Cassie Model Research Articles

Study of the contact angle and roughness effects on mercury intrusion porosimetry (MIP) analysis in natural/real carbonate rocks using massive pure minerals and synthetic carbonate rocks

Studying pore networks in rocks is critical for understanding reservoir properties, with mercury intrusion porosimetry (MIP) being a key laboratory method. MIP involves capillary intrusion of mercury, with intrusion pressure (P) related to capillary diameter (d) by the Washburn equation, incorporating mercury properties like contact angle (θ) and surface tension (γ). While a constant contact angle of 140° is typically assumed for MIP, it can vary based on rock mineralogy and surface roughness. This study aims to analyze how contact angle variations and surface roughness affect MIP analysis of carbonate rocks. Initially, contact angle data was obtained for calcite, dolomite, and quartz with varying roughness levels. Synthetic rocks were then constructed using these minerals. MIP was performed using the typical 140° contact angle and a calculated contact angle from the Cassie model, which considers surface composition fraction. Natural rock MIP analysis followed, with contact angles varying due to mineral composition and roughness. The study found higher contact angles than the standard 140°, affecting pore size distributions up to 30%. Natural rock pore network curves were adjusted based on synthetic rock data analysis. These findings emphasize the need for accurate contact angle selection in MIP for precise pore distribution analysis and contribute to the further study of carbonate rocks.

Water repellence of biomimetic structures fabricated via femtosecond laser direct writing

Femtosecond laser direct writing based on two-photon polymerization (TPP), which is a sub-classification of vat photopolymerization, has the advantages of unlimited geometrical freedom and high resolution, and has attracted significant interests from scientists and engineers in recent years. In the present study, TPP fabrication was performed using a laser equipment with wavelength of 514 nm. The collimated beam diameter before the focusing lens was measured as 5 mm and the focused laser spot diameter was calculated as 280 nm. Key TPP processing parameters were investigated for the fabrication of nanowires, and micro/ nanoscale biomimetic structures, including cone and pinecone structures. The finest nanowire has a diameter of 105 nm and is achieved at the laser power of 0.8 μW (near the laser polymerization threshold). For the three-dimensional (3D) structures, laser power, layer thickness and hatch spacing would influence the fabrication accuracy. Generation of a stiff 3D cone structure would require a minimum laser power of 1.4 μW when the hatch spacing and layer thickness are 200 nm. The optimum processing parameters (laser power 2.2 μW, hatch space and layer thickness 100 nm) can generate structures with dimensions close to the design values. For pinecones with nano features, the scanning strategies play a significant role in the nano fabrication accuracy. A row of pinecones and cones were fabricated and tested for their water repellence performance. The relationship between the performance and the nano cone density was investigated. The pinecone structures exhibit superior performance to the ones with no nano-scale structures, indicating that improved hydrophobicity can be achieved by designing the micro/nano hierarchical structures. The increased number density of the nano cones in a micro/nano hierarchical structure was found to profoundly enhance the water repellence of the structures. The mechanisms were discussed with Wenzel and Cassie models.

Wetting model of rough solid surfaces and the effect of aggregate properties on epoxy resin binder-aggregate interface wetting

In order to study the effect of aggregate characteristics on the wetting of epoxy resin binder-aggregate interface, based on the Wenzel model and Cassie model, this paper established a new wetting model of the irregular rough surface. The model regularizes the rough solid surface and can calculate the wetting depth and apparent contact angle between different irregular rough solids and liquids. The texture parameters of aggregates, the surface tension of test liquids and the contact angles of different liquids-aggregates were tested by laser confocal tester and optical contact angle measuring instrument. It was found that the surface texture parameters of different aggregates were quite different. The relative error between the apparent contact angle calculated by the prediction model and the contact angle measured by the test was less than 15 %, indicating that the prediction model had excellent prediction effect. Through the analysis of the wetting model, it is found that the surface tension of the test liquid, the lithology of the solid aggregate, the surface roughness and the texture structure are the important control parameters affecting the wetting. The surface morphology of rough solid can be designed by changing the resolution k and depth H of micropores, so as to control the wettability of solid aggregate surface and epoxy resin aggregate.

Black-box models for liquid nitrogen arc and its parameters optimization by PSO algorithm

Sulphur Hexafluoride (SF6) has been widely utilized in the Gas Insulated Switchgear (GIS) due to its great insulation ability. However, SF6 has great greenhouse effect. Liquid nitrogen (LN2) has been considered as a promising substitute for the SF6 gas because of its good insulation, arc quenching and cost effectiveness. To accurately simulate the LN2 switch, it is essential to establish a mathematical model for the LN2 arc. Black-box models have been commonly used in describing the dynamic characteristics of gas arc in circuit breaker simulations. There are numerous types of black-box models for gas arc, yet there is no literature available about the application of black-box model for the LN2 arc. This paper aims to establish the black-box model of LN2 arc. Based on the experimental data, several kinds of black-box models including Mayr, Cassie, Schwarz, Habedank and TP KEMA models were established, and their parameters were optimized by the Particle Swarm Optimization (PSO) algorithm. The performance of these black-box models was evaluated by the conductance error. The results indicated that black-box models can be employed for LN2 arc simulations, and the TP KEMA model exhibits the best performance with minimal conductance errors throughout the entire arcing process.

Characteristics and Model of Heterogeneous Wettability in a Marine-Continental Transitional Shale Reservoir: Insights from Organic Matter, Minerals, and Microstructure

Heterogeneous wettability is characterized by a spotted-wet or mixed-wet state. It has a great influence on reservoir evaluation and the efficient development of shale gas reservoirs. In this study, reservoir properties of several core plugs from the Permian Shanxi–Taiyuan formations were studied. These formations are typical marine-continental transitional shale located in the Southern North China Basin. To investigate the effects of reservoir properties on heterogeneous wettability, we measured the water–air contact angle and compared it with other properties such as organic petrology, organic geochemistry, mineralogy, and microstructure features, including pore-fractures and surface roughness. The results reveal a negative correlation of vitrinite content with contact angle, in addition to the high clay content and residual polar groups within type III kerogen, indicating that the Shanxi–Taiyuan shales with a high maturity level still have a higher affinity to water. The contact angle of the core samples decreases with increasing surface roughness, partially due to the influence of pore-fracture development. The crossplots indicate that the majority of pore-fractures that exist in the shale preferentially tend to be water-wet. Therefore, the heterogeneous wettability of shale is dominated by the random mixture and arrangement of hydrophilic and hydrophobic components as well as the complexity of the microstructure, such as the rough pore wall. Furthermore, on the basis of improving and examining the Cassie model, a triangle method and a detailed workflow for evaluating the heterogeneous wettability of shale are proposed by comprehensively analyzing “three factors”, including pore structure, mineral components, and organic matter. The test results demonstrate that the Shanxi–Taiyuan shales are mainly water-wet (controlled by organic factor) and neutral-wet, which evidently differ from the marine Longmaxi shale with a wide distribution covering the zones of strongly water-wet, weakly water-wet (controlled by pore factor), and weakly water-wet (neutral-wet). The proposed approach can be applied to promptly and comprehensively evaluate and predict the heterogeneous wettability of shales during shale oil and gas exploration.

Ground Fault Identification in Distribution Network Based on MMC Injection Detection Signal Strategy

In order to improve the identification efficiency and accuracy of distribution network ground fault identification methods, this paper proposes a distribution network ground fault identification method based on MMC injection detection signal strategy. Extract the fault information of distribution network grounding line, calculate the current component of three-phase current, and obtain the grounding fault data of distribution network.The detection current of distribution network is obtained by injection signal detection strategy. The fault information matrix is formed by using the detection current information, and the time-frequency characteristics of MMC injection detection signal strategy are obtained according to the actual situation.The wavelet transform is used to remove the clutter in the fault feature vector, and the normalized processing is used to obtain and process the ground fault vector.According to the wavelet function, the characteristics of the distribution network ground fault signal are determined. Cassie model and Mayr model are used to obtain the final distribution network ground fault identification model to realize the distribution network ground fault identification.The experimental results show that the accuracy of the method can reach 96.1%, and the time of fault identification is only 25s. The above results show that the method can effectively improve the effectiveness of distribution network ground fault identification.

Numerical Simulation of Vapor Dropwise Condensation Process and Droplet Growth Mode

Compared with film condensation, dropwise condensation based on droplet growth can significantly improve the condensing equipment’s water collection and thermal efficiency in the vapor condensate system. Therefore, as a critical behavior affecting the evolution of dropwise condensation, research on droplet growth is of great significance to further understanding the evolutionary characteristics and heat transfer mechanism of dropwise condensation. In this paper, a model for simulating the entire evolution process of dropwise condensation is improved and constructed, and the evolution process of dropwise condensation with different condensation nucleus densities on the vertical wall is simulated based on certain assumptions. Moreover, parameters such as evolution rate and size contribution are proposed to measure droplet growth’s influence on the evolution process of dropwise condensation. In the simulation, the Cassie model was used to describe the condensation growth of droplets. The neighbor finding algorithm and conservation law are coupled to simulate the coalescence growth process of droplets. Through the comparison of the theoretical model and experimental results, it is indicated that the simulation method in this paper is highly reliable. The simulation results demonstrate that more than 95% of the maximum droplet size of dropwise condensation is derived from coalescence growth, and its growth rate can characterize the evolution rate of dropwise condensation. The evolution rate reveals a linear growth trend with the increase of condensate nucleus density, and the average heat flux shows an increasing trend followed by a decreasing trend, reaching the peak, qaverage = 30.5 kW·m−2, at the NS = 5 × 109 m−2. The surfaces with a high coalescence frequency can increase the contribution of the coalescence growth to the maximum droplet size more effectively and, conversely, the contribution of condensation growth is weakened, which is less than 1% at the NS = 7.5 × 109 m−2.

Laser crystallization of amorphous TiO2 on polymer

The deposition of crystalline TiO2 on polymers can boost its use in a large plethora of applications. In this work, we deposited, through the low-temperature atomic layer deposition (LT-ALD) technique, a thin layer of amorphous TiO2 on polymethyl-methacrylate (PMMA), and afterwards, we induced a phase transition from amorphous to crystalline anatase by pulsed UV-laser irradiation. A pulsed UV laser with a low penetration length was used to avoid the heating and damaging of the polymeric substrate. The diffusion of the heat and the temperature behaviour were simulated and discussed. We studied experimentally the effect of the laser fluence and pulse number on the amorphous-crystal transition. We observed the presence of two thresholds for the formation of the crystalline phase: on the fluence and the number of laser shots. Moreover, widening of pre-existing cracks is observed, as soon as fluence and the number of pulses increase. To improve further the quality of the deposited layer, we introduced a ZnO interlayer between TiO2 and the PMMA substrate. The effect of this interlayer was also discussed. Lastly, wettability, as a measure of the overall quality of the layer, was measured and interpreted by using the Cassie model.

Modelling alternating current effects in a submerged arc furnace

Abstract Modelling the production of silicon in a submerged arc furnace (SAF) requires accounting for the wide range of timescales of the different physical and chemical processes: the electric current which is used to heat the furnace varies over a timescale of around $10^{-2}\,$ s, whereas the flow and chemical consumption of the raw materials in the furnace occurs over several hours. Models for the silicon furnace generally either include only the fast-timescale, or only the slow-timescale processes. In a prior work, we developed a model incorporating effects on both the fast and slow timescales, and used a multiple-timescales analysis to homogenise the fast variations, deriving an averaged model for the slow evolution of the raw materials. For simplicity, in the previous work we focussed on the electrical behaviour around the base of a single electrode, and prescribed the current in this electrode to be sinusoidal, with given amplitude. In this paper, we extend our previous analysis to include the full electrical system, modelled using an equivalent circuit system. In this way, we demonstrate how the two furnace-modelling approaches (on the fast and slow timescales) may be combined in a computationally efficient way. Our previously derived model for the arc resistance is based on the assumption that the dominant heat loss from the arc is by radiation (we will refer to this as the radiation model). Alternative arc models include the empirical Cassie and Mayr models, which are commonly used in the SAF literature. We compare these various arc models, explore the dependence of the solution of our model on the model parameters and compare our solutions with measurements from an operational silicon furnace. In particular, we show that only the radiation arc model has a rising current-voltage characteristic at high currents. Simulations of the model show that there is an upper limit on the length of the furnace arc, above which all the current bypasses the arc and flows through the surrounding material.

Parameter Determination Method of Cassie-Mayr Hybrid Arc Model Based on Magnetohydrodynamics Plasma Theory

This paper proposes an improved alternating current (AC) arc model based on the Cassie-Mayr hybrid model and magnetohydrodynamics (MHD) theory. The undetermined parameters of the traditional Cassie-Mayr arc model are mainly obtained by subjective methods such as empirical value, approximate expression, and indirect estimation which are complex, inaccurate, and dependent on experimental data. To overcome these disadvantages, an axisymmetric two-dimensional arc model is established based on the MHD theory, and the undetermined parameter values of the Cassie-Mayr hybrid arc model are obtained based on the results of MHD numerical simulation. The accuracy of the proposed modified Cassie-Mayr model is verified by comparing with experimental data, and the results of the modified Cassie-Mayr model, traditional Mayr model, and Cassie model are discussed. The arc characteristics of serval loads are studied and analyzed based on the modified model.

Stable superhydrophobic and conductive surface: Fabrication of interstitial coral-like copper nanostructure by self-assembly and spray deposition

Water permeation is an important issue in both fundamental research and industrial applications. In this work, stable superhydrophobic copper surfaces were obtained by self-assembly and spray deposition on cotton fabrics. Scanning electron microscopy revealed that micro/nano dual-scale coral-like structures were established by the stacking of copper nanoparticles, thus forming a stable Cassie model for superhydrophobic feathers. The water contact angle of the surface was 161°, while the slide angle was as low as 3°. Chemical bonds were formed between substructures and copper nanoparticles by molecular grafting, which improved its mechanical stability, since the surface was verified to maintain a large contact angle after long-distance abrasion and folding. Compared with the superhydrophilic copper surface, the superhydrophobic coating showed better corrosion resistance in 3.5 wt% NaCl solution and artificial sweat. Combined with the inherent conductivity of copper, fabrics have potential applications in the new generation of advanced textiles.

Influence of surface morphology and surface free energy on the anticoagulant properties of nanocone‐shaped ZnO films

AbstractThe anticoagulant properties of materials are easily affected by the surface properties, which provide belief for designing and developing effective anticoagulant materials to achieve long‐term stable application of blood‐contacting implants and devices. Here, various nanocone‐shaped ZnO films were prepared by simple electrochemical deposition followed by hydrothermal method, and modified with polyethylene glycol (PEG10000, a hydrophilic substance). The influence of surface morphology and surface free energy on the anticoagulant properties of ZnO nanofilms was explored. Both hydrophilic (CA < 40°, surface modified with PEG10000) and superhydrophobic (CA > 150°, surface with rough needle‐like structure) ZnO nanofilms have good anticoagulant properties. Compared with the free energy of the film surface, the surface microstructure of ZnO nanofilms has a greater impact on the anticoagulant properties. After the ZnO nanofilms were modified with PEG, the contact model of water on the surface conforms to the Wenzel model instead of the Cassie model. The number of adhesive platelets was largely reduced, and the hemolysis rate is less than 5%, indicating the better blood compatibility. These characteristics are of special significance for the development of nanomaterials with good anticoagulation.

Calcium Carbonate@silica Composite with Superhydrophobic Properties.

In this paper, spherical calcium carbonate particles were prepared by using CaCl2 aqueous solution + NH3·H2O + polyoxyethylene octyl phenol ether-10 (OP-10) + n-butyl alcohol + cyclohexane inverse micro emulsion system. Then, nanoscale spherical silica was deposited on the surface of micron calcium carbonate by Stöber method to form the composite material. Scanning electron microscope (SEM), X-ray powder diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), Thermogravimetric analysis (TGA) and X-ray photoelectron spectroscopy (XPS) were used to characterize the morphology and structure of the composite material. It is found that the surface of the composite material has a micro-nano complex structure similar to the surface of a “lotus leaf”, making the composite material show hydrophobicity. The contact angle of the cubic calcium carbonate, spherical calcium carbonate and CaCO3@SiO2 composite material were measured. They were 51.6°, 73.5°, and 76.8°, respectively. After modification with stearic acid, the contact angle of cubic and spherical CaCO3 were 127.1° and 136.1°, respectively, while the contact angle of CaCO3@SiO2 composite was 151.3°. These results showed that CaCO3@SiO2 composite had good superhydrophobicity, and the influence of material roughness on its hydrophobicity was investigated using the Cassie model theory.

Review of super-hydrophobic materials research

We reviewed the research on super-hydrophobic materials. Firstly, we introduced the basic principles of super-hydrophobic materials, including the Young equation, Wenzel model, and Cassie model. Then, we summarized the main preparation methods and research results of super-hydrophobic materials, such as the template method, soft etching method, electrospinning method, and sol-gel method. Among them, the electrospinning method that has developed in recent years is a new technology for preparing micro/nanofibers. Finally, the applications of super-hydrophobic materials in the field of coatings, fabric and filter material, anti-fogging, and antibacterial were introduced, and the problems existing in the preparation of super-hydrophobic materials were pointed out, such as unavailable industrialized production, high cost, and poor durability of the materials. Therefore, it is necessary to make a further study on the application of the materials in the selection, preparation, and post-treatment.

A Porous Media Leakage Model of Contact Mechanical Seals Considering Surface Wettability

The fluid leakage channel found in contact mechanical seals belongs to the microchannel category. Thus, upon further inspection, the influence of surface wettability and other factors neglected in previous studies becomes obvious. The porous leakage model of contact mechanical seals considering the surface wettability presented in this paper was based on the Cassie model and slip theory. The variations of the microchannel slip length and the velocity under various wettability conditions were studied and the relationship between the slip length and the apparent contact angle was established. Moreover, using porous media theory, the theoretical model of the leakage rate in contact mechanical seals considers the surface wettability depending on various parameters. The observed parameters included the surface contact angle, sealing medium pressure, viscosity coefficient, fractal dimension, and maximum pore diameter. The simulation results obtained using the proposed model have shown that the leakage rate increases with the increase of the apparent contact angle. Particularly when the contact pressure is small, the influence of the surface wettability is more significant. Furthermore, the leakage rate results obtained via the proposed model were compared to those of existing models. The comparison confirmed that the proposed model is applicable and that the necessity of considering wettability significantly affects the leakage rate calculation accuracy. The proposed model lays a foundation for further improving the calculation accuracy, making it easier for both the researchers and practitioners to suppress the leakage in contact mechanical seals.

Interrupter Size Effect of High‐Voltage Gas Circuit Breaker on Thermal Interruption Performance and Current Zero Properties

Small model interrupters are convenient to investigate interrupting performance of high‐voltage gas circuit breakers in terms of efficiency. However, the equivalence of interruption phenomena of small model interrupters (e.g., interrupting performance, interruption criteria, and geometric sensitivity) to product‐scale interrupters has not been clarified. Interrupting tests with small and large model interrupters were carried out with the dimensions of the interrupter as parameters to clarify the effects of modified interrupter dimensions on blast pressure and interrupting performance. Arc voltage and arc conductance were measured to acquire detailed electrical behavior in the thermal interrupting phase. In the results, small model interrupters showed the same performance trends as geometrically modified large model interrupters. By introducing an interrupter size factor, the boundary of the extinction peak of the arc voltage and arc conductance at 200 ns before current zero that distinguishes the success and failure of interruption for both small and large models agreed well. Moreover, the arc parameters determined by Cassie and Mayr arc models were analyzed with consideration to interrupter size factor. In conclusion, the interrupter size factor was validated from the point of arc phenomena and an equivalence of small model to product‐scale interrupter was confirmed. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Copper nanoparticle decorated non-woven polypropylene fabrics with durable superhydrophobicity and conductivity

In this study, a facile method was prepared to fabricate highly flexible, conductive and superhydrophobic polymer fabrics. Copper nanoparticles (CuNPs) were decorated on polypropylene fabrics using a simple spraying method and superhydrophobicity was obtained after vacuum drying for 4 h without any surface modifier. Accumulation of CuNPs constituted coral-like rough micro-nano structures, forming a stable Cassie model and endowing the surface with dense charge transport pathways, thus resulting in excellent superhydrophobicity (water contact angle ∼159°, sliding angle ∼2.3°) and conductivity (sheet resistance ∼0.92 Ω sq−1). The fabrics displayed superior waterproof and self-cleaning properties, as well as great sustainability in the water. Additionally, the superhydrophobicity and conductivity can be almost maintained after heat treatment, wear testing, water droplet impinging, weak alkali/acid treatment and repeated bending-kneading tests. These superhydrophobic and conductive fabrics that are free from moisture and pollution can be a reliable candidate to solve the water-penetration issue in the rapid development of flexible electronics.

Antifrosting Performance of a Superhydrophobic Surface by Optimizing the Surface Morphology.

Improving the antifrosting ability of stainless steel is crucial. In previous reports, many efforts have been dedicated to enhancing the antifrosting performance of superhydrophobic surface by fabricating different surface morphology. However, no researchers have proposed what kind of surface morphology can effectively prevent the frost based on the theory of superhydrophobic surfaces. In this article, we build a simulation model to study the effects of different surface morphology on antifrosting based on the Cassie model. We find that the higher the proportion of air between the droplet and the substrate, the better the antifrosting performance of the superhydrophobic surface. Therefore, we propose one superhydrophobic surface (denoted as sample #R) fabricated by selective growth. It can contain more air between the droplet and the surface. Further frosting experiments at a low temperature of -21 °C and a humidity of 75% show that 15% frost coverage on sample #R can be delayed to 63 h, as compared to less than 3 h for untreated stainless steel. In addition, the preparation method is generally applicable to other metals. Therefore, this work provides new insights into the rational design of a superhydrophobic surface with antifrosting in a harsh environment.

Controllable superhydrophobic surfaces with tunable adhesion on Mg alloys by a simple etching method and its corrosion inhibition performance

Through a simple chemical etching and surface modification, superhydrophobic surfaces with tunable water adhesion were prepared on rolled Mg-3Al-1Zn (AZ31) and Mg-9Al-1Zn (AZ91) alloy sheets. The different water adhesion is described by three different wetting model, i.e. Wenzel, Cassie impregnating, and Cassie model. An in-depth investigation on anti-corrosion performances of low adhesive superhydrophobic AZ31 and AZ91 surfaces reveals that dense microstructure can effectively improve the stability of Cassie state, thus facilitating durable anti-corrosion ability. Simultaneously, the superhydrophobic surfaces with tunable water adhesion are demonstrated to be feasible in the application of low-loss transport of microdroplet. In addition, the as-fabricated superhydrophobic surfaces show high-temperature stability and chemical stability in a large range of temperature and pH, respectively. It is expected that this research can shed light on designing new anti-corrosion and tunable adhesive superhydrophobic surfaces, and as-fabricated superhydrophobic Mg alloys are promising in medical instruments, transport systems, micro-fluidic devices, and so on.

Fabrication of micro-patterned ZrO2/TiO2 composite surfaces with tunable super-wettability via a photosensitive sol-gel technique

A patterned ZrO2/TiO2 composite surface consisted of ZrO2 bulges and TiO2 dimples was prepared utilizing a photosensitive sol-gel technique, which has a peak-valley hierarchical structure and presents excellent non-light activated superhydrophilicity. After modification by low-surface-energy molecules of 1H,1H,2H,2H-perfluorooctyltrichlorosilane (FOTS), the wettability was consequentially changed into sliding superhydrophobicity with a water contact angle (WCA) of 158° and a sliding angle of 8°. Ultraviolet irradiation was finally performed to degrade the FOTS layer on TiO2 dimples of the FOTS-modified ZrO2/TiO2 surface, and the obtained pinning effect could make the surface exhibit unique sticky superhydrophobicity with WCA of 154° and strong adhesion to water. It was also revealed that the formation mechanism of sticky superhydrophobicity is quite different from the reported petal model and metastable model, and it can be explained by a novel intermediate model between Wenzel and Cassie models. More interestingly, the sticky superhydrophobic surface was used as a “mechanical hand” to capture water droplets from the sliding superhydrophobic surface and transfer to the superhydrophilic surface, suggesting that it has a huge potential in water droplet transportation.