Magneto-Controlled Tubular Liquid Actuators with Pore Engineering for Liquid Transport and Regulation

Liquid manipulation using tubular actuators finds diverse applications ranging from microfluidics, printing, liquid transfer to micro-reactors. Achieving flexible and simple regulation of manipulated liquid droplets during transport is crucial for the tubular liquid actuators to perform complex and multiple functions, yet it remains challenging. Here, a facile tubular actuator for directional transport of various liquid droplets under the control of an externally applied magnetic field is presented. The surfaces of the actuator can be engineered with submillimeter-sized through-hole pores, which enables the liquid droplet to be easily modulated in the transport process. Furthermore, the liquid actuator with featured through-hole pores is expanded to function as a switch in an integrated external electric circuit by magnetically controlling the motion of a conductive liquid droplet. This work develops a strategy for regulating liquid droplets in the tubular actuation systems, which may inspire ideas for designing functional liquid actuators with potential applications in microfluidics, microchemical reaction, liquid switch, and liquid robotics.

The synaptonemal complex assembles between meiotic chromosomes by wetting

Exchange of genetic information between the parental chromosomes during sexual reproduction is controlled by a conserved structure called the synaptonemal complex. It is composed of axes (stiff chromosomal backbones), and a central region that assembles between two parallel axes. To form exchanges, the parental chromosomes must be drawn together and aligned by the synaptonemal complex. However, its mechanism of assembly remains unknown. Here we identify an axis-central region interface in C. elegans composed of the axis component HIM-3 and the central region component SYP-5. Weaker interface prevented complete synaptonemal complex assembly, and crucially, altered its canonical layered ultrastructure. Informed by these phenotypes, we built a thermodynamic model for synaptonemal complex assembly. The model recapitulates our experimental observations, indicating that the liquid-like central region can move chromosomes by wetting the axes without active energy consumption. More broadly, our data show that condensation can bring about tightly regulated nuclear reorganization.

New piperidinium surfactants with carbamate fragments as effective adjuvants in insecticide compositions based on imidacloprid

BACKGROUND

Surfactants, particularly non-ionic ones, are widely used as adjuvants in pesticide formulations due to their ability to maintain pesticide effectiveness without changing solution properties, such as pH. While non-ionic surfactants are generally low-toxic, stable, and excellent dispersants with high solubilization capabilities, they may be less effective than cationic surfactants, which offer superior surface activity, transport properties, and antimicrobial action. This study investigates the efficacy of new piperidinium surfactants with carbamate fragments as adjuvants in insecticide formulations containing imidacloprid. The efficacy of these formulations is being assessed against greenhouse whitefly, a pest known to harm cultivated and ornamental flowering plants.

RESULTS

The aggregation behavior of piperidinium surfactants containing carbamate fragments was investigated, and their wetting effect was evaluated. Synthesized surfactants have lower CMC values compared to their methylpiperidinium analogue. The effect of piperidinium surfactants on the insecticide concentration on the surface and inside tomato leaves was assessed using spectrophotometric methods. It was found that the introduction of piperidinium surfactants with carbamate fragment at a concentration of 0.1% wt. allows for decrease in lethal concentration of imidacloprid up to 10 times, thereby testifying the marked increase in the effectiveness of imidacloprid against the greenhouse whitefly insect pest (Trialeurodes vaporariorum). It was shown that the main factors responsible for the enhanced efficacy of the insecticide were the ability of the surfactant to increase the concentration of imidacloprid on the leaf surfaces and improve their penetration into the plant.

CONCLUSION

The presented work employed a comprehensive approach, which significantly increases the generalizability of the results obtained and provides the ability to predict the effect and target selection of adjuvants. © 2024 Society of Chemical Industry.

Carbon-Based Nanocomposite Membranes for Membrane Distillation: Progress, Problems and Future Prospects

The development of an ideal membrane for membrane distillation (MD) is of the utmost importance. Enhancing the efficiency of MD by adding nanoparticles to or onto a membrane's surface has drawn considerable attention from the scientific community. It is crucial to thoroughly examine state-of-the-art nanomaterials-enabled MD membranes with desirable properties, as they greatly enhance the efficiency and reliability of the MD process. This, in turn, opens up opportunities for achieving a sustainable water-energy-environment nexus. By introducing carbon-based nanomaterials into the membrane's structure, the membrane gains excellent separation abilities, resistance to various feed waters, and a longer lifespan. Additionally, the use of carbon-based nanomaterials in MD has led to improved membrane performance characteristics such as increased permeability and a reduced fouling propensity. These nanomaterials have also enabled novel membrane capabilities like in situ foulant degradation and localized heat generation. Therefore, this review offers an overview of how the utilization of different carbon-based nanomaterials in membrane synthesis impacts the membrane characteristics, particularly the liquid entry pressure (LEP), hydrophobicity, porosity, and membrane permeability, as well as reduced fouling, thereby advancing the MD technology for water treatment processes. Furthermore, this review also discusses the development, challenges, and research opportunities that arise from these findings.

Wetting Effect Induced Depletion and Adsorption Layers: Diffuse Interface Perspective

When a multi-component fluid contacts arigid solid substrate, the van der Waals interaction between fluids and substrate induces a depletion/adsorption layer depending on the intrinsic wettability of the system. In this study, we investigate the depletion/adsorption behaviors of A-B fluid system. We derive analytical expressions for the equilibrium layer thickness and the equilibrium composition distribution near the solid wall, based on the theories of de Gennes and Cahn. Our derivation is verified through phase-field simulations, wherein the substrate wettability, A-B interfacial tension, and temperature are systematically varied. Our findings underscore two pivotal mechanisms governing the equilibrium layer thickness. With an increase in the wall free energy, the substrate wettability dominates the layer formation, aligning with de Gennes' theory. When the interfacial tension increases, or temperature rises, the layer formation is determined by the A-B interactions, obeying Cahn's theory. Additionally, we extend our study to non-equilibrium systems where the initial composition deviates from the binodal line. Notably, macroscopic depletion/adsorption layers form on the substrate, which are significantly thicker than the equilibrium microscopic layers. This macroscopic layer formation is attributed to the interplay of phase separation and Ostwald ripening. We anticipate that the present finding could deepen our knowledge on the depletion/adsorption behaviors of immiscible fluids.

'Rewritable' and 'liquid-specific' recognizable wettability pattern

Bio-inspired surfaces with wettability patterns display a unique ability for liquid manipulations. Sacrificing anti-wetting property for confining liquids irrespective of their surface tension (γLV), remains a widely accepted basis for developing wettability patterns. In contrast, we introduce a 'liquid-specific' wettability pattern through selectively sacrificing the slippery property against only low γLV (<30 mN m-1) liquids. This design includes a chemically reactive crystalline network of phase-transitioning polymer, which displays an effortless sliding of both low and high γLV liquids. Upon its strategic chemical modification, droplets of low γLV liquids fail to slide, rather spill arbitrarily on the tilted interface. In contrast, droplets of high γLV liquids continue to slide on the same modified interface. Interestingly, the phase-transition driven rearrangement of crystalline network allows to revert the slippery property against low γLV liquids. Here, we report a 'rewritable' and 'liquid-specific' wettability pattern for high throughput screening, separating, and remoulding non-aqueous liquids.

Unveiling the Role of PTFE Surface Coverage on Controlling Gas Diffusion Layer Water Content

Gas diffusion layers (GDLs) are usually coated with a hydrophobic agent to achieve a delicate balance between liquid and gas phases to maximize mass transport. Yet, most GDL numerical models to date have assumed an average contact angle for all materials, thereby eliminating the possibility of studying the role of the polytetrafluoroethylene (PTFE) content. This study introduces two mixed wettability algorithms to predict the mixed wetting behavior of GDLs composed of multiple materials. The algorithms employ contact angle and distance to solid materials to determine the critical capillary pressure for each pore voxel. The application of the algorithms to the estimation of capillary pressure vs saturation curves for two GDLs, namely, a micro-computed tomography (μ-CT) reconstructed SGL 39BA GDL and a stochastically reconstructed Toray 120C GDL, showed that, in agreement with experimental data, the addition of PTFE resulted in a decrease in saturation at a given capillary pressure. For Toray-120C, the mixed wettability model was capable of reproducing experimentally observed features in the intrusion curve at low saturation that could not be reproduced with a single wettability model, providing a clear link between PTFE coverage and intrusion at low saturation. Numerical results also predicted an increased breakthrough pressure and a decrease in saturation with increasing PTFE, in agreement with experimental observations. The decreased saturation at breakthrough improves gas transport through the layer while maintaining the layer's ability to remove water. Diffusivity simulations confirm the increase in diffusivity at breakthrough with increasing PTFE, thereby providing a rationale for the addition of PTFE, as well as for the optimal amount. This study emphasizes the importance of multimaterial wetting models and calls for more detailed investigations into PTFE and ionomer distributions in GDLs and catalyst layers, respectively.

Thickness of Nanoscale Poly(Dimethylsiloxane) Layers Determines the Motion of Sliding Water Drops

Layers of nanometer thick polydimethylsiloxane (PDMS) are applied as hydrophobic coatings because of their environmentally friendly and chemically inert properties. In applications such as heat exchangers or fog harvesting, low water drop friction on surfaces is required. While the onset of motion (static friction) has been studied, the knowledge of dynamic friction needs to be improved. To minimize drop friction, it is essential to understand which processes lead to energy dissipation and cause dynamic friction? Here, the dynamic friction of drops on PDMS brushes of different thicknesses is measured, covering the whole available velocity regime. The brush thickness L turns out to be a predictor for drop friction. 4-5 nm thick PDMS brush shows the lowest dynamic friction. A certain minimal thickness is necessary to form homogeneous surfaces and reduce the attractive van der Waals interaction between water and the substrate. The increase in dynamic friction above L = 5 nm is also attributed to the increasing viscoelastic dissipation of the capillary ridge formed at the contact line. The height of the ridge is related to the brush thickness. Fluorescence correlation spectroscopy and atomic force measurements support this interpretation. Sum-frequency generation further indicates a maximum order at the PDMS-water interface at intermediate thickness.

Ultimately Adaptive Fluid Interfacial Phospholipid Membranes Unveiled Unanticipated High Cellular Mechanical Work

Living cells actively interact biochemically and mechanically with the surrounding extracellular matrices (ECMs) and undergo dramatic morphological and dimensional transitions, concomitantly remodeling ECMs. However, there is no suitable method to quantitatively discuss the contribution of mechanical interactions in such mutually adaptive processes. Herein, a highly deformable "living" cellular scaffold is developed to evaluate overall mechanical energy transfer between cell and ECMs. It is based on the water-perfluorocarbon interface decorated with phospholipids bearing a cell-adhesive ligand and fluorescent tag. The bioinert nature of the phospholipid membranes prevents the formation of solid-like protein nanofilms at the fluid interface, enabling to visualize and quantify cellular mechanical work against the ultimately adaptive model ECM. A new cellular wetting regime is identified, wherein interface deformation proceeds to cell flattening, followed by its eventual restoration. The cellular mechanical work during this adaptive wetting process is one order of magnitude higher than those reported with conventional elastic platforms. The behavior of viscous liquid drops at the air-water interface can simulate cellular adaptive wetting, suggesting that overall viscoelasticity of the cell body predominates the emergent wetting regime and regulates mechanical output. Cellular-force-driven high-energy states on the adaptive platform can be useful for cell fate manipulation.

Non-Aqueous Polyhedral Liquid Marbles Stabilized with Polymer Plates Having Surface Roughness

Hydrophobic polymer plates with smooth and rough surfaces are used as a stabilizer for cubic liquid marbles (LMs) to study the effect of surface roughness on their formation. The smooth and rough polymer plates can stabilize LMs using liquids with surface tensions of 72.8-26.6 and 72.8-22.9 mN m-1, respectively. It is clarified that the higher the surface roughness, the lower the surface tension of the liquids are stabilized to form the LMs. These results indicated that the introduction of surface roughness improves the hydrophobicity of the polymer plates and the rough polymer plates can stabilize LMs using liquids with a wider surface tension range. Electron microscopy studies and numerical analyses confirmed that the LMs can be formed, when the Cassie-Baxter wetting state, where θY>90° (θY: the contact angle on smooth surfaces) and θR>90° (θR: the contact angle on rough surfaces), and the metastable Cassie-Baxter wetting state, where θY<90° and θR>90°, are realized. Finally, the synthesis of cubic polymer particles are succeeded by free radical polymerization of the cubic LMs containing a hydrophobic vinyl monomer (dodecyl acrylate) in a solvent-free manner.

Photoswitchable Endocytosis of Biomolecular Condensates in Giant Vesicles

Interactions between membranes and biomolecular condensates can give rise to complex phenomena such as wetting transitions, mutual remodeling, and endocytosis. In this study, light-triggered manipulation of condensate engulfment is demonstrated using giant vesicles containing photoswitchable lipids. UV irradiation increases the membrane area, which can be stored in nanotubes. When in contact with a condensate droplet, the UV light triggers rapid condensate endocytosis, which can be reverted by blue light. The affinity of the protein-rich condensates to the membrane and the reversibility of the engulfment processes is quantified from confocal microscopy images. The degree of photo-induced engulfment, whether partial or complete, depends on the vesicle excess area and the relative sizes of vesicles and condensates. Theoretical estimates suggest that utilizing the light-induced excess area to increase the vesicle-condensate adhesion interface is energetically more favorable than the energy gain from folding the membrane into invaginations and tubes. The overall findings demonstrate that membrane-condensate interactions can be easily and quickly modulated via light, providing a versatile system for building platforms to control cellular events and design intelligent drug delivery systems for cell repair.

Spontaneous Wetting Induced by Contact-Electrification at Liquid-Solid Interface

Wettability significantly influences various surface interactions and applications at the liquid-solid interface. However, the understanding is complicated by the intricate charge exchange occurring through contact electrification (CE) during this process. The understanding of the influence of triboelectric charge on wettability remains challenging, especially due to the complexities involved in concurrently measuring contact angles and interfacial electrical signals. Here, the relationship is investigated between surface charge density and change of contact angle of dielectric films after contact with water droplets. It is observed that the charge exchange when water spared lead to a spontaneous wetting phenomenon, which is termed as the contact electrification induced wetting (CEW). Notably, these results demonstrate a linear dependence between the change of contact angle (CA) of the materials and the density of surface charge on the solid surface. Continuous CEW tests show that not only the static CA but also the dynamics of wetting are influenced by the accumulation charges at the interface. The mechanism behind CEW involves the redistribution of surface charges on a solid surface and polar water molecules within liquid. This interaction results in a decrease in interface energy, leading to a reduction in the CA. Ab initio calculations suggest that the reduction in interface energy may stem from the enhanced surface charge on the substrate, which strengthens the hydrogen bond interaction between water and the substrate. These findings have the potential to advance the understanding of CE and wetting phenomena, with applications in energy harvesting, catalysis, and droplet manipulation at liquid-solid interfaces.

Taguchi Optimization of Wetting, Thermal and Mechanical Properties of Sn-1.0wt.%Ag-0.5wt.%Cu Alloys Modified with Bi and Sb

This study was conducted on SAC105 (Sn-1wt.%Ag-0.5wt.%Cu) lead-free solder modified with Bi and Sb. The wetting, melting point, and mechanical properties were analysed with the addition of 1~5 wt.%Bi and 1~5 wt.%Sb for SAC105 base alloy. The wetting characteristics were assessed by wetting time (zero cross time, ZCT) obtained from wetting balance tests. The mechanical properties were analysed by tensile tests. Considering two factors (Bi, Sb), a three-level (0, 1, 2 wt.%) design of experiment (DOE) method array was applied for Taguchi optimization. The results indicated that the solder wetting increased as Bi content increased, while it decreased with Sb. The ZCT decreased with increasing Bi content up to 4 wt.%, while it increased proportionally to Sb content. The melting point, measured using a differential scanning calorimeter (DSC), showed that the melting point tended to decrease according to Bi increase, while it increases depending on the Sb content. Increase in Bi and Sb levels resulted in enhanced tensile strength in the mechanical properties tests, with Bi having a more noticeable impact. The Taguchi optimized conditions for the Bi and Sb studies were found to be 2 wt.%Bi and 2 wt.%Sb. This led to an optimal set of 0.9 s of wetting time, a 222.55 °C melting point, a 55 MPa tensile strength, and a 50% elongation.

Effects of Different Oxidation Methods on the Wetting and Diffusion Characteristics of a High-Alumina Glass Sealant on 304 Stainless Steel

Glass-to-metal seals are a very important element in the construction of vacuum tubes, electric discharge tubes, pressure-tight glass windows in metal cases, and metal or ceramic packages of electronic components. This paper presents the influence of different pretreatment methods on the high-temperature wettability of 304 stainless steel by high-alumina glass sealing. The pretreatment of the steel included laser surface melting and pre-oxidizing. The bonding characteristics of glass and stainless steel directly depend on the wettability in terms of the measured wetting angle, the type of oxide formed at the stainless steel surface, and the microstructural changes during the manufacturing process. The oxide film thickness on the stainless steel surface was evaluated to determine the optimal parameters. The film was wetted with high-alumina glass powder at different temperatures. The results showed that pre-oxidation decreased the wetting angle from 56.2° to 33.6°, while for the laser-melted surface, the wetting angle decreased from 49.8° to 31.5°. Scanning electron microscopy (SEM) revealed that the oxide film on the laser-melted surface was thicker and denser than that formed on the pre-oxidized surface. The present work shows that laser surface melting has a greater beneficial influence on the wetting and diffusion characteristics of 304 stainless steel sealed by high-alumina glass.

Resonance Modes of Water Drops Pinned to a Vibrating Rectangular Post

We studied the effects of vertical vibrations on a water drop that was pinned to the sharp edges of a rectangular post. By varying the frequency and amplitude of the vertical displacement, distinct resonance peaks were observed using a simple optical technique. The vibrational spectra of the first two modes exhibited two closely spaced peaks, which corresponded to standing waves that exist along the major and minor contour lengths of the drops. The values of the resonance frequencies can be explained rather well by a simple model, which was originally proposed for axially symmetric drops.

Toward vanishing droplet friction on repellent surfaces

Superhydrophobic surfaces are often seen as frictionless materials, on which water is highly mobile. Understanding the nature of friction for such water-repellent systems is central to further minimize resistance to motion and energy loss in applications. For slowly moving drops, contact-line friction has been generally considered dominant on slippery superhydrophobic surfaces. Here, we show that this general rule applies only at very low speed. Using a micropipette force sensor in an oscillating mode, we measure the friction of water drops approaching or even equaling zero contact-line friction. We evidence that dissipation then mainly stems from the viscous shearing of the air film (plastron) trapped under the liquid. Because this force is velocity dependent, it can become a serious drag on surfaces that look highly slippery from quasi-static tests. The plastron thickness is found to be the key parameter that enables the control of this special friction, which is useful information for designing the next generation of ultraslippery water-repellent coatings.

Droplet slipperiness despite surface heterogeneity at molecular scale

Friction determines whether liquid droplets slide off a solid surface or stick to it. Surface heterogeneity is generally acknowledged as the major cause of increased contact angle hysteresis and contact line friction of droplets. Here we challenge this long-standing premise for chemical heterogeneity at the molecular length scale. By tuning the coverage of self-assembled monolayers (SAMs), water contact angles change gradually from about 10° to 110° yet contact angle hysteresis and contact line friction are low for the low-coverage hydrophilic SAMs as well as high-coverage hydrophobic SAMs. Their slipperiness is not expected based on the substantial chemical heterogeneity of the SAMs featuring uncoated areas of the substrate well beyond the size of a water molecule as probed by metal reactants. According to molecular dynamics simulations, the low friction of both low- and high-coverage SAMs originates from the mobility of interfacial water molecules. These findings reveal a yet unknown and counterintuitive mechanism for slipperiness, opening new avenues for enhancing the mobility of droplets.

Unraveling the role of vaporization momentum in self-jumping dynamics of freezing supercooled droplets at reduced pressures

Supercooling of water complicates phase change dynamics, the understanding of which remains limited yet vital to energy-related and aerospace processes. Here, we investigate the freezing and jumping dynamics of supercooled water droplets on superhydrophobic surfaces, induced by a remarkable vaporization momentum, in a low-pressure environment. The vaporization momentum arises from the vaporization at droplet's free surface, progressed and intensified by recalescence, subsequently inducing droplet compression and finally self-jumping. By incorporating liquid-gas-solid phase changes involving vaporization, freezing recalescence, and liquid-solid interactions, we resolve the vaporization momentum and droplet dynamics, revealing a size-scaled jumping velocity and a nucleation-governed jumping direction. A droplet-size-defined regime map is established, distinguishing the vaporization-momentum-dominated self-jumping from evaporative drying and overpressure-initiated levitation, all induced by depressurization and vaporization. Our findings illuminate the role of supercooling and low-pressure mediated phase change in shaping fluid transport dynamics, with implications for passive anti-icing, advanced cooling, and climate physics.

Wetting and Spreading Behavior of Axisymmetric Compound Droplets on Curved Solid Walls Using Conservative Phase Field Lattice Boltzmann Method

Compound droplets have received increasing attention due to their applications in many several areas, including medicine and materials. Previous works mostly focused on compound droplets on planar surfaces and, as such, the effects of curved walls have not been studied thoroughly. In this paper, the influence of the properties of curved solid wall (including the shape, curvature, and contact angle) on the wetting behavior of compound droplets is explored. The axisymmetric lattice Boltzmann method, based on the conservative phase field formulation for ternary fluids, was used to numerically study the wetting and spreading of a compound droplet of the Janus type on various curved solid walls at large density ratios, focusing on whether the separation of compound droplets occurs. Several types of wall geometries were considered, including a planar wall, a concave wall with constant curvature, and a convex wall with fixed or variable curvature (specifically, a prolate or oblate spheroid). The effects of surface wettability, interfacial angles, and the density ratio (of droplet to ambient fluid) on the wetting process were also explored. In general, it was found that, under otherwise identical conditions, droplet separation tends to happen more likely on more hydrophilic walls, under larger interfacial angles (measured inside the droplet), and at larger density ratios. On convex walls, a larger radius of curvature of the surface near the droplet was found to be helpful to split the Janus droplet. On concave walls, as the radius of curvature increases from a small value, the possibility to observe droplet separation first increases and then decreases. Several phase diagrams on whether droplet separation occurs during the spreading process were produced for different kinds of walls to illustrate the influences of various factors.

Durable Janus membrane with on-demand mode switching fabricated by femtosecond laser

Despite their notable unidirectional water transport capabilities, Janus membranes are commonly challenged by the fragility of their chemical coatings and the clogging of open microchannels. Here, an on-demand mode-switching strategy is presented to consider the Janus functionality and mechanical durability separately and implement them by simply stretching and releasing the membrane. The stretching Janus mode facilitates unidirectional liquid flow through the hydrophilic micropores-microgrooves channels (PG channels) fabricated by femtosecond laser. The releasing protection mode is designed for the in-situ closure of the PG channels upon encountering external abrasion and impact. The protection mode imparts the Janus membrane robustness to reserve water unidirectional penetration under harsh conditions, such as 2000  cycles mechanical abrasion, 10 days exposure in air and other rigorous tests (sandpaper abrasion, finger rubbing, sand impact and tape peeling). The underlying mechanism of gridded grooves in protecting and enhancing water flow is unveiled. The Janus membrane serves as a fog collector to demonstrate its unwavering mechanical durability in harsh real-world conditions. The presented design strategy could open up new possibilities of Janus membrane in a multitude of applications ranging from multiphase separation devices to fog harvesting and wearable health-monitoring patches.

Metatranscriptomes of two biological soil crust types from the Mojave desert in response to wetting

We present eight metatranscriptomic datasets of light algal and cyanolichen biological soil crusts from the Mojave Desert in response to wetting. These data will help us understand gene expression patterns in desert biocrust microbial communities after they have been reactivated by the addition of water.

The effect of crystallographic orientation ofα-Al2O3on the wetting behavior and adhesion characteristics of aluminum droplets

To solve the problem of adhesion of aluminum fluid to the inner wall of the vacuum ladle in the aluminum electrolysis industry, molecular dynamics simulation is performed to research the wetting behavior of Al droplets on the surfaces of theα-Al2O3substrates C (0001), M (11-00), and R (11-02) at 1073 K. Meanwhile, the adhesion characteristics of the Al droplet are evaluated by the potential of the mean force (PMF) for the separation of the Al droplets from different surfaces of theα-Al2O3substrate. The results show that the wetting behavior of Al droplets on theα-Al2O3substrate is influenced by the different crystallographic orientations. The diffusion of Al droplets in thex-o-yplane of the substrate exhibits isotropic. The PMF and the interfacial potential energy reveal that the magnitude of the adhesion work in the solid-liquid separation of Al droplets fromα-Al2O3substrates follows the order C (0001) > R (11-02) > M (11-00). These findings characterize the wetting properties and adhesion behavior of Al droplets on an atomic scale and provide a theoretical basis for the selection of materials for the inner wall of the vacuum ladle.