach for constructing Lyapunov function in quadratic form of a differential system. First, positive polynomial system is obtained via the local property of the Lyapunov function as well as its derivative. Then, the positive polynomial system is converted into an equation system by adding some variables. Finally, numerical technique is applied to solve the equation system. Some experiments show the efficiency of our new algorithm

Schiff base functionalized silica aerogels for enhanced removal of Pb (II) and Cu (II): Performances, DFT calculations and LCA analysis

Schiff base silica aerogels (SCA-X) were synthesized using amino-containing organosilanes and salicylic aldehyde as functional monomers with ethyl orthosilicate hydrolysis condensation as carrier. The influence of SCA-X on the adsorption of Pb (II) and Cu (II) under different adsorption conditions was evaluated, including the effect of solution pH, isotherm, kinetics, thermodynamics and adsorption mechanism. The batch adsorption experiments showed that SCA2 had the optimum adsorption capacity for Pb (II) (357.1 mg/g) and Cu (II) (243.9 mg/g), leading to adsorption equilibrium within 120 min and 360 min, respectively. After six adsorption–desorption cycles, SCA2 still possessed satisfactory adsorption for Pb (II) and Cu (II), demonstrating the reusability of the SCA2 adsorbent material. Kinetic studies indicated that the adsorption process could be described by a pseudo- second-order kinetic model, adsorption isotherms were in accordance with the Langmuir model, indicative of monomolecular layer adsorption. Thermodynamics evaluation revealed the nature of the adsorption process was an endothermic spontaneous process. XPS analysis combined with DFT calculations confirmed that the inter- action mechanism between SCA2 and Pb (II) occurred through the coordination between the nitrogen atom donor in the Schiff base and the oxygen atom donor in the benzene ring, while the interaction between SCA2 and Cu (II) occurred mainly through the coordination between the nitrogen atom in the Schiff base and Cu (II). Life Cycle Assessment (LCA) was introduced to analyze the environmental impact of the SCA2 fabrication process and eco-friendly approaches were provided, which eventually provided theoretical evidence for the application of as-prepared material in the handling of heavy metal effluents

Selective adsorption of Pb (II) and Cu (II) on mercapto-functionalized aerogels: Experiments, DFT studies and LCA analysis

Mercapto-functionalized aerogels (MA-X) were fabricated using γ-mercaptopropyltrimethoxysilane (MPTMS) as a modification reagent to eliminate Pb (II) and Cu (II) ions from wastewater. Mercapto-functionalized aerogel (MA2) with the MPTMS/TEOS molar ratio of 0.5 exhibited the maximum adsorption amounts of 163.99 mg/g for Pb (II) and 172.41 mg/g for Cu (II) in single ion system, respectively. In binary ion system, selective adsorption experiments revealed that the equilibrium adsorption capacity for Cu (II) (161.29 mg/g) was significantly greater than Pb (II) (90.42 mg/g), and the selectivity factor α showed greater selectivity for Cu (II), demonstrating that Cu (II) was more readily adsorbed on MA2. The results showed that adsorption was consistent with pseudo- second order model and Langmuir model. Thermodynamic results demonstrated that adsorption phenomenon was an exothermic reaction that occurred spontaneously. XPS analysis and density functional theory (DFT) simulations showed that the main mechanism for the adsorption of Pb (II) and Cu (II) on MA2 was through coordination chelation of the –SH groups with Pb (II) and Cu (II). DFT calculations showed a lower adsorption energy (Eads) of Cu (II) ( 2.72 eV) with respect to Pb (II) ( 0.80 eV), indicating that Cu (II) was more stably adsorbed on MA2 and more difficult to exchange by Pb (II). In order to determine the environmental impact of the MA2 preparation process, a life cycle assessment (LCA) was conducted and contribution of each material to MA2 production was analyzed. Finally, a strategy that is environmentally friendly and effective has been pro-posed in order to facilitate MA-X adsorbents production and to improve their application for the treatment of heavy metal polluted wastewater