Random Rough Surfaces Research Articles

A general contact model for rough surfaces based on the incremental concept

It is now commonly accepted that real contact area rises linearly with increasing normal load for the contact of rough solids. However, the coefficient of proportionality is distinct in various models and simulations. This study advances a general method to determine the area-load proportionality based on the incremental contact concept. A pair of loose bounds on the coefficient of proportionality for general Gaussian random rough surfaces and a tight one working in the thermodynamic limit are derived. The resultant predictions are in accord with numerical results presented in literature. The current study might offer some deep insight into the role of surface morphologies in contact of rough elastic solids.

A Molecular Dynamics Perspective on the Impacts of Random Rough Surface, Film Thickness, and Substrate Temperature on the Adsorbed Film’s Liquid–Vapor Phase Transition Regime

While recent studies have proven an unexpected liquid–vapor phase transition of adsorbed liquid films, a comprehensive description of the mechanisms of different types of phase change regimes over realistic representations of random rough surfaces is absent in the literature. The current comprehensive study investigates the effects of a gold random rough surface, liquid film thickness, and substrate temperature on the liquid–vapor phase change regime of an adsorbed sodium liquid film, considering the evaporator section of a wicked heat pipe (WHP) using a molecular dynamics (MD) simulation. At first, to generate a realistic random rough surface, a new and promising method is proposed that is entirely based on MD simulations. Then, to simulate the evaporator section of a WHP, a unique configuration for eliminating the vapor domain is developed. The simulation results reveal that three distinct regimes, namely, normal evaporation, cluster boiling, and film boiling, could be identified, which are presented on two-dimensional diagrams with the substrate temperature and liquid film thickness as coordinates for the ideally smooth and random rough surfaces. The results also manifest that even though using the random rough surface could lead to different phase transition regimes, the type of regime depends mainly on the substrate temperature and liquid film thickness. Furthermore, this study displays two different modes for normal evaporation. Also, it is shown that the impacts of the liquid film thickness and substrate temperature on the mode of normal evaporation are much more significant than the surface roughness.

Numerical investigation on dynamic characteristics of the droplet impacting on a random rough surface

Water management is a significant problem affecting the reliability and stability of proton exchange membrane fuel cells (PEMFC), in which droplet wall collision is the critical factor affecting the liquid water transmission in the gas channel. The surface roughness directly affects the spreading deformation of the droplet after impacting. This study's influence of surface roughness on the dynamic process of a single droplet of micrometer level impacting random rough surfaces was numerically investigated. Based on the Weierstrass–Manderlbrot (W-M) fractal theory, three-dimensional random rough surfaces with five roughness levels were established, and the dynamic process of droplet impact on the random rough surface was captured. The contour features of the droplet were analyzed, and the results showed that rough peaks hinder the spreading and retracted process of droplets, resulting in a thicker liquid film deposited on the rough surface, which is not conducive to liquid water discharge. The higher roughness level makes it difficult for droplets to gather into liquid film after hitting the wall and further hinders the discharge of liquid water from the flow channel. Therefore, when micrometer-sized droplets collide with a wall velocity of about 10 m/s, the roughness Ra should be controlled below 0.4 μm, which is conducive to the formation of thin liquid film after droplet impact and the effective discharge of water, which is crucial to maintaining the performance and life of PEMFC.

Combined effect of random porosity and surface defect on fatigue lifetime of additively manufactured micro-sized Ti6Al4V components: An investigation based on numerical analysis and machine learning approach

Surface defects and internal porosities resulting from the additive manufacturing process contribute to a scatter in fatigue lifetime, increasing uncertainty in applications such as aerospace engineering. This study proposes a combined approach of machine learning and finite element modelling to explore the interaction between random porosity distribution and high surface roughness on the fatigue lifetime of micro-sized additively manufactured parts. To achieve this, a high-fidelity finite element model is constructed with randomly distributed porosities and surface defects. A fatigue lifetime estimation model, developed using a combination of continuum damage mechanics and the theory of critical distance, is then applied to predict lifetime using effective stress extracted from simulations. A total of 1200 simulations are conducted using these models to examine the interaction effects of subsurface porosity and surface defects on localized stress distribution and fatigue lifetime. Subsequently, two machine learning algorithms, Support Vector Regression and Kernel Ridge Regression, are employed to estimate fatigue lifetime, accounting for the effects of randomly distributed subsurface porosities and surface defects. Eighty percent of the developed finite element models are employed to construct an input dataset, incorporating geometrical features of pores, and to train the algorithms, while the remaining 20% are reserved for verification purposes. The observed results demonstrate that the combined effect of random porosity and surface defects increases fatigue scatter behaviour, leading to greater uncertainty in lifetime prediction. Furthermore, the machine learning algorithms exhibit promising prediction performance.

Theoretical study on contact current density in the boundary of random rough surfaces

We theoretically calculate here how random roughness affects the contact current density and equivalently contact resistance by utilizing a perturbative expansion method. Then, By taking into consideration self-affine roughness on the surface of the solids, we find the contact current density. The obtained results illustrate the total contact current exhibits significant dependence on the properties of the self-affine rough surface such as root-mean-square of roughness and Hurst exponent. Assuming a lower value of root-mean-square roughness for a solid in a higher potential compared to another which is connected to a lower potential, results in a decrement of the total contact current compared to the current between solids without roughness. By considering similar rough parameters for both solids, the contribution of the perturbed contact current becomes zero. Moreover, repercussions by considering the conductivity contrast between components are explored.

Influence of surface roughness on the fluid flow in microchannel

Surface roughness is a crucial factor of fluid flow in microfluidic channels. Most of the existing studies focus on the effect of regular microstructured surfaces on fluid flow, while researchs about the impact of random rough surfaces on fluid flow remains limited. Therefore, in this study, a random rough surface model and two microstructured surface models were established, and the effects surface roughness on the fluid flow at Wenzel state and Cassie-Baxter state were studied using COMSOL multi-physics simulation software. Our findings reveal that both the flow velocity and the fluid flow rate at the microchannel outlet decreases with the surface roughness increases. Notably, the flow rate and velocity of the fluid flow at Cassie-Baxter state is higher than that of fluid flow at Wenzel state.

Calculation of operational parameter variation of infinitely long slider bearings with stochastic roughness

In the framework of stochastic representation of surface roughness, a novel Reynolds-type Equation has been derived recently by the authors and utilized to calculate the average values of a bearing’s operational parameters. To acquire an improved insight to the hydrodynamic lubrication phenomena in rough bearings, the stochasticity of the operational parameters should be described, by calculating their higher-order moments, such as the variation. The present work aims at deriving equations for calculation and quantification of these higher-order moments. More specifically, in the present paper equations for the variation of a slider bearing operational parameters (pressure, load carrying capacity, friction force and friction coefficient) are derived. The obtained results are validated against the deterministic Reynolds Equation solution, for a series of bearings with different random Gaussian surface roughness profiles, over a wide range of bearing design and operational parameters.

Self-Assembled Organic Aerogel and Sponges for Rapid and Effective Absorption of Oil from Oil- Contaminated Soil Samples

Crude oil spills pose significant risks to both marine ecosystems and human populations. Traditional remediation techniques have their limitations, prompting the exploration of innovative approaches. This study introduces a novel method involving the synthesis of a self-assembled sponge and organic aerogel. These materials were further modified using hexamethyldisilazane (HMDS) and dodecyltrimethoxysilane (DTMS) to impart hydrophobic properties. Characterization via SEM examination and FTIR spectroscopy revealed distinctive features, including bands at approximately 1050 cm-1 and 790 cm-1, indicative of alkyl side chain stretching by Si-O-C and C-H, respectively, enhancing the hydrophobicity of the materials. The SEM images depicted a random rough surface with abundant pores, facilitating oil adsorption from contaminated samples. Notably, after seven cycles of use with contaminated soil samples, the organic aerogel exhibited exceptional oil removal capacity, achieving 100% efficiency according to the Sears method. This innovative sponge and organic aerogel-based approach represents a promising advancement in environmental remediation, offering a highly efficient and sustainable solution for oil spill cleanup.

On the effect of the height distribution function in adhesion of non Gaussian random rough surfaces, and a simple analytical model (BAM)

Two apparently very different theories of adhesion of rough surfaces called BAM (bearing-area-model), and that of Persson–Tosatti lead to similar predictions concerning the stickiness of Gaussian surfaces: the role of roughness is mainly governed by the low wavevector content of the PSD. Here, we study the adhesion of non-Gaussian surfaces by means of a DMT-based simplified BEM (Boundary-Element-Method), and report a clear difference in the adhesion and stickiness of surfaces with different height distribution function. We then obtain analytical equations for a generalized BAM model. Results of the extended BAM theory compare reasonably well with numerical BEM-DMT predictions. We also notice that any theory based on the surface energy, would show instead insensitivity to height distribution.

Study on Plastic Deformation Removal Mechanism and Dislocation Change in Nanogrinding of Single Crystal Silicon Carbide with Random Rough Surface

This investigation centers on exploring the plastic deformation removal mechanism and dislocation dynamics in the nanogrinding of single‐crystal silicon carbide featuring a randomly rough surface. To simulate this, an approach combining the Weierstrass–Mandelbrot fractal surface function with molecular dynamics is employed. Randomly rough surface contours are generated using the Weierstrass–Mandelbrot fractal surface function. By adjusting the fractal dimension, an ideal representation of single‐crystal silicon carbide with randomly rough surfaces is obtained. By combining plastic deformation detection methods, the process of workpiece sliding, plowing, and chip removal is studied, and the plastic deformation removal mechanism of random rough surface grinding is explored. Combining postprocessing methods such as sheer strain and dislocation trajectory, the morphological changes and transformation mechanisms of dislocations are analyzed. Notably, at grinding depth of 33.18 nm, the activation of slip systems induces dislocation formation, enabling plastic deformation. Furthermore, at depths exceeding 144.00‐nm, the emergence of stacking faults on the random rough surface is observed. Throughout the grinding procedure, plastic deformation of debris occurs, leading to the formation of plastic bulges on both sides of the tool, and the debris generated during processing does not impact the defects encountered during secondary grinding of the rough surface.

Dynamic behaviors and heat transfer characteristics of impacting droplets on heated superhydrophobic surfaces with randomly distributed rough structures: Numerical simulation and theoretical analysis

Due to the extensive usage of superhydrophobic surfaces, numerous studies have investigated the dynamics and heat transfer of a droplet impacting on superhydrophobic surfaces. However, previous studies did not consider the actual superhydrophobic surfaces with randomly distributed rough structures, especially so in heat transfer of droplet impacting on superhydrophobic surfaces with random rough structures. To address this issue, a multiple distribution function phase-field lattice Boltzmann model was developed to model the droplet impacting on randomly rough surfaces. After experimental validation, this model was used in the analysis of the impacting dynamics and heat transfer characteristics. The differences between actual randomly rough surface and ideal smooth surface were revealed. Herein, random rough structures significantly influence the wetting state and heat transfer of impacting droplet on solid surface. Moreover, the effects of roughness on droplet bouncing ability and the total transferred heat were evaluated. The results show that the random rough surface with smaller skewness, a kurtosis of 3.0, and a standard deviation of 0.3 μm could simultaneously promote impacting droplet to rebound from the surface and to reduce the total transferred heat. Subsequently, the predictive correlation for total transferred heat was proposed based on the roughness parameters. This work provides novel insights into the design of rough structures on functional superhydrophobic surfaces.

Generalized Perturbation Theory for Weakly Deformed Microdisk Cavities

AbstractA perturbation treatment is derived for weakly deformed microdisk cavities in a more generalized scenario, where both resonant and non‐resonant surface scattering processes coexist. It is proved that the originally developed nondegenerate and degenerate perturbation theories are simplified forms of the generalized theory in special cases. The validity of the perturbation theory is verified by the comparison with a full numerical method for two generic classes of deformed microdisk cavities: locally notched microdisks and smooth globally deformed microdisks. The simulation of these two classes of microdisk cavities using the perturbation theory unveils the distinct characteristics of optical modes from the ones predicted by the original nondegenerate and degenerate perturbation theories in the generalized scenario. Furthermore, a hybrid‐scattering‐based exceptional point is introduced for deformed microdisk cavities in the generalized scenario by using the perturbation theory. The exceptional point exhibits higher nonorthogonality over the originally proposed resonant‐scattering‐based exceptional point, as non‐resonant scattering processes provide an additional degree of freedom. Full numerical simulations demonstrate that the exceptional point is more robust against random surface roughness at cavity boundary than the resonant‐scattering‐based exceptional point.

The effect of layer thickness on the geometry and capillary performance of strut-based heat pipe wicks manufactured by laser powder bed fusion

Additive manufacturing (AM) can be used to fabricate heat pipes and two-phase heat sinks which have integrated wicking structures. These devices can be customized and have superior performance when compared with devices with conventionally fabricated wicks. The current work investigates the impact of build rate on the capillary performance of AM wicks fabricated by laser powder bed fusion (LPBF). The build rate was examined by varying the layer thickness from 30 µm to 80 µm for four different strut-based wick geometries: (i) body-centered cubic (BCC), (ii) face-centered cubic (FCC), (iii) simple cubic (SC), and (iv) fluorite. The mass rate-of-rise method was used to quantify the wick hydraulic parameters (namely wick permeability, K, and effective pore radius, reff). Layer thickness has a significant influence on wick permeability; layer thickness of 40 µm result in the highest value for all configurations but have a small effect on the effective pore radius. Layer thickness of 40 µm and 60 µm reached the highest K/reff ratio, primarily because of the permeability increase. We attribute this to poor build quality such as missing struts and less defined edges which facilitate low resistance to fluid flow. The SC 60 and BCC 40 configurations achieved the maximum capillary performance with K/reff of 1.34 µm and 1.42 µm, respectively. Overall, it was found that while increasing the build rate by varying layer thickness may affect the part build quality, it promotes hydraulic performance for some configurations by creating random rough surface morphologies and arteries, which help increase permeability.

Synthetic Aperture Radar Imaging Below a Random Rough Surface

AbstractMotivated by applications in unmanned aerial based ground penetrating radar for detecting buried landmines, we consider the problem of imaging small point like scatterers situated in a lossy medium below a random rough surface. Both the random rough surface and the absorption in the lossy medium significantly impede the target detection and imaging process. Using principal component analysis we effectively remove the reflection from the air‐soil interface. We then use a modification of the classical synthetic aperture radar imaging functional to image the targets. This imaging method introduces a user‐defined parameter, δ, which scales the resolution by allowing for target localization with sub wavelength accuracy. Numerical results in two dimensions illustrate the robustness of the approach for imaging multiple targets. However, the depth at which targets are detectable is limited due to the absorption in the lossy medium.

Dynamics analysis of spur gears considering random surface roughness with improved gear body stiffness

In previous calculation of gear mesh stiffness, the gear body is typically treated as a deformable elastic ring, and the stiffness of the gear body is determined using Sainsot's empirical formula. In this paper, a new calculation method for determining the gear body stiffness based on the analytical finite element-potential energy method is proposed, and its feasibility is verified by the finite element method. A new nonlinear dynamic model for a spur gear system is established, taking into account the time-varying backlash and random surface roughness. This model aims to investigate the dynamical responses of the gear system under various parameters, including rotational speed, shaft hole radius and surface roughness. The results indicate that the proposed method for calculating the stiffness of the gear body is significantly more accurate than Sainsot's empirical formula, as it closely aligns with the finite element method. This leads to a more precise calculation of the time-varying mesh stiffness. The gear dynamics model incorporating random surface roughness exhibits a heightened degree of realism and complexity in its dynamic phenomena. This study provides a valuable reference for the future development of dynamic gear systems.

A straightforward spectral emissivity estimating method based on constructing random rough surfaces

Spectral emissivity is an essential and sensitive parameter to characterize the radiative capacity of the solid surface in scientific and engineering applications, which would be non-negligibly affected by surface morphology. However, there is a lack of assessment of the effect of roughness on emissivity and a straightforward method for estimating the emissivity of rough surfaces. This paper established an estimating method based on constructing random rough surfaces to predict rough surface (Geometric region) emissivity for metal solids. Based on this method, the emissivity of ideal gray and non-gray body surfaces was calculated and analyzed. The calculated and measured spectral emissivities of GH3044, K465, DD6, and TC4 alloys with different roughness were compared. The results show that the emissivity increases with the roughness degree, and the enhancement effect weakens with the increase of roughness or emissivity due to the existing limit (emissivity ε = 1.0). At the same time, the roughness would not change the overall spectral distribution characteristics but may attenuate the local features of the spectral emissivity. The estimated results are in good agreement with the experimental data for the above alloys’ rough surfaces. This study provides a new reliable approach to obtaining the spectral emissivity of rough surfaces. This approach is especially beneficial for measuring objects in extreme environments where emissivity is difficult to obtain. Meanwhile, this study promotes an understanding of surface morphology’s effect mechanism on emissivity.

A Novel Method of Designing Random Rough Surface Considering Its Contact Force-Deformation Characteristic Requirement

Abstract The height probability distribution (HPD) of random rough surface topography has significant effect on its contact behaviors. In this paper, an optimization model to calculate the optimal HPD of random rough surface topography to make its contact force-deformation characteristic satisfy the given target force-deformation characteristic was established. In the solution to calculate the optimal HPD, using Bezier interpolation curve to represent the curve of HPD function and using the positions of the control points of Bezier interpolation curve as optimization variables were proposed. The solution was validated by numerical simulations implemented using MATLAB. The effect of the number of the control points on the minimum objective function value was investigated. Through analyzing the obtained result, we found the most appropriate number of the control points is 35. Comparison with the method using height parameters as optimization variables in literature was implemented. It was found that the proposed method is applicable to broader types of contact force-deformation characteristic requirements than the method using height parameters as optimization variables.

Effects of Interface Morphology on the Shear Mechanical Properties of Sand-Concrete Interfaces.

The morphology of the contact surface between cast-in-place engineering structures and soil is generally random. Previous research focusing on the shear mechanical properties of soil-concrete interfaces has predominantly concentrated on the role of interface roughness by constructing regular concrete surface types, largely neglecting the potential impact of the roughness morphology (i.e., the morphology of the concrete surface). In this study, concrete blocks with the same interface roughness and different roughness morphologies were constructed based on the sand-cone method, including random rough surface, triangular groove surface, rectangular groove surface, trapezoid groove surface, and semicircular groove surface. A series of direct shear tests were conducted on the rough and smooth sand-concrete interfaces, as well as on natural sand. Through these tests, we examined the shear mechanical behavior and strength of the sand-concrete interfaces, and analyzed the underlying shear mechanisms. The results showed that: (i) the interface morphology had little effect on the variation in the shear stress-displacement curve of sand-concrete interfaces, and it had a significant influence on the shear strength of the interfaces; (ii) under the same normal stress, the shear strength of the sand-concrete interfaces with a random rough surface was the greatest, followed by the triangular groove surface, while the shear strength of the rectangular groove surface proved the lowest; (iii) the shear strength of the sand-concrete interfaces with the same roughness was affected by the size of the contact area between the concrete plane and the sand, that is, a larger contact area correlated with a decrease in shear strength. It can be concluded that the shear strength value of a sand-concrete surface with the triangular groove is the closest to the shear strength of a random rough interface. By gaining a deep understanding of the effects of different contact surface morphologies on shear strength and shear behavior, significant insights can be provided for optimizing engineering design and enhancing engineering performance.

Numerical study on the effects of viscous heating and random rough surface on cavitating flow in fuel injection nozzles

A transient numerical model was developed to investigate cavitating flow in fuel injection nozzles, incorporating the effects of viscous heating and latent heat of phase change. A three-dimensional Gaussian rough surface generated by Monte Carlo simulation was compared to a wall function correction-based roughness model to assess the impact of surface roughness on both flow and thermal fields. Results demonstrated that viscous heating increased fuel temperature significantly near the nozzle wall, whereas latent heat had minimal effect due to the diesel fuel's low thermal sensitivity. The random rough surface performed better than the wall function correction-based model in inducing local cavitation, reflecting sub-micron scale roughness, and revealing significant randomness in velocity, temperature, and cavitation fields. Roughness height and correlation length were found to be critical factors characterizing surface roughness, where an increase in roughness height and a decrease in correlation length predicted a rougher surface and enhanced effect of viscous heating. The ratio of these two parameters showed a clear linear relationship with temperature rise. Geometric and localized cavitation were observed, leading to temperature increases caused by cavity evolution and collapse. These insights are valuable for improving fuel atomization and combustion efficiency.

Electromagnetic scattering characteristics of a hypersonic vehicle with a microrough surface in the millimeter wave band

The rough structure may affect the flow field and electromagnetic (EM) scattering characteristics of a hypersonic vehicle. In this study, the EM scattering characteristics of the hypersonic vehicle RAM C-II with a microrough surface were investigated in the millimeter wave band. We first simulated the flow field of a smooth RAM C-II vehicle and calculated the radar cross section (RCS) in the wideband using the physical optics method. The calculation results show that many factors contribute to the variation in the RCS; however, it is occasionally difficult to predict. We then used a one-dimensional Gaussian random rough surface to generate a RAM C-II with a microrough surface through a point-coordinate transformation and simulated its flow field. The electron density flow field of the rough surfaced aircraft fluctuates greatly on the wall. Finally, we calculated the RCS of RAM C-II with different values of roughness in the millimeter wave band. The change of surface structure can be reflected in millimeter waves, and the RCS is determined by both plasma and rough structure.