Principle Of Conservation Of Energy Research Articles

Complete RITZ Set of Ro-Vibrational Energy Levels of 16O3 Deduced from Experimental Spectra: Critical Analysis of Transition Frequencies in Spectroscopic Databases

In this work, we provide the most complete to date reference data for 28 572 rovibrational levels of the electronic ground state of the ozone 16O3 molecule up to the maximum rotational quantum numbers J = 80, Ka = 29 determined from 75 290 experimental transitions covering the range (0.3–7999) cm−1. These energy levels belong to 98 vibrational states extending up to 96.7% of the first dissociation threshold D0 of the molecule. The energy determination procedure is based uniquely on the fundamental Ritz-Planck-Einstein energy conservation principle without use of any approximate Hamiltonian models. A dedicated RITZ computer code produces uncertainties and the correlation matrix for all derived energy levels and permits the prediction of confidence intervals for all dipole-allowed transitions among these levels. The rms deviation of the RITZ transitions for microwave experimental data up to the THz range is 2.6 × 10−6 cm−1. For infrared transitions up to the fundamental and second overtone and combinational bands, including 10 and 5 µm regions important for atmospheric and astrophysical applications, the rms deviation is 1.8 × 10−4 cm−1. For the entire set of lines, the rms deviation is 5.5 × 10−4 cm−1 with the overall dimensionless weighted standard deviation of 0.7. Most of the energy level data is original. For the regions above 6000 cm−1, where empirical data have been previously obtained in the literature from CRDS laser measurements, our data agree well with the published values but provide a more realistic uncertainty analysis. Detailed comparisons of the RITZ transitions with the HITRAN2020 database are discussed and related recommendations are suggested.

Theoretical model for predicting the yield strength of metal materials under electrically-assisted deformation

In this paper, based on the Force-Heat equivalence energy density principle, considering the thermal and athermal effects caused by current, the theoretical model for the current density dependent yield strength of metallic materials is developed. The novelty of this work lies in the fact that no adjustable fitting parameters were introduced during the modeling process, and both the Joule heating effect and the energy changes brought about by free electrons were considered in the contribution to the yield behavior of metallic materials, on which basis a critical energy density related to yield under the action of electric current was proposed. This model reveals the quantitative relationships between elastic modulus, steady-state temperature, electrical resistivity, thermal conductivity, current density, and yield strength under the action of current. The theoretical prediction results have achieved good consistency with experimental results. Furthermore, based on the principles of energy conservation and the assumption of steady-state, a theoretical expression was derived to predict the steady-state temperature caused by Joule heating. In addition, the results of the model analysis indicate that increasing the electrical resistivity of the material or decreasing its thermal conductivity can both facilitate plastic deformation and processing in electrically-assisted forming processes, especially at high current densities. This work provides an effective method for quantitatively evaluating the yield strength of metallic materials under the action of electric current, which can offer theoretical basis and optimization guidance for the extensive application and further development of electrically-assisted processes.

A robust 3D finite element framework for monolithically coupled thermo-hydro-mechanical analysis of fracture growth with frictional contact in porous media

This paper presents the formulation of a robust integrated framework for the coupled multiphysics and multiple fracture growth analysis in porous media. The finite element-based thermo-hydro-mechanical method for fracture growth with frictional contact (THMf-g) simultaneously solves monolithically coupled equations, incorporating contact and frictional constraints from fracture sliding. It also implements an adaptive process to update fields and geometries during fracture growth, effectively modeling emerging new surfaces. The thermo-hydro-mechanical fields are derived from fundamental principles of mass, momentum, and energy conservation and discretized numerically using the finite element method. Fractures are represented as sub-dimensional surfaces embedded within the volume of the porous medium. The growth of multiple fracture is modeled based on stress intensity factors at fracture tips, with fracture aperture and permeability emerging as dynamic properties of the system. The main novelty of this work lies in extending the implicitly solved monolithic coupling to include frictional and growth modeling for multiple non-planar fractures of emerging geometry in three dimensions. This includes the direct incorporation of cubic terms in the fracture flow equations and convection terms in the heat transfer equations, adopting an incremental method to solve these coupled, nonlinear equations. To ensure energy conservation, the heat equations are resolved using an implicit scheme, establishing a velocity dependency on pressure fields and introducing quadratic terms into the heat equation. Furthermore, the heat transfer equation has been revised to account for the work done on the fluid, enhancing the accuracy of thermal modeling. A contact mechanics leader–follower strategy tracks a conformal mesh split at each fracture, accounting explicitly for permeability changes during deformation and growth, effectively reducing computational complexity and cost. The iterative process for applying these constraints and the solution of the coupled THMf-g with friction and growth is described. The method does not require calibrated material properties or artificial length scale parameters, and relies on laboratory-measured properties with direct physical interpretation. A detailed algorithm is presented, including the updating of apertures and handling of new surfaces during the simulation, accounting for the variability of fracture permeability and its interplay with contact and friction during the non-linear solution. Several validating numerical experiments are benchmarked against analytical solutions, demonstrating the accuracy and reliability of the proposed framework in capturing complex fracture behavior and multiphysics interactions in porous media.

Two novel semi-analytical coefficients of restitution models suited for nonlinear impact behavior in granular systems

This study proposes two novel semi-analytical coefficients of restitution (CoR) models to predict nonlinear impact behavior in granular systems. The models address energy loss at the end of the compression phase, redefining a characteristic length to enhance the equation of motion for colliding particles. The first, the inverse CoR model, derives from the inverse collision approach, introducing a length parameter for its analytical solution. The second, the energy CoR model, is proposed by integrating the damping force in conjunction with the energy conservation principles. Both models are semi-analytical since the characteristic length is numerically determined. Despite differing in derivation, both models account for initial impact velocity and material properties. Comparative analysis highlights their advantages over existing models, with validation through experimental data. Simulations confirm that the models yield accurate predictions for both metal and nonmetal contacts, at high and low impact speeds.

Ballistic response of an airbag with parallel ribs under spherical projectile impact

The airbag-type inflatable structure with ribs was developed, composited from thermoplastic polyurethane (TPU) membranes. Ballistic impact tests were conducted on pre-inflated airbags to assess the airbag’s dynamic response. A set of Split Hopkinson Tensile Bar (SHTB) experiments were conducted on TPU membranes at strain rates ranging from 3000 to 12,000 s−1 to derive a strain-rate dependent constitutive model for TPU under ballistic impact conditions. Based on the fluid cavity inflation method, a finite element model was employed to analyze the structural response of the airbag. Based on the principle of energy conservation, an innovative theoretical model for the impact of airbags considering internal pressure has been established. The results indicate a strong agreement between the numerical, theoretical, and experimental results concerning the impact process and ballistic limit. It was observed that as the internal pressure rises, the ballistic limit of the airbag decreases. The theoretical model indicates that with an increase in internal pressure and the spacing of the center ribs, the initial strain energy of the membrane increases, leading to a decrease in the kinetic energy dissipation of the airbag to the projectile and subsequently reducing the ballistic limit of the airbag. This research provides a theoretical foundation and basis for the structural design and analysis of energy dissipation patterns in inflatable structures. It expands the potential applications of inflatable composite structures in the field of ballistics.

A novel extraction method for combustion feature of CI engine in electric hybrid power based on engine instantaneous speed

Hybrid power systems represent a crucial avenue for the advancement of vehicle power, offering a novel framework and context for the intelligent evolution of internal combustion engines. The governance of internal combustion engines stands as the cornerstone of power intelligence, with in-cylinder combustion control serving as a pivotal research focus within the realm of internal combustion engine regulation. The accurate assessment of cylinder state in hybrid power systems forms the foundation for effective in-cylinder combustion control. This paper introduces an approach to extract cylinder combustion state (cylinder work and CA50) based on instantaneous speed signals. First, the instantaneous speed signal undergoes processing using synthetic speed algorithms, followed by an evaluation of algorithm effectiveness. Subsequently, the theoretical derivation of the relationship between synthesized speed signals and cylinder state is established based on conservation of energy principles, leading to a method for extracting cylinder state. Finally, experimental validation is conducted at 270 steady-state operating points (varied speeds and load ratios) and 2 dynamic processes to verify prediction accuracy using the proposed method. The results demonstrate precise prediction capabilities for both cylinder work and CA50, with prediction errors falling within ≤10 % for CA50 and ≤9 % for cylinder work; moreover, 97 % of steady-state operating points exhibit error ranges within 5 % or less and the average error of dynamic process is 5 %.

Estimation of thermal emission from mixture of CO2 and H2O gases and fly-ash particles

Abstract In the present work the thermal emission from gases and particle mixture is studied comprehensively. The mixture consist of CO2 and H2Ogases along with fly-ash particles and their spectral radiative properties are obtained from HITEMP database and Mie theory, respectively. The Line-by-line method, known for high accuracy is used to estimate radiative heat transfer from gases and particle mixture. Three distinct cases, i.e, pure absorption/emission, pure scattering, and their combined effects are investigated. The spectral radiative transfer equation is solved by finite angle method (FAM) and the correctness of the results is ensured by principle of energy conservation. The anisotropic scattering is modeled using the Henyey-Greenstein method. The influence of radiative properties of the participating medium, along with wall and cavity temperatures, on heat transfer and emission spectrum is evaluated. The radiative heat transfer enhances with introduction of the particles in the gaseous mixture. For pure scattering medium, the emission spectrum on each wall differs and also varies from the emission spectrum of the emitting wall. The particle influence grows notably with higher volume fractions in gaseous mixture. While there is a notable contribution of anisotropic scattering in a purely scattering medium, its significance diminishes in an absorbing, emitting, and scattering medium.

Analytical model for laser cutting in porous media

Laser cutting in porous media presents both challenges and opportunities for various applications. Laser cutting requires a deep understanding of heat transfer, materials, and laser physics, and can involve nonlinear and transient effects. There is a lack of literature regarding modelling laser cutting in porous media. Using conservation of energy principle, an analytical model has been developed to calculate the total laser power required to cut a porous media without the need for complex numerical simulations.The model incorporates a new correlation for calculating waste power due to heat transfer into the surrounding during laser cutting as well as modifications to the energy balance equation to incorporate the effect of porosity and fluid saturation.The model has been validated with experimental data of cutting porous media (carbonate rock) and corroborated well. Model validation showed around 10 % accuracy for fluid saturated rock samples and around 17 % accuracy for dry rock samples. Also it has been observed that the level of accuracy improves with lower Peclet number (i.e. lower cutting speed).The proposed analytical model has been used to examine the effect of Peclet number, porosity, fluid saturation, rock type and material thickness on laser cutting performance. The methodology described in this article can be used as a guideline to calculate laser power requirements and size the laser equipment at an early stage prior to the manufacturing process.

Design of A PFR For the Production of 1,000,000 Tons Per Year of Ethyl Acetate from Esterification of Acetic Acid and Ethyl Alcohol

The research considered the design or size of a plug flow reactor for the production of 1,000,000 tons of ethyl acetate per year from the esterification of acetic acid and ethyl alcohol in the presence of an acid catalyst. The PFR design models for volume, height, diameter, space time, space velocity, quantity of heat generated, quantity of heat generated per unit volume of the reactor as well as the temperature effect models were developed using the conservation principle of mass and energy at steady state operation of the reactor. The developed models were simulated using MATLAB at initial feed and operating temperature of 299.830k and 343.15k respectively and fractional conversion variation between 0 to 0.95 at an interval of 0.05. At a maximum conversion of 0.95, the PFR size specification for volume, height, diameter, space time, space velocity, quantity of heat generated and the quantity of heat generated per unit volume of the reactor was 15.2774m3, 4.2691m, 2.1346m, 2.9956sec., 0.3338sec-1, 12821.5800j/s and 839.2536j/sm3 respectively. The effect of the operating parameters on the performance or functional parameters of the reactor are presented in profiles as shown in figure 2 to 12 and the profile behaviour or trend were in agreement with process behaviour of PFR steady state operation in various literatures. The research have shown that in order to ensure sustainability and continuous production of ethyl acetate to meet the global demand of the economic and viable product, the plug flow reactor have demonstrated a good performance characteristics as a reacting media for the esterification process especially in the energy efficiency of the process as well as the product yield.

Ballistic characteristics of ceramic core sandwich structures

The ceramic core sandwich structure (CCSS) is a lightweight material with advantages of high anti-ballistic impact performance, high energy absorption and high specific strength. The ballistic performances of the CCSS with metal face plates hit vertically by projectiles with the nose shapes of conical, flat, and hemispherical are studied analytically and numerically in this paper. Based on the principle of energy conservation, an analytical model of ballistic characteristics of the sandwich ceramic core structure is developed. Numerical calculations are conducted, and the numerical model has been verified by experimental results from references by others. In addition, the analytical results agree well with finite element results. The effects of shape of projectile head, the thickness ratio of three plates of CCSS, and the ratio of shear strength of ceramic core to yield strength of metal face plates on the ballistic characteristics of the CCSS are discussed. It is shown that the conical-nosed projectile achieved the highest ballistic limit velocity (BLV) and the sharper nose increases the normal stress at the impact area thereby enhancing the BLV. The thickness of the ceramic core significantly influences the resistance of the CCSS and the thicker ceramic core enhances the ability of CCSS to absorb kinetic energy from the projectile. Furthermore, an appropriate increase in the yield strength of face plates can enhance the anti-ballistic impact performance of the CCSS. These insights have practical implications for the design of protective systems in military and civilian applications, where optimizing materials for impact resistance is crucial.

A remote monitoring method for gateway electric energy meters based on electric energy, voltage and current conservation decomposition

Abstract A remote monitoring technique for gateway electricity meters is introduced that leverages conservation principles of electric energy, voltage, and current. It aims to tackle issues related to errors in electric energy meters and transformers that are challenging to distinguish, as well as the high costs associated with on-site testing. The ridge regression is used to solve the formulas for bus power and current conservation to obtain gateway metering points’ error and current loops’ error. The voltage loop error is determined through an averaging method, which is then used to calculate the error in electric energy meters. The voltage consistency method is used to synchronize the time bias between gateway electricity meters, ensuring accurate calculations. The analysis results indicate that the proposed method effectively monitors the operating status of gateway electric energy meters and offers greater accuracy compared to benchmarks. This method can timely discover suspected inaccurate electricity meters, aiding in their maintenance and efficient operation.

Optimization of thermal performance in hybrid nanofluids for parabolic trough solar collectors using Adams–Bashforth–Moulton method

Solar energy is an environment-friendly renewable energy source that fulfills the energy consumption requirements of the world economy. Concentrated solar power is the most advanced technology that efficiently absorbs concentrated solar energy. This article investigates the solar energy storage and entropy generation in concentrated parabolic trough solar collectors for hybrid nanofluid flow due to a spinning tube inserted at the receiver's center. The effect of copper nanoparticles and multi-walled carbon nanotube mixture is studied using water-based fluid. Also, the influence of an external magnetic field is investigated with thermophoresis and Brownian motion of nanoparticles. The governing equations for the nanofluid flow are derived using the conservation principles of mass, momentum, energy, and concentration with boundary layer assumptions and no-slip boundary conditions. The governing equations are numerically solved using Adam Bashforth and Adam Moulten's fourth-order predictor-corrector numerical scheme along with the shooting approach. The numerical outcomes for the fluid velocity, temperature, Nusselt number, and entropy formation against various influential physical parameters have been discussed using graphs. It is observed that the augmenting Eckert number, thermophoretic diffusion parameter, and Brownian motion parameter escalates the thermal profiles. Also, an escalation of the radiation parameter and Lewis number enhances the Nusselt number. Thermal energy storage in solar collectors utilizing different terminologies is crucial for improving the efficiency and performance of solar thermal collectors.

Energy-based damage assessment method for masonry walls under seismic and fire loads

The evaluation of the out-of-plane (OOP) behavior for infilled walls is a critical aspect of regional seismic and fire resilience assessment. This study presents a detailed finite element (FE) model that comprehensively captures the seismic and fire behaviors of masonry walls. The FE model incorporates key factors governing the thermo-mechanical behavior of masonry walls, including temperature-dependent material properties, nonlinearities in geometry and material, block cracking and crushing, and mortar damage. Then, an energy-based damage criterion is proposed based on the principle of energy conservation, leveraging the combined mixed fracture energy and internal energy of elements. In addition, this study defines the damage levels of masonry walls under OOP loading and fire and determines corresponding damage indices using the proposed energy-based damage criterion. This criterion is further compared with a stiffness-based damage criterion. Finally, the proposed damage assessment method is employed to evaluate the damage evolution of infilled walls under seismic, fire and post-earthquake fire scenarios, and to conduct a fragility analysis. The results demonstrate a high degree of agreement between the predicted and measured damage states of masonry walls under seismic and fire loads. More severe seismic damage does not always result in diminished fire resilience. Evaluating post-earthquake fire damage requires considering the impact of displacement directions caused by earthquakes and fires.

Закладка виноградника на основе принципов энерго-ресурсосбережения

Abstract. The article contains materials that form the basis of a feasibility study (FS) for laying a vineyard (from planting to fructification), developed according to the principle of energy and resource conservation provided for in the project assignment. The project documentation is being developed in order to optimize the complex of sequential technological operations and production processes aimed at creating a sustainably functioning viticultural economy. The general principles of energy and resource conservation include: the latest achievements of science and best practices in the field of viticulture, rational use of land funds, thanks to preliminary soil surveys, optimized varietal composition, design of plantings and compact placement of arrays with the prospect of irrigation, reduction of energy losses to the level of operationally unavoidable, the use of highly concentrated, complex agrochemicals and methods of their application, the availability of appropriate infrastructure, design estimates optimized with the prospect of improvement and modernization (energy and resource-saving object estimates), planned economic productivity of plantations, measures to maintain the economic fertility of soils corresponding to the biological requirements of grape culture, which determines the stability and productivity of perennial plantations. Methodological approaches and current methods, publications of a recommendatory nature used for the development of a feasibility study are indicated. The successive stages of the development of project documentation are considered, the techniques that contribute to reducing the costs of production processes are outlined. The recommended regionalized and promising assortment of grapes for the formation of highly productive stable ampelocenoses ensuring stable highly profitable functioning of enterprises of the grape-growing industry in the Krasnodar region is presented and justified. The recommended current varietal composition of plantings is compiled taking into account the edaphoclimatic conditions of the design object, the agrobiological characteristics of grape varieties, as well as taking into account current global trends in the organization of a sustainably functioning highly efficient industrial enterprise for the production of viticulture products. Keywords: ampelocenosis, project assignment, long-term planning, varietal policy, energy and resource conservation

Theoretical investigation of hysteresis loops in free-surface flow under sluice gates for power-law channels

ABSTRACT In the present study, a new theoretical framework and analytical solutions to the problem of hysteresis loops due to hydraulic jump in power-law open channels under supercritical flows are introduced. This investigation primarily focuses on the flow dynamics encountered at a vertical sluice gate across channels of various shapes: rectangular, parabolic, and triangular. By the application of energy and momentum conservation principles, the dual flow configurations emerging under identical initial conditions are shown. An intensive analytical computational analysis led to the development of approximate theoretical models, facilitating the prediction of hysteresis loops for a wide range of Froude numbers and dimensionless channel geometry parameters. Several illustrative examples were treated and the results show a high degree of accuracy of the proposed models in predicting the hysteresis loops. The present research contributes to a novel methodology for enhancing predictions regarding the behavior of supercritical flows and the design of open channels for specific scenarios of the hysteresis phenomenon.

Spectral-based estimation of chlorophyll content and determination of background interference mechanisms in low-coverage rice

The chlorophyll content is a vital indicator of rice growth and nutritional status. However, estimating the rice chlorophyll content using spectral-based techniques at the early tillering stage is challenging because of background interference. Using the energy conservation principle, this study explained the spectral variation and background interference mechanisms of clear, muddy, and green algae-covered backgrounds. We developed mathematical interference models for the three types of backgrounds and determined their interference degree and influence mode. We developed rice chlorophyll content estimation models for unclassified and classified (clear, muddy, and green algae-covered) backgrounds using 12 preprocessing, four wavelength selection, and three modeling methods, and we explored the importance of background classification. Moreover, we found that the optimal chlorophyll content estimation model for the clear background was SS+UVE+CNN, with R2 and RMSE values of 0.786 and 13.191 in the training set and 0.741 and 15.327 in the test set, respectively; that for the muddy background was MSC+GA+CNN, with R2 and RMSE values of 0.914 and 10.425 in the training set and 0.660 and 16.844 in the test set, respectively; and that for the green algae-covered background was DC+GA+CNN, with R2 and RMSE values of 0.904 and 9.111 in the training set and 0.688 and 17.694 in the test set, respectively. Our study could provide valuable insights into reducing and correcting background interference during proximal remote sensing data collection.

Impact of freeze recovery method on high-speed fracture in metal cylindrical shells

The freeze recovery method (FRM) is a crucial approach for investigating the high-speed fracture process of metal cylindrical shells under explosive loading. However, the precise impacts of the recovery process on the deformation and fracture behavior of such shells remain unclear, significantly constraining the widespread application of this method in high-speed fracture studies. This paper quantitatively evaluates the effects of the expansion contour, fracture mode, and damage state of intermediate shells at different stages of fracture development using a crack evolution simulation method and nondestructive crack detection technique. The recovered shell contour can effectively represent the free expansion contour of the shell at the equivalent moment, with an error of less than 4%. Impact induces tensile cracks on the outer wall of the shell, which leads to changes in the local fracture mode. A method of crack elimination and equivalence in the damage statistics of the recovered shell is proposed to address this effect. The recovered shell can characterize the damage evolution during free expansion at the equivalent moment after eliminating the influence of excess tensile cracks. Based on the principle of stress analysis and energy conservation, the formation mechanism of tensile cracks in the outer wall of the shell is explored, and the correlation between tensile cracks and recovery time is elucidated. The study shows that the impact of fracture damage caused by freezing recovery is gradually reduced over time. The improved freezing recovery method based on the hard recovery principle is successfully used to recover the multistage intermediate shell, meeting the demand for obtaining the transient physical model in the high-speed fracture field.

Effects of cushion gas pressure and operating parameters on the capacity of hydrogen storage in lined rock caverns (LRC)

Hydrogen storage in lined rock cavern (LRC) provides versatile site selection, safety, and stability, making it a crucial option. In this study, a thermodynamic mathematical model was established to describe hydrogen storage in LRC. This model is based on the principles of mass, momentum, and energy conservation while accounting for the authentic compressibility of hydrogen. The thermodynamic fluctuations throughout the seasonal cycle in LRC were computed using the COMSOL Multiphysics software. The results indicate that when the hydrogen storage reaches the operating pressure, the lower the cushion gas pressure, the greater the hydrogen injection amount, and the higher the utilization rate of storage capacity. With a cushion gas pressure of 3 MPa, the storage capacity utilization rate exceeds that at 15 MPa by 41 %. The injection rate of 0.5 kg/s results in a temperature increase of 12 °C compared to 0.27 kg/s, indicating twice the temperature rise at the 0.27 kg/s injection rate. An increase in injection temperature corresponds to higher temperature within the hydrogen storage cavern upon completion of gas injection, thereby reducing the time needed for gas injection to reach maximum operating pressure. A lower initial cavern temperature results in a longer time for hydrogen storage to reach maximum operating pressure.

Lid driven flow and heat transfer due to various positions of slit in a square cavity: FEM approach

A detailed analysis of flow and heat transfer due to moving slit within the various positions of the square cavity is discussed. The slit is strategically positioned and examined at three distinct locations within the square cavity i.e. left, middle and right. Constraints of the square cavity are defined for horizontal and vertical walls. The top horizontal wall is considered to be adiabatic while the other three walls of the cavity are cold. The upper surface of slit is heated and movable towards the left side of the square cavity while the other three walls are immovable and cold. The fluid flow dynamics and heat transfer within the enclosed cavity are governed by fundamental principles of mass, momentum and energy conservation. These governing principles manifest as intricate mathematical equations, specifically nonlinear partial differential equations accompanied with boundary conditions. The key parameters under consideration include the Reynolds number (250≤Re≤1500) and Richardson number (0.01≤Ri≤5) at a fixed Prandtl number (Pr=6.2). These parameters are analysed through variations in velocities, temperature profiles, isotherms and streamlines. In the computational framework, the momentum and temperature equations are addressed through quadratic interpolation, while linear interpolation is applied to handle the pressure equation. The numerical solution, utilizing Newton's technique and the PARADISO solver, is rigorously validated against existing research methodologies, establishing its methodological reliability. Higher Reynolds numbers shift the primary vortex towards the middle and create corner recirculation zones, more uniform heat distribution, while higher Richardson numbers increase buoyancy forces, reducing isotherm contours and affecting heat distribution. The local Nusselt number increases with the increase in Reynolds numbers but shows small changes with the increase in Richardson number. The value of Nusselt number decreases as the position of slit changes from left to right.

Phase diagram for nanodroplet impact on solid spheres: From hydrophilic to superhydrophobic surfaces

The impact of droplets on solid surfaces is a crucial fluid phenomenon in the additive industry, biotechnology, and chemistry, where controlling impact dynamics and duration is essential. While extensive research has focused on flat substrates, our understanding of impact dynamics on curved surfaces remains limited. This study seeks to establish phase diagrams for the process of droplet impact on solid spheres and further quantitatively describe the effect of curvature through theoretical analysis. It aims to determine the critical conditions between different impact outcomes and also establish a scaling relationship for the contact time. Here, the post-impact outcome regimes occurring for a wide range of Weber numbers (We) from 1.2 to 173.8, diameter ratio (λ) of solid spheres to nanodroplets from 0.25 to 2, and surface wettability (θ) from 21° to 160°, through the molecular dynamics simulation method (MD) and theoretical analysis. The MD simulations reveal that the phase diagrams of droplet impacts on hydrophilic, hydrophobic, and superhydrophobic spheres differ, with specific distinctions focusing on rebound and three different forms of dripping. Furthermore, a theoretical model based on the principle of energy conservation during impact on superhydrophobic surfaces has been developed to predict the critical conditions between rebound and dripping states, showing good agreement with simulation results. Additionally, a new scaling relationship of contact time for droplet impact on superhydrophobic spherical surfaces has also been established by extending and modifying the existing models, which also agrees well with the simulated results. These insights provide a foundational understanding for designing surface structures.