Pillar Height Research Articles

Study on instability mechanisms and control of coal pillar spalling and coal crumbs leakage during working face crossing faults

The stability of coal pillars in fault areas is crucial for ensuring the safe passage of working faces. Based on field observations, frequent coal pillar spalling and substantial tectonic coal crumbs leakage, as well as tilting of hydraulic supports, are observed when working faces transition from primary coal to tectonic coal. To analyze the instability mechanisms behind these phenomena, this paper establishes a mechanical model of coal pillars in fault areas and analyzes the distribution of tectonic stresses and factors affecting the stability of coal pillars. The results indicate that horizontal tectonic stress adheres to an exponential function dependent on the angle factor, where (k0) is a parameter associated with the friction angle of the coal body, the dip angle of the fault, and the friction angle of the fault plane. The stability of coal pillars is influenced by factors such as roof and floor pressures, coal pillar integrity, mining height, and shield support force, with coal pillar integrity being the most critical. To ensure the smooth passage of working faces through faults, this study proposes a combined control technique of “inclined mining” and “grouting,” including reducing mining heights, adjusting the slope of working face advancement, and pre-grouting of coal pillars. Industrial experiments conducted on-site have shown improved integrity of tectonic coal, enabling the working face to pass through faults smoothly and significantly increasing production efficiency.

Bouncing dynamics of a droplet impacting onto a superhydrophobic surface with pillar arrays

A superhydrophobic surface (SHS) patterned with pillar arrays has been demonstrated to achieve excellent water repellency and is highly effective for self-cleaning, anti-icing/frosting, etc. However, the droplet impact dynamics and the related mechanism for contact time (tc*) reduction remain elusive, especially when different arrangements of pillar arrays are considered. This study aims to bridge this gap by exploring a droplet impinging on an SHS with square pillar arrays in a cuboid domain. This fluid dynamics problem is numerically simulated by applying the lattice Boltzmann method. The influences of the droplet diameter (D*), the Weber number (Wew), and the pillar spacing and height (s* and h*) on the droplet dynamics and tc* are investigated. The numerical results show that the droplet can exhibit different bouncing patterns, normal or pancake bouncing, depending on Wew, s*, and h*. Pancake bouncing usually occurs when Wew ≥1.28, h*≥1, and s* ≈ 1, yielding a small tc*. Among all cases, a small tc* can be attained when the conversion rate of kinetic energy to surface energy (ΔĖsur*) right after the impacting exceeds a critical value around 0.038. This relation broadens that given in A. M. Moqaddam et al. [J. Fluid Mech. 824, 866–885 (2017)], which reported that the large total change of surface area renders small tc*. Furthermore, the maximum impacting force remains nearly the same in all cases, regardless of the bouncing patterns.

Dropwise condensation on subcooled micropillar surfaces with 3D lattice Boltzmann method

In this investigation, an alternative geometric formula is proposed to address the force between fluid nodes and fluid ghost nodes, with the aid of which the contact angles can be varied in the range of 48.3°∼131.9°. This formula is applied to the three-dimensional double-distributed thermal lattice Boltzmann method being proved to be accurate and reliable by single droplet condensation. The effects brought by varying micropillar size on the kinetic properties of condensed droplets, including nucleation, growth, coalescence and jumping, are investigated in detail. The results show that the droplet wetting state tends to be the suspended Cassie state as the width and spacing of the micropillars are decreased, and the condensed droplets can merge and jump off the micropillar surface. In the meantime, the average droplet number increases, the average diameter and the diameter of dominant droplets decrease, thus reducing the condensate coverage. When the micropillar spacing is small, increasing the micropillar height results in the condensed droplet state being changed from Wenzel to Cassie state, and the percentage of small droplets also increases. Instead, when the micropillar spacing is large, by increasing micropillar height, droplets can nucleate in the middle of micropillars, and the percentage of large droplets is improved due to increased heat transfer area. In this study, the surface self-cleaning capability is strongest with the combination of dimensionless pillar height 0.4, spacing 0.1 and width 0.1, which reduces the condensate coverage by 66 % compared to its plain competitor.

Binary imidazolium based aqueous ionic liquid droplet on a rough surface: a molecular dynamics study

Ionic liquids (ILs) have garnered immense attention due to their tunable physicochemical properties. In this study, we delve into the wetting behaviour and interfacial properties of aqueous binary IL mixtures containing [EMIM] [BF4] and [HMIM] [BF4] on both smooth and rough graphite surfaces. Employing classical molecular dynamics simulations, we systematically explored the effects of IL concentration and surface morphology on wetting phenomena. To ensure the equilibrium of the systems, we began by calculating the interaction energies between the components. Subsequently, contact angles were computed, shedding light on the wetting characteristics of the aqueous binary IL mixtures. We meticulously examined the density profiles of the IL systems from the substrate to unravel the dominance of one IL over the other, exploiting the hydrophilic nature of [EMIM] [BF4] and the hydrophobic nature of [HMIM] [BF4]. A comprehensive analysis of hydrogen bond distribution allowed us to discern the intricate nature of these aqueous binary IL droplets. We probed the changes in intermolecular forces within the aqueous IL solution by investigating surface tensions. The tunability of these ILs emerges as a significant aspect of our study, paving the way for their tailored application in engineering and scientific domains. Schematic diagram showing the density distribution of hydrophilic and hydrophobic ILs ([EMIM] [BF4] and [HMIM] [BF4]) in water and also the hydrogen bond (HB) distribution of anion ([BF4]−) water inside the droplet on a pillared surface with a surface fraction ( f ) of 0.4 and pillar height of H = 4 .

Design, fabrication, and characterization of 1–3 piezoelectric composite air-coupled ultrasonic transducers with micro-membrane filter matching layer

Air-coupled ultrasonic transducers are widely used in various fields of nondestructive material characterization. This paper presents the fabrication and performance characterization of 1–3 piezoelectric composite air-coupled ultrasonic transducers operating at frequencies ranging from 400 kHz to 600 kHz. The transducers are fabricated using a dice-and-fill method with PZT-5 as the active material. A double-layer matching strategy is employed, utilizing hollow glass microsphere filled epoxy resin as the first matching and bonding layer. Additionally, micro-membrane filters with different pore sizes are used as the second matching layer. Thermoplastic adhesive TPU is utilized to bind the micro-membrane filter and the first matching layer. Due to the low acoustic impedance of the hollow glass microsphere filled epoxy resin and micro-membrane filter, acoustic impedance mismatch is reduced. Finite element simulation is used to determine the optimal ceramic volume fraction and ceramic pillar height of the 1–3 piezoelectric composites. When the pore size of the micro-membrane filter is 0.8 μm, the transducer achieves the lowest two-way insertion loss of −56.86 dB and the highest −6 dB bandwidth of 15.6 %, making it feasible for through mode applications.

Influence of Thickness of Weak Bedding Planes at Various Positions Within Pillar Height on Strength: a Numerical Modelling Study

Influence of Thickness of Weak Bedding Planes at Various Positions Within Pillar Height on Strength: a Numerical Modelling Study

Pancake bouncing of impacting nanodroplets on smooth and nanopillared surfaces

Reducing the contact time of impacting droplets on solid surfaces has become a research focus due to its promising application prospects in self-cleaning, anti-erosion, and anti-icing. In this study, the pancake bouncing of nanodroplets is investigated through molecular dynamics simulations, achieving a remarkable reduction in contact time. Two distinct patterns of pancake bouncing are identified when nanodroplets impact smooth and nanopillared surfaces with different bouncing mechanisms. The first pancake bouncing pattern with holes on smooth surfaces is attributed to internal-flow collision induced by multiple retraction centers. The second pancake bouncing pattern on nanopillared surfaces results from the storage and release of sufficient surface energy due to liquid penetration and requires satisfying both the timescale and energy criterion. Subsequently, theoretical models for two criteria are developed, which promote two parameter groups (−(s2 + 2ws)h(wcosθ0)−1 and We–1/3Re–1/3R02) corresponding to the surface and droplet. Based on these two parameter groups, a phase diagram is established and indicates the triggering conditions for the second pancake bouncing patterns. Finally, it is further revealed that by increasing the pillar height from smooth to nanopillared surfaces, the bouncing regime is transformed from the first pancake bouncing pattern, regular bouncing, to the second pancake bouncing pattern.

Hybrid Bright-Dark-Field Microscopic Fringe Projection System for Cu Pillar Height Measurement in Wafer-Level Package.

Cu pillars serve as interconnecting structures for 3D chip stacking in heterogeneous integration, whose height uniformity directly impacts chip yield. Compared to typical methods such as white-light interferometry and confocal microscopy for measuring Cu pillars, microscopic fringe projection profilometry (MFPP) offers obvious advantages in throughput, which has great application value in on-line bump height measurement in wafer-level packages. However, Cu pillars with large curvature and smooth surfaces pose challenges for signal detection. To enable the MFPP system to measure both the top region of the Cu pillar and the substrate, which are necessary for bump height measurement, we utilized rigorous surface scattering theory to solve the bidirectional reflective distribution function of the Cu pillar surface. Subsequently, leveraging the scattering distribution properties, we propose a hybrid bright-dark-field MFPP system concept capable of detecting weakly scattered signals from the top of the Cu pillar and reflected signals from the substrate. Experimental results demonstrate that the proposed MFPP system can measure the height of Cu pillars with an effective field of view of 15.2 mm × 8.9 mm and a maximum measurement error of less than 0.65 μm.

A novel characteristic curve for thermoelectric cooler application in realistic thermal circumstances: Theory and experiment

On the materials level, the performance of thermoelectric (TE) devices can be defined by the thermoelectric figure of merit (zT). This, however, does not provide a complete picture due to the complex interplay between electronic and thermal transport properties and the uncertain thermal impedance matching between external and internal thermal resistances in different realistic thermal circumstances. Appropriate design of individual material properties and geometry parameters considering the realistic thermal circumstance can greatly enhance the device-level performance of TE devices. In this work, we develop a framework to clarify such interactions in thermoelectric coolers (TEC) with a newly proposed q-h characteristic curve, which can be used to identify how a TEC design is of effectiveness for a specific realistic thermal circumstance. The effects of zT, the individual TE material properties (i.e., thermal conductivity k, electrical conductivity σ and Seebeck coefficient S) as well as the geometry parameters (i.e., pillar height and filling factor) on the q-h characteristic curve are theoretically and experimentally investigated, respectively. TEC modules with higher zT, short pillars and high filling factor show stronger capability to handle high heat flux load, especially for the cases with high heat dissipation coefficient at hot side. The thermal property (k) and electrical properties (σ and S) are responsible for the low heat flux load (e.g., wearable TEC) and high heat flux load (e.g., on-chip TEC cooling), respectively. For wearable TEC, increasing the internal thermal resistance can prevent the back flow heat, which can be achieved with tall pillars, low filling factor and optimizing zT towards lowering thermal conductivity k. For on-chip TEC cooling, reducing the Joule heating and increasing the thermoelectric effect become dominant factors in lowering the code-side temperature of TEC modules. This can be achieved with short pillars, high filling factor and optimizing zT towards increasing the power factor S2σ. This work provides significant insights into the complex interplay between material-level properties, device-level parameters and the external thermal circumstance in determining the performance of TEC devices. The results enable researchers to design optimal TEC devices for realistic applications with different boundary conditions.

Transition of Liquid Drops on Microstructured Hygrophobic Surfaces from the Impaled Wenzel State to the "Fakir" Cassie-Baxter State.

Low adhesion of liquids on solid surfaces can be achieved with protrusions that minimize the contact area between the liquid and the solid. The wetting state where an air cushion forms under the drop is known as the Cassie-Baxter state. Surfaces where liquids form macroscopic contact angles above 150° are called superhydrophobic and superhygrophobic, if we refer to water or any liquid, respectively. The Cassie state is desirable for applications, but it is usually unstable compared to the Wenzel state, where the drop is in direct contact with the rough surface. The Cassie-to-Wenzel transition can be triggered by an increase in pressure and vibrations, but the inverse Wenzel-to-Cassie is much more difficult to observe. Here, we examine under what conditions the Wenzel-to-Cassie transition is triggered when the microscopic contact angle changes abruptly. For this, we applied a lubricant of low surface tension around drops that were in the Wenzel state on microstructured surfaces. The increase of the microscopic contact angle lifted the drop from the rough surface, when the pillar height and spacing are large and small, respectively. Numerical calculations for the drop-lubricant interface showed that the surface geometry requirements for the Wenzel-to-Cassie transition are stricter than the ones for the stability of the Cassie state. A surface geometry where the Cassie state is more stable than the Wenzel for a given Laplace pressure of the drop may not always allow the Wenzel-to-Cassie transition to take place. Therefore, the stability of the Cassie state is a necessary but insufficient condition for the inverse transition.

Pillar height regulated droplet impact dynamics on pillared superhydrophobic surfaces

Superhydrophobic surfaces that promote rapid droplet detachment have many significant engineering applications including self-cleaning, anti-icing, drag reduction. Adding macrotextures to superhydrophobic materials can markedly modify the dynamics of water impacting them, either by triggering a non-axisymmetric, center-assisted recoil or inducing pancake-like bouncing. However, the effect of pillar heights on superhydrophobic surfaces has received limited attention. Here, we have systematically investigated the role of the size ratio of pillar height-to-droplet radius (Q) on bouncing dynamics, including spreading, penetrating depth, contact time, bubble entrapment, impact pressure, and impact force, through numerical simulations. We show that droplet impact on superhydrophobic surfaces can generate two modes of bubble entrapment: one is an impinging cavity bubble, and the other is a recoiling cavity bubble, depending on Q. Furthermore, for low Weber number (We), droplet impacts may generate three peaks of impact force for superhydrophobic surfaces with high Q. For high We, only two peaks of impact force are generated during a droplet striking the superhydrophobic surface. However, the secondary peak in the impact force will weaken or may even disappear completely as Q increases, which was hitherto unknown. Interestingly, we also observe that despite lower impact force during droplet recoil compared to droplet impact, higher penetration depths are more easily achieved during the recoil stage. These findings shed light on the role of pillar heights in droplet impact dynamics, offering valuable insights for designing superhydrophobic surfaces.

An In-Depth Investigation of Micropillar Array Columns for the Separation of Finite-Sized Particles by Hydrodynamic Chromatography.

The exact moment approach (EMA) is adopted to predict, without any fitting parameters, the plate height curves for polystyrene microparticles of different sizes in micropillar array columns performed by hydrodynamic chromatography. The EMA allows us to decouple the contribution of horizontal and vertical dispersion terms and thus investigate the influence of pillar height and interpillar distance on separation performance. In the convection-controlled regime, we found that axial dispersion is mainly controlled by the vertical dispersion term, the latter being due to the flow-arresting top and bottom walls. This vertical contribution can be estimated from the axial dispersion in rectangular, open tubular channels formed between the pillars. Henceforth, plate height curves can be accurately predicted by simply adding the estimated vertical term to the horizontal dispersion term evaluated from 2D simulations. This finding allowed us to understand that, to improve separation performance, it is advisible to decrease the interpillar distance (expected result) and decrease the pillar height (counterintuitive result).

Molecular dynamics simulation study on the wetting characteristics of carbon dioxide droplets on smooth and rough surfaces

A thorough investigation of the wetting behavior of carbon dioxide (CO2) is crucial for enhancing carbon capture efficiency and improving carbon storage and sequestration processes. This work investigates the wetting characteristics of CO2 droplets on smooth and rough Cu-like surfaces using molecular dynamics simulations. The results indicate that an increase in surface energy causes a linear decrease in the contact angle of CO2 droplets on smooth surfaces. An increase in temperature enhances the wetting tendency of the smooth surface toward CO2 droplets. On CO2-phobic surfaces, CO2 droplets tend to detach from the surface, causing the contact angle to increase. On neutral surfaces, CO2 droplets generally maintain wettability, with contact angles remaining almost unchanged. On CO2-philic surfaces, CO2 droplets rapidly wet and spread to form liquid film layers, causing the contact angle to decrease rapidly. In addition, constructing rough surfaces is beneficial for enhancing the surface CO2-phobic property, but the wettability of CO2 droplets varies slightly on different rough surfaces (cylindrical pillars, square pillars, and grooves), the fluctuation of contact angles of CO2 droplets on the grooved surface is relatively small. For square pillared surfaces, in contrast to smooth surfaces, as the surface energy increases, the CO2-phobic property of CO2-phobic surfaces is enhanced, and neutral surfaces can be transformed into CO2-phobic surfaces, with the CO2-philic property of CO2-philic surfaces enhanced. For CO2-phobic square pillared surfaces (α = 0.08), the wetting morphology and wetting modes of CO2 droplets on the square pillared surface are jointly influenced by both the pillar height and the interpillar spacing. When the interpillar spacing is constant, there exists a critical pillar height that can induce the transition of the wetting mode of CO2 droplets from Wenzel to Cassie state.

Enhancing carbon capture: Exploring droplet wetting and gas condensation of carbon dioxide on nanostructured surfaces

The investigation of carbon dioxide (CO2) condensation on heat exchange surfaces is essential to the advancement of carbon capture, utilization, and storage (CCUS) technology. Molecular dynamics simulations are employed to explore the wetting and condensation behavior of CO2 on nanostructured surfaces. The results indicate that the contact angle of CO2 droplets on nanostructured surfaces is greater than that on smooth surfaces. Increasing the pillar height (h) or solid fraction (f) induces the transition of CO2 droplets from the Wenzel to Cassie state, resulting in an increased contact angle. Nanostructured surfaces significantly enhance the nucleation rate, with molecules initially nucleating at the bottom of the pillars. A higher h or f accelerates the nucleation rate during the condensation. Droplets in the Wenzel state exhibit higher heat transfer efficiency than those in the Cassie state. Additionally, the formation of Cassie-state CO2 droplets undergoes a dewetting transition, altering the heat conduction mode. The dewetting behavior of CO2 droplets favors their detachment from the surface, potentially reducing the initial heat resistance. Therefore, appropriately increasing h and f can promote nucleation and droplet growth, enhancing dewetting transition and mass transfer performance. These simulation results hold great importance for inspiring the design of future CO2-phobic surfaces and guiding CO2 condensation production.

Decision Intelligence-Based Predictive Modelling of Hard Rock Pillar Stability Using K-Nearest Neighbour Coupled with Grey Wolf Optimization Algorithm

Pillar stability is of paramount importance in ensuring the safety of underground rock engineering structures. The stability of pillars directly influences the structural integrity of the mine and mitigates the risk of collapses or accidents. Therefore, assessing pillar stability is crucial for safe, productive, reliable, and profitable underground mining engineering processes. This study developed the application of decision intelligence-based predictive modelling of hard rock pillar stability in underground engineering structures using K-Nearest Neighbour coupled with the grey wolf optimization algorithm (KNN-GWO). Initially, a substantial dataset consisting of 236 different pillar cases was collected from seven underground hard rock mining engineering projects. This dataset was gathered by considering five significant input variables, namely pillar width, pillar height, pillar width/height ratio, uniaxial compressive strength, and average pillar stress. Secondly, the original hard rock pillar stability level has been classified into three types: failed, unstable, and stable, based on the pillar’s instability mechanism and failure process. Thirdly, several visual relationships were established in order to ascertain the correlation between input variables and the corresponding pillar stability level. Fourthly, the entire pillar database was randomly divided into a training dataset and testing dataset with a 70:30 sampling method. Moreover, the (KNN-GWO) model was developed to predict the stability of pillars in hard rock mining. Lastly, the performance of the suggested predictive model was evaluated using accuracy, precision, recall, F1-score, and a confusion matrix. The findings of the proposed model offer a superior benchmark for accurately predicting the stability of hard rock pillars. Therefore, it is recommended to employ decision intelligence models in mining engineering in order to effectively prioritise safety measures and improve the efficiency of operational processes, risk management, and decision-making related to underground engineering structures.

Structural Effects of 3D Inkjet-Printed Ni(O)-YSZ Pillared Electrodes on Performances of Solid Oxide Electrochemical Reactors.

Increasing densities of reaction sites for gaseous reactants in solid oxide electrochemical reactors (SOERs), is a key strategy for achieving enhanced performance in either fuel cell or electrolysis modes. Fabrication of 3D structured components in SOERs can enhance those densities of reaction sites, which is achieved by 3D inkjet printing with high reproducibility, having developed inks with appropriate properties. First, the effects of pillar geometries on SOER performances are predicted through numerical simulations, enabling subsequent 3D printing to focus on the more effective geometries. Herein, the study reports the results of experimental validation of those predictions by evaluating the electrochemical performances of cells with various heights of 3D inkjet-printed Ni(O)- yttria stabilized zirconia (YSZ) pillars and YSZ pillars. Those measurements prove that increasing pillar heights generally increases SOER peak power densities in fuel cell mode and increased current densities at the thermoneutral potential (1.285V) in steam electrolysis mode, as predicted by simulations. With increasing pillar heights, more limitations in performance enhancement are found with YSZ electrolyte pillars than with Ni-YSZ pillars, again as predicted by simulations. The subsequent microstructural analysis of Ni-YSZ pillars proves the suitability of the Ni(O)-YSZ composite particle ink formulation and the reliability of 3D printing.

The effects of periodic textured substrate to control diffusion angle on the conversion efficiency of dye-sensitized solar cells

We suggested improving the conversion efficiency of dye-sensitized solar cells (DSSCs) by the micro-nano periodic textures to control the diffusion angle of the incident light for certain absorbed wavelengths of the used dye. A periodic texture (Prd-Tx) was designed to enhance the light path of the wavelength of DSSCs’ dye absorption with a wide process window by optical simulation (pitch: 1400 nm, pillar diameter: 460–560 nm, pillar height: more than 500 nm). The Prd-Tx was fabricated by photolithography processes and nanoimprinting (pitch: 1400 nm, pillar diameter: 500 nm, pillar height: 1000 nm). The Prd-Tx increased the DSSCs’ conversion efficiency (η of 3.13%), surpassing our previous best result (refabricated W-Tx, η of 3.08%). It was considered that the ohmic loss was suppressed owing to the Prd-Tx enhanced electrical conductivity at the interface between the transparent electrode, F-doped tin oxide (FTO), and TiO2.

The Antibacterial Activity of Hierarchical Patterns of Nanostructured Silicon Fabricated Using Block Copolymer Micelle Lithography

Herein, the fabrication of four different nanostructured silicon surfaces by using a combination of block copolymer micelle lithography is reported on. Nanoparticle hard masks are evaluated for their ability to produce single‐height nanoneedle arrays. Low‐density (3 features μm−2) and high‐density (201 features μm−2) single‐height arrays are produced from Au or α‐Fe2O3 masks, respectively. These single‐height arrays are then used as substrates to produce nanostructured surfaces with two distinct nanoneedle arrays concerning height, diameter, and density. These dual‐height arrays have feature densities of 31 and 9 features μm−2. All surface types are then tested for their antibacterial activity against Gram‐negative bacteria, Pseudomonas fluorescens, over 24 h. No difference in surface coverage of P. fluorescens when comparing the structured silicon surface types to planar controls is observed. However, all of the structured silicon types show an increase in dead cell surface coverage ranging from 9 to 29% compared to planar controls. Density of the pillars appears to be more important than the difference in height of pillars when it comes to antibacterial activity. This work seeks to add to the literature by investigating the effects of feature density, as well as the impact of a dual‐height arrangement of nanoneedles against P. fluorescens.

Enhancing toughness through geometric control of the process zone

Material architecture provides an opportunity to alter and control the fracture process zone shape and volume by redistributing the local stresses at a crack tip. Properly designed structures can enlarge the plastic zone and enhance the effective toughness. Here, we use a pillar array as a model structure to demonstrate how variations in geometry at a crack tip control the size and shape of the plastic zone and can be used to engineer the effective toughness. Elastic–plastic finite element simulations are used to quantify how the pillar width, spacing, and height can be varied to tailor the size and shape of the plastic zone. A set of analytical mechanics models that accurately estimate the shape, volume, and resulting toughness as a function of the base material properties and geometry are also presented. A case study extends the analysis to sets of non-regular pillar arrays to illustrate how architecture can be used to alter toughness along the crack path.

NUMERICAL SIMULATION OF DROP SPREADING OVER A PILLARED SURFACE

Understanding drop-level interactions with micron-size pillars over flat textured surfaces is required in applications such as condensation of water vapor from a humid environment. Accordingly, the spreading of water drops with diameters of ~ 45 μm over micro-pillars has been studied. The studied cylindrical pillars had a diameter of 3.2 μm, whereas the height and pitch were varied from 15 to 20 μm and 6 to 9 μm, respectively. The impact velocity was varied from 0.02 to 1.89 m/s. The stability of the equilibrium and the transitions in the Cassie-Wenzel wetting states were examined. Three-dimensional simulations showed that drops rebound in closely spaced pillars. In contrast, for a relatively large pitch, drops may rebound and partially or entirely wet the pillars. These details depended on the impact velocity and pillar height. The structure and mechanism of moving contact lines over a pillared surface during impact was also examined. In the simulations, the spreading details were correctly reproduced when a time-dependent contact angle model was adopted, which took into account the nonlinear contribution of friction as well as hysteresis owing to finite pinning. The presence of pinning sites at the edges of the pillars was found to be a major factor affecting the possibility of rebounding and the resulting spreading rate. The simulations of drop shapes using this approach matched the experimental results reported in the literature.