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In this paper, the effects of surface wettability and topography on a droplet, which is driven by a body force to pass through grooved walls, are studied by using the multiphase lattice Boltzmann model. At small scale, the shape and velocity of the droplet were found to be strongly affected by the wettability and configuration of the wall. The drag on the droplet moving over grooved surfaces was found to decrease as the wall hydrophobicity increases. It was also found that the wettability decides whether the droplet fills or does not fill the whole grooves.

We have used standard fractal analysis and Markov approach to obtain further insights on roughness and multifractality of different surfaces. The effect of coating rates on generating topographic rough surfaces in copper thin films with same thickness has been studied using atomic force microscopy technique (AFM). Our results show that by increasing the coating rates, correlation length (grain sizes) and Markov length are decreased and roughness exponent is decreased and our surfaces become more multifractal. Indeed, by decreasing the coating rate, the relaxation time of embedding the particles is increased.

The onset of thermal instability with hybrid nanoparticles Al₂O₃–Cu in nanofluid is investigated with the combined effects of variable gravity, variable heat source and Lorentz force in a porous medium. Its applications are in many areas like chemical engineering, geophysics, astrophysics, etc. Based on literature, many gravity variations are assumed in the present analysis, along with a space-dependent heat source/sink parameter that varies along the width of the channel. The finite difference-based Lobatto IIIa method has been applied to solve the system under no nanoparticle flux and rough boundary conditions, and approximate analytical results are generated for some special cases. The roughness parameters (${\lambda }_1,{\lambda }_2$), Darcy number (Da), gravity variation function ($G(z)$), and Chandrasekhar number (Q) delay the onset of convection and thus stabilize the system. It is also observed that an increase in the Lewis number Le, power index in variable heat source, and the nanoparticle Rayleigh concentration number Rn decreases the critical Rayleigh number $R_{\theta ,c}$ which destabilizes the system, and increases the critical wave number, which enlarges the convection cell size. In the case of exponential variation ($1-e^z$) in the gravity variation parameter, the system becomes stabilized due to a delay in the onset of convection. In addition, we have considered multilayer perceptron-artificial neural network (MLP-ANN) computation to predict the critical Rayleigh number as per function of important controlling parameters. The data set of 625 observations is chosen keeping 70% for testing, 15% for training and 15% for validation using efficient Levenberg−Marquardt back propagation algorithm with optimal accuracy measures i.e., root mean square deviation (RMSE), root mean relative error (RMRE) and $R^2$ (coefficient of determination). Finally, the regression plots are drawn that correlate, target and output data.

Scaling region identification is of great importance in calculating the fractal dimension of a rough surface profile. A new method used to identify the scaling region is presented to improve the calculation accuracy of fractal dimension. In this method, the second derivative of the double logarithmic curve is first calculated and the $K$-means algorithm method is adopted to identify the scaling region for the first time. Then the margin of error is reasonably set to get a possible scaling region. Finally, the $K$-means method is used again to obtain a more accurate scaling region. The effectiveness of the proposed method is compared with the existing methods. Both the simulation and experimental results show that the proposed method provides more precise results for extracting the scaling regions and leads to a higher calculation precision of fractal dimensions.

Understanding the fundamental mechanisms of vapor condensation on rough surfaces is crucial to a wide range of industrial applications. A hybrid thermal lattice Boltzmann model of the condensation heat transfer process on downward-facing rough surfaces characterized by the Cantor fractal is developed and numerically analyzed to investigate the condensation phase change behaviors on rough hydrophobic and hydrophilic surfaces. The dynamic behaviors of vapor condensation, including the evolutions of vapor–liquid interface, heat flux, condensate mass, and temperature distribution, on the hydrophilic and hydrophobic rough surfaces are presented and compared with corresponding smooth surfaces. The results indicate that the rough surface preferred a filmwise condensation under hydrophilic conditions but a hybrid dropwise–filmwise condensation under hydrophobic conditions. On the rough hydrophobic surface, the liquid film can rapidly adsorb droplets, maintaining a high-efficiency dropwise condensation. The absorption of droplets accelerates the liquid film growth and detachment process on the rough hydrophobic surface, which reduces the time-averaged thermal resistance of the filmwise region. These two behaviors together enhance condensation heat transfer on the downward-facing rough hydrophobic surface. Besides, stable dropwise condensation could also be formed on smooth hydrophilic surfaces and has better heat transfer performance than corresponding hydrophobic surfaces under the same heat transfer condition.

With the increasing demand for energy, heat and mass transfer through porous media has been widely studied. To achieve accuracy in studying the behavior of heat transfer, a good knowledge of the effective thermal conductivity (ETC) of porous materials is needed. Because pore structure dominates the ETC of porous materials and effective stress leads to a change in pore structure, effective stress is one of the key influencing factors affecting ETC. In this study, considering the structure of surface roughness and pore size, based on fractal theory, a novel analytical solution at the pore scale for ETC of porous materials under stress conditions is proposed. Furthermore, in this model, capillaries in porous materials saturated with multiple phases have sinusoidal periodically constricted boundaries. The derived ETC model is validated against available experimental data. Moreover, the influences of the effective stress, initial effective porosity, roughness structure characterization, and wetting phase saturation on the ETC are analyzed. Compared with previous models, the rough surfaces of porous materials and the coupling of heat conduction and mechanics are taken into consideration to make the model more reasonable. As a result, this ETC model can better reveal the mechanism of heat conduction in porous media under stress conditions.

The C/SiC composite is a promising material for ablation-resistant thermal protection in near-space hypersonic environments. The formation of an SiO₂ oxide layer through passive oxidation on the surface of the composite is a significant factor influencing its performance. It is essential to accurately predict the thickness of the SiO₂ oxide layer and the recession and mass loss of the C/SiC composite during passive oxidation. The SiO₂ oxide layer is a typical porous media exhibiting self-similarity and thus fractal theory can be applied to establish the relation between the oxygen flow rate and microstructural parameters of the oxide layer. The Weierstrass–Mandelbrot (WM) function is employed to simulate the rough interfaces between the SiO₂ oxide layer and the C/SiC composite to evaluate the influence of the fractal dimensions of the oxide layer on the performance of thermal protection of the C/SiC composite. The results show that the C/SiC composite exhibits improved thermal protection performance when accompanied by a lower tortuosity fractal dimension and a higher pore area fractal dimension of the oxide layer. Conversely, the composite demonstrates enhanced ablation resistance with a higher tortuosity fractal dimension and a lower pore area fractal dimension of the oxide layer. The predictions of the calculation model show good agreement with the experimental data and demonstrate the critical influence of microstructural parameters of the oxide layer on passive oxidation of the composite, providing practical implications for designing materials with desired thermal protection or ablation resistance properties.

An adaptive meshless computational system is introduced in this paper to solve two-dimensional elastoplastic contact mechanics. An adaptive element-free Galerkin-finite element coupling computational model based on the gradient of strain energy and a linear programming technique with the initial stiffness method for elastoplastic contact problems are combined. Principle explanation and program realization are carried out. The modularization concept in software engineering is used, and the adaptive change of the influence domain radius and the elastoplastic property of material are also taken into account by the system. A rigid cylinder making contact with an elastic plane is analyzed to validate the system. Some key parameters in adaptive calculation are studied. The adaptive meshless computational system is also applied to elastoplastic contact of rough surfaces. Comparisons of the adaptive refinement solution with the uniform refinement solution are made, and the results show the satisfactory accuracy and efficiency of the solutions from the adaptive refinement model.

There are mainly two kinds of contact mechanics models for rough surfaces. One is based on the statistical characteristic parameters and depends on the measurement scale of rough surface topography. The other is based on the fractal parameters, which is independent of the measurement scale. However, most of the contact models for rough surfaces based on fractal theory use the size that is corresponding to the contact area of an asperity or the sample length as the base diameter of an asperity to describe the initial profile of asperities. As a result, the obtained deformation mechanism of asperities is not correct. To solve this problem, a new fractal characterization method for rough surfaces based on the fractal dimension $D$, fractal roughness $G$ and the highest asperity height is proposed, and then a fractal contact model independent of the measurement scale is established. The contact mechanism of asperities and variation trends of the real contact area and contact stiffness are discussed. When the contact pressure of the rough surface is less than its yield strength, its normal contact stiffness can be expressed as the first derivative of the contact pressure versus the normal compression, regardless of the deformation forms of asperities.

This paper investigates the importance of creep and relaxation functions in modeling the Hertzian contact problem between linear nonaging viscoelastic materials and viscoelastic rough surfaces. We provide novel analytical and semi-analytical solutions to these functions for various materials, including Generalized Maxwell, Generalized Kelvin, and Burgers’ rheological materials. Closed-form and semi-analytical solutions are developed for several specific cases with high practical applications, such as the contact between incompressible solids, a rigid material and an incompressible material, and two solids with no volumetric viscous strain. They are extensions of existing solutions given in the literature. A simple computation procedure based on the discretized integral technique is proposed for the general case of contact between linear nonaging viscoelastic materials. This proposed method is easy to implement in practical applications such as the interpretation of viscoelastic indentation tests for material characterization and the implementation of viscoelastic contact in finite/discrete element simulations.

Friction as well as asperity interactions have significant influence on the contact area and force of rough surfaces. In this work, a single-asperity, elastoplastic contact model, considering friction, is established by means of continuum mechanics and power-exponential functions. Then, the deformation of the asperity interactions is modeled by the displacement of the average line for asperity height. Using fractal theory, the actual deformation and contact stiffness of an asperity are derived, which take the friction and asperity interactions into account. Furthermore, the actual contact area and normal stiffness models for fractal surfaces are developed, accounting for friction and asperity interactions. The accuracy of the developed models is confirmed by using published experimental results. The developed models are closer to experimental results than the reported fractal contact models. Finally, the effects of the friction coefficient and surface morphology parameters on contact characteristics are discussed.

In this study, porous silica nanoparticles were fabricated in the absence of organic surfactant template at room temperature by a facile one-step dialysis method. By using a dialysis system comprising an ammonia solution as the dialysate, a series of porous silica nanoparticles with a rough surface (e.g., raspberry-like) were obtained by the initiation of a homogeneous ternary tetraethylsilicate-water-ethanol system with different ammonia solution concentrations. The specific surface area and pore volume of porous nanoparticles were regulated by changing the dialysate concentrations. N₂ adsorption–desorption measurements revealed that the porous silica nanoparticles owned both mesopores and micropores and exhibited a type IV isotherm, hence, these nanoparticles can be used as mesoporous silica nanoparticles (MSNs). The Au@MSN nanocomposite can be used as a catalyst for the typical reduction of 4-nitrophenol to 4-aminophenol by NaBH₄ and exhibited excellent catalytic performance.