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High-purity copper is essential for fabricating advanced microelectronic devices, particularly integrated circuit interconnects. As the industry increasingly emphasizes scalable and efficient purification methods, this study investigates the multi-physics interactions during the semi-continuous directional solidification process, utilizing a Cu-1 wt.%Ag model alloy. Coupled simulation calculations examine the spatial distribution patterns of the impurity element silver (Ag) within semi-continuously solidified ingots under varying pulling rates and melt temperatures. The objective is to provide technical insights into the utilization of the semi-continuous directional solidification method for high-purity copper purification. The findings reveal that increasing the pulling rate and melt temperature leads to a downward shift in the solid–liquid interface relative to the mold top during processing. Alongside the primary clockwise vortex flow, a secondary weak vortex emerges near the solid–liquid interface, facilitating the migration of the impurity element Ag toward the central axis and amplifying radial impurity fluctuations. Furthermore, diverse pulling rates and melt temperature conditions unveil a consistent trend along the ingot’s height, which is characterized by an initial increase in average Ag content, followed by stabilization and then a rapid ascent during the late stage of solidification, with higher pulling rates and melt temperatures expediting this rapid ascent. Leveraging these insights, a validation experiment using 4N-grade recycled copper in a small-scale setup demonstrates the effectiveness of the semi-continuous directional solidification process for high-purity copper production, with copper samples extracted at 1/4 and 3/4 ingot heights achieving a 5N purity level of 99.9994 wt.% and 99.9993 wt.%, respectively.

Protocell models play a pivotal role in the exploration of the origin of life. Vesicles are one type of protocell model that have attracted much attention. Simple single-chain amphiphiles (SACs) and organic small molecules (OSMs) possess primitive relevance and were most likely the building blocks of protocells on the early Earth. OSM@SAC vesicles have been considered to be plausible protocell models. Pyrite (FeS2), a mineral with primitive relevance, is ubiquitous in nature and plays a crucial role in the exploration of the origin of life in the mineral–water interface scenario. “How do protocell models based on OSM@SAC vesicles interact with a mineral–water interface scenario that simulates a primitive Earth environment” remains an unresolved question. Hence, we select primitive relevant sodium monododecyl phosphate (SDP), isopentenol (IPN) and pyrite (FeS2) mineral particles to build a protocell model. The model investigates the basic physical and chemical properties of FeS2 particles and reveals the effects of the size, content and duration of interaction of FeS2 particles on IPN@SDP vesicles. This deepens the understanding of protocell growth mechanisms in scenarios of mineral–water interfaces in primitive Earth environments and provides new information for the exploration of the origin of life.

In this study, molecular dynamics (MD) simulations were employed to elucidate the processes and underlying mechanisms that govern the adsorption and accumulation of gas (represented by N2) at the hydrophobic solid–liquid interface, using the GROMACS program with an AMBER force field. Our findings indicate that, regardless of surface roughness, the presence of water molecules is a prerequisite for the adsorption and aggregation of N2 molecules on solid surfaces. N2 molecules dissolved in water can cluster even without a solid substrate. In the gas–solid–liquid system, the exclusion of water molecules at the hydrophobic solid–liquid interface and the adsorption of N2 molecules do not occur simultaneously. A loosely arranged layer of water molecules is initially formed on the hydrophobic solid surface. The two-stage process of N2 molecule adsorption and accumulation at the hydrophobic solid/liquid interface involves initial adsorption to the solid surface, displacing water molecules, followed by N2 accumulation via self-interaction after saturating the substrate’s surface. The process and underlying mechanisms of gas adsorption and accumulation at hydrophobic solid/liquid interfaces elucidated in this study offer a molecular-level understanding of nano-gas layer formation.

PbF2 single crystals are usually grown in the temperature gradient region by the Bridgman–Stockbarger method. Temperature distribution during the growth process is particularly important for the preparation of high-quality crystals. In this study, the temperature field during the growth of the PbF2 single crystals was simulated based on the finite element method. The temperature distribution and temperature gradient changes in the crucible were investigated at different growth stages, including the seeding, shouldering, and iso-diameters stages. The calculated results show that as the crucible position continues downward during the growth process, the axial temperature gradient increases and then decreases from the bottom to the top of the crucible, with almost flat isotherms near the solid–liquid interface where the axial temperature gradient is larger. At the shoulder below the crucible, the solid–liquid interface was improved by adjusting the tilt angle. Furthermore, based on a novel design of the heat-insulating baffle, the concave solid–liquid interface in the iso-diameter stage can be effectively adjusted to realize a lower radial temperature gradient. This study provides theoretical guidance for the optimization of the growth of high-quality PbF2 crystals by the Bridgman method.

Zeta potential (ζ potential) is a significant parameter to characterize the electric property of the electric double layer (EDL), which is important at the solid–liquid interface. Non-uniform ζ potential could be developed on a chemically uniform solid–liquid interface due to external flow. However, its influence on the flow has never been concerned. In this investigation, we numerically studied the influence of non-uniform 2D ζ potential on the flow at the solid–liquid interface. It is found, that even without any external electric field and only considering the influence of 2D ζ potential distribution, swirling flow can be generated near EDL, according to the rotational electric volume force. The streamwise vortices, which are important in the turbulent boundary layer, are theoretically predicted in this laminar flow model when considering the 2D distribution of ζ potential, implying the necessity of considering the origin of streamwise vortices of the turbulent boundary layer from the perspective of electrokinetic flow. In addition, the ζ potential distribution can promote the wall shear stress. Therefore, more attention must be paid to shear-sensitivity circumstances, like biomedical, medical devices, and in vivo. We hope that the current investigation can help us to better understand the effect of charge distribution on interfacial flow and provide theoretical guidance for the development of related applications in the future.

A system of steady lamellar eutectic growth in directional solidification is considered with the case of small tangent values of the contact angles. The mathematical model is given in the non-dimensional rectangular coordinate system and the uniformly valid asymptotic solutions are obtained based on the method of the asymptotic expansions. The necessary condition for existing asymptotic solutions was obtained. The results indicate that the curvature undercooling and the solute undercooling determined the patterns of the solid–liquid interface. The dimensional average undercooling presents a relationship with eutectic spacing and pulling velocity. It can be seen that the dimensional average undercooling in front of both phases is not equal, and the total average undercooling as a function of the lamellar eutectic spacing exhibits a minimum. The minimum undercooling spacing decreases with an increase in the pulling velocity, which is in good agreement with Jackson and Hunt’s results.

The adsorption mechanism of different polymers containing ionic polyamino acids monomers in the chain structure at the solid–liquid interface was investigated. Initially, the influence of molecular weight and solution pH on simple polyamino acids (poly(L-aspartic acid) and poly(L-lysine) binding was determined. Considering the obtained dependencies, the polymer adsorption layer conformation was proposed in the systems containing block copolymers (both diblock and symmetrical triblock) consisting of polypeptide as well as poly(ethylene glycol) fragments. The presented studies focused on the application of two experimental methods. The polymer adsorption was carried out using the batch method and the adsorbate concentration was determined spectrophotometrically. Then, the turbidimetric measurements were taken. The analysis of the obtained results showed that the adsorption process of block copolymers depends on two factors. Firstly, the solution pH determines both the nature of the interactions of the copolymer structural units with the solid surface and the conformation of the polypeptide chains. The second parameter influencing the adsorption layer structure is the ratio of the lengths of both blocks. Introducing a short PEG fragment into the polymer main chain may improve the polymer adsorption properties by increasing the number of interactions with the adsorbent surface.

In the preparation of a superamphiphobic surface, the most basic method is to reduce the surface free energy of the interface. The C—F bond has a very low surface free energy, which can significantly change the wettability of the solid–liquid interface and make it a hydrophobic or oleophobic, or even superamphiphobic surface. Based on the analysis of a large number of research articles, the preparation and application progress in fluoropolymer emulsion were summarized. After that, some corresponding thoughts were put forward combined with our professional characteristics. According to recent research, the status of the fluoropolymer emulsion preparation system was analyzed. In addition, all related aspects of fluoropolymer emulsion were systematically classified in varying degrees. Furthermore, the interaction between fluoropolymer structure and properties, especially the interaction with nanomaterials, was also explored. The aim of this review is to try to attract more scholars’ attention to fluorocarbon interfacial materials. It is expected that it will make a certain theoretical and practical significance in the preparation and application of fluoropolymer.

In order to establish the tangential contact stiffness and damping model of the solid–liquid interface by tangential exciting vibration force under mixed lubrication, the finite difference method was firstly used to solve the average flow equation considering the effect of roughness on the lubrication effect, and the bearing capacity, shear force, and friction coefficient of the oil film were obtained, and thereby the dynamic tangential contact stiffness and damping of the oil film under tangential harmonic excitation were calculated. Then, according to the relationship between the normal deformation and the load of the solid contact microconvex body in the elastic/elastic–plastic/plastic deformation stage, integrating the tangential stick–slip theory, considering the effect of fluid lubrication on the solid contact friction coefficient, and tangential dynamic excitation, the tangential contact stiffness and damping of the microconvex body in three deformation stages were calculated. Furthermore, the dynamic tangential contact stiffness and damping of the solid–liquid interface were obtained by summing the solid surface contact part and the solid–liquid contact part in parallel according to the assumption of microconvex Gaussian distribution. Finally, through simulation analysis and experiments, the variation of the tangential dynamic contact stiffness and damping of the solid–liquid interface with normal load, tangential exciting frequency, and displacement amplitude was revealed and verified.

The morphology of the solid-liquid (S-L) interface is crucial for the directionally solidified microstructures of various alloys. This paper investigates the effect of vertical high magnetic field (VHMF) on the morphology evolution of the S-L interface and the solidified microstructure during the directional solidification of Zn-2wt.%Bi immiscible alloy. The results indicate that the morphology of the S-L interface is highly dependent on the VHMF, resulting in various solidified microstructures. When the growth rate was 1 μm/s, the aligned droplets were formed directly at the disturbed S-L interface under a 1 T VHMF. However, the stability of the S-L interface was improved to form a stable Bi-rich fiber under a 5 T VHMF. When the growth rate was 5 μm/s, the S-L interface was changed from cellular to dendritic to cellular again with increasing magnetic flux density. A theory regarding constitutional supercooling and efficient solute diffusion has been proposed to explain the S-L interface transition under the VHMF. The difference in the effective diffusion capacity of the solute originates from the thermoelectric magnetic effect and the magneto-hydrodynamic damping effect. The present work may initiate a new method to transform the solidified microstructures of immiscible alloys via an applied magnetic field during directional solidification.

Temperature dependence of solid–liquid interfacial properties during crystal growth in nickel was investigated by ensemble Kalman filter (EnKF)-based data assimilation, in which the phase-field simulation was combined with atomic configurations of molecular dynamics (MD) simulation. Negative temperature dependence was found in the solid–liquid interfacial energy, the kinetic coefficient, and their anisotropy parameters from simultaneous estimation of four parameters. On the other hand, it is difficult to obtain a concrete value for the anisotropy parameter of solid–liquid interfacial energy since this factor is less influential for the MD simulation of crystal growth at high undercooling temperatures. The present study is significant in shedding light on the high potential of Bayesian data assimilation as a novel methodology of parameter estimation of practical materials an out of equilibrium condition.

The influences of Li content on the corrosion behavior of TC4 (Ti6Al4V) titanium alloy were explored when the TC4 titanium alloy was immersed in Al–Li alloy melt containing 0%, 1%, and 2% lithium at 680 °C, 700 °C, and 720 °C for 0.5 h, 1 h, and 2 h. The structure and growth law of the diffusion reaction layer at solid–liquid interface were studied, and the growth kinetic equation of the diffusion reaction layer was established. In addition, Ti content in Al–Li alloy melt was determined and its dissolution rate was calculated. The results showed that with the increase of lithium content in the melt, the thickness of the diffusion reaction layer (DRL) between TC4 titanium alloy and the melt increased significantly, and the activation energies of the diffusion reaction obtained were 141.28 kJ·mol−1 in liquid Al, 86.62 kJ·mol−1 in liquid Al–1Li alloy, and 43.42 kJ·mol−1 in liquid Al–2Li alloy, respectively. The dissolution rate of Ti in Al–Li alloy melts increased with the increase of lithium content in melts. When the holding time reached 3 h in a TC4 crucible, the content of Ti dissolved in the Al–2Li alloy melt was 0.105 wt%.

Using molecular dynamics simulation and a newly developed COMB3 potential, the in-plane ordering and diffusion constant profiles at the homogeneous (100), (110), and (111) interfaces between solid and liquid Al have been examined. We found that the in-plane ordering characterized by 2-D density maps and 2-D structure factors existed in the first 6, 10, and 3 out-of-plane layers at the (100), (110), and (111) interfaces, respectively, showing a strong dependence on substrate orientation. In layers with in-plane ordering, the diffusion constant is greatly reduced relative to its value in the bulk liquid, while the influence of layers without in-plane ordering is negligible. The three diffusivity components turn out to be isotropic at the homogeneous interfaces. The Al-Al interfaces studied here will serve as an important reference in comparisons of the structure and properties of different solid-liquid interfaces, which will greatly support the design of grain refiners.

Liquid layering, which is a general phenomenon adjacent to the solid substrates, is less understood for its role in heterogeneous nucleation. In this work, the structural features and dynamics of the liquid Al layers induced by the (0001) sapphire and the (0001) TiB2 substrates, respectively, are quantitatively compared based on the ab initio molecular dynamics simulations. An almost fully ordered liquid Al layer is observed adjacent to the TiB2 substrate above the Al melting point, while the liquid layers near the sapphire substrate are weakly ordered with virtually no in-plane translational symmetry. Further liquid layering is facilitated by the ordered liquid layer near the TiB2 substrate, while impeded by the low in-plane ordering of the liquid layers near the sapphire substrate, resulting in different nucleation behaviors for the two systems. The difference in the liquid layering is caused, in part, by the lower adsorption strength at the sapphire–liquid Al interface than that at the TiB2–liquid Al interface. Additionally, the compressive stress imposed on the liquid layers seriously hinders the sapphire-induced liquid layering. We conclude from this work that the interfacial adsorption strength and mismatch alter the heterogeneous nucleation by influencing the features of the substrate-induced liquid layering.

Temperature dependence of solid-liquid interfacial properties during crystal growth in nickel was investigated by ensemble Kalman filter (EnKF)-based data assimilation, in which the phase-field simulation was combined with atomic configurations of molecular dynamics (MD) simulation. Negative temperature dependence was found in the solid-liquid interfacial energy, the kinetic coefficient, and their anisotropy parameters from simultaneous estimation of four parameters. On the other hand, it is difficult to obtain a concrete value for the anisotropy parameter of solid-liquid interfacial energy since this factor is less influential for the MD simulation of crystal growth at high undercooling temperatures. The present study is significant in shedding light on the high potential of Bayesian data assimilation as a novel methodology of parameter estimation of practical materials an out of equilibrium condition.