Roughness Length Scale Research Articles

Influence of metal–support interaction on the surface structure of gold nanoclusters deposited on native SiOx/Si substrates

The structure of small gold nanoclusters (around 2.5 nm) deposited on different silica-on-silicon (SiOx/Si) substrates is investigated using several characterization techniques (AFM, XRD, EXAFS and GISAXS). The grain morphology and the surface roughness of the deposited gold cluster layers are determined by AFM. The in-plane GISAXS intensity is modelled in order to obtain information about the cluster size and the characteristic length scale of the surface roughness. The surface morphology of the deposited clusters depends on whether the native defect-rich (n-SiOx/Si) or the defect-poor substrate obtained by thermal treatment (t-SiO2/Si) is used. Gold clusters show a stronger tendency to aggregate when deposited on n-SiOx/Si, resulting in films characterized by a larger grain dimension (around 20 nm) and by a higher surface roughness (up to 5 nm). The more noticeable cluster aggregation on n-SiOx/Si substrates is explained in terms of metal-support interaction mediated by the defects located on the surface of the native silica substrate. Evidence of metal-support interaction is provided by EXAFS, demonstrating the existence of an Au-O distance for clusters deposited on n-SiOx/Si that is not found on t-SiO2/Si.

Mean force structure and its scaling in rough-wall turbulent boundary layers

AbstractThe combined roughness/Reynolds number problem is explored. Existing and newly acquired data from zero pressure gradient rough-wall turbulent boundary layers are used to clarify the leading order balances of terms in the mean dynamical equation. For the variety of roughnesses examined, it is revealed that the mean viscous force retains dominant order above (and often well above) the roughness crests. Mean force balance data are shown to be usefully organized relative to the characteristic length scale, which is equal or proportional to the width of the region from the wall to where the leading order mean dynamics become described by a balance between the mean and turbulent inertia. This is equivalently the width of the region from the wall to where the mean viscous force loses leading order. For both smooth-wall and rough-wall flows, the wall-normal extent of this region consistently ends just beyond the zero-crossing of the turbulent inertia term. In smooth-wall flow this characteristic length is a known function of Reynolds number. The present analyses indicate that for rough-wall flows the wall-normal position where the mean dynamics become inertial is an irreducible function of roughness and Reynolds number, as it is an inherent function of the relative scale separations between the inner, roughness, and outer lengths. These findings indicate that, for any given roughness, new dynamical regimes will typically emerge as the Reynolds number increases. For the present range of parameters, there appear to be three identifiable regimes. These correspond to the ratio of the equivalent sand grain roughness to the characteristic length being less than, equal to, or greater than$O(1)$. The relative influences of the inner, outer, and roughness length scales on the characteristic length are explored empirically. A prediction for the decay rate of the mean vorticity is developed via extension of the smooth-wall theory. Existing data are shown to exhibit good agreement with this extension. Overall, the present results appear to expose unifying connections between the structure of smooth- and rough-wall flows. Among other findings, the present analyses show promise toward providing a self-consistent and dynamically meaningful way of identifying the domain where the wall similarity hypothesis, if operative, should hold.

Increasing Energy Storage in Electrochemical Capacitors with Ionic Liquid Electrolytes and Nanostructured Carbon Electrodes

The potential pathways to increase the energy storage in electric double-layer (EDL) supercapacitors using room-temperature ionic liquid electrolytes and carbon-based nanostructured electrodes are explored by molecular dynamics simulations. A systematic comparison of capacitances obtained on nanoparticles of various shape and dimensions showed that when the electrode curvature and the length scale of the surface roughness are comparable to ion dimensions, a noticeable improvement in the capacitive storage is observed. The nanoconfinement of the electrolyte in conductive electrode pores further enhances the capacitance due to mismatch in ion–electrode surface interactions and strong electrostatic screening. We show that nanoporous structures made of arrays of conductive carbon chains represent a synergy of all three favorable factors (that is, high curvature, atomic scale roughness, and nanoconfinement) and can generate non-Faradic capacitance ranging from 260 to 350 F/g, which significantly exceeds the performance of the current generation of nanostructured electrodes.

Surface Roughness Effects in the Region Between High Wave Number and High Bearing Number Limited Lubricant Flows

The ability to predict surface roughness effects is now well established for gas bearings that satisfy the requirements for either high wave number–limited or high bearing number–limited conditions. However, depending on the parameters involved, a given bearing configuration may not satisfy either of these limited requirements for analysis of roughness effects. Well-established methods for the analysis of surface roughness effects on gas lubrication are not yet available outside of these two limited regions. With that as motivation, this paper then reports an analytical investigation of rough surface gas-bearing effects for the region bounded on one side by high wave number–limited conditions and on the other by high bearing number–limited effects. It emphasizes the gas-bearing region, where shear-driven flow rate and pressure-driven flow rate due to surface roughness are of the same order of magnitude. This paper makes use of the compressible continuum form of the Reynolds equation of lubrication together with multiple-scale analysis to formulate a governing lubrication equation appropriate for the analysis of striated roughness effects collectively subject to high bearing number (Λ→∞), high inverse roughness length scale (β→∞), and unity order of magnitude-modified bearing number based on roughness length scale (Λ2=Λ/β=O(1)). The resulting lubrication equation is applicable for both moving and stationary roughness and can be applied in either averaged or un-averaged form. Several numerical examples and comparisons are presented. Among them are results that illustrate an increased sensitivity of bearing force to modified bearing number for Λ2=O(1). With Λ2 in this range, bearings with either moving or stationary roughness exhibit increased force sensitivities, but the effects act in opposite ways. That is, while an increase in modified bearing number causes a decrease in force for stationary roughness, the same increase in modified bearing number causes an increase in force for moving roughness.

Influence of bed patchiness, slope, grain hiding, and form drag on gravel mobilization in very steep streams

AbstractSteep streams are a major portion of channel networks and provide a link to transport sediment from hillslopes to lower gradient rivers. Despite their importance, key unknowns remain, perhaps foremost of which is evaluating in steep streams empirical laws for fluvial sediment transport developed for low‐gradient rivers. To address this knowledge gap, we painted sediment in situ over 3 years to monitor incipient sediment motion and sediment‐patch development in five small (drainage areas of 0.04–2 km2) and steep (slopes of 5–37%) tributaries of Elder Creek, California, United States. We found that channel beds organized into size‐sorted sediment patches which displayed active fluvial transport of gravel annually, consistent year‐to‐year patch median grain sizes, partial transport of bed material, and significantly higher values of critical Shields stress for incipient sediment motion compared to that observed for lower gradient rivers. The high critical Shields stresses (up to ≈0.5 for the median grain size) agree within a factor of ~3 to theoretical predictions which account for slope‐dependent hydraulics, grain hiding, and sediment patches. For grains of approximately the same size as the roughness length scale, slope‐dependent hydraulics and bed patchiness are the dominant controls on critical Shields stress values, while grain hiding is important for grains larger or smaller than the roughness length scale. Form drag exists in our monitored tributaries but has a smaller influence than the above effects. Our field observations show fluvial processes contribute to sediment mobilization in steep channels which are often considered to be dominated by debris flows.

Development of surface relief on polycrystalline metals due to sputtering

The characteristics of surface microrelief that appear in sputtering experiments with polycrystalline metals of various grain sizes have been studied. Specimens with grain sizes varying from 30–70nm in the case of crystallized amorphous alloys, to 1–3μm for technical tungsten grade and 10–100μm for recrystallized tungsten were investigated. A model is proposed for the development of roughness on polycrystalline metals which is based on the dependence of sputtering rate on crystal orientation. The results of the modeling are in good agreement with experiments showing that the length scale of roughness is much larger than the grain size.

Hierarchical or Not? Effect of the Length Scale and Hierarchy of the Surface Roughness on Omniphobicity of Lubricant-Infused Substrates

Lubricant-infused textured solid substrates are gaining remarkable interest as a new class of omni-repellent nonfouling materials and surface coatings. We investigated the effect of the length scale and hierarchy of the surface topography of the underlying substrates on their ability to retain the lubricant under high shear conditions, which is important for maintaining nonwetting properties under application-relevant conditions. By comparing the lubricant loss, contact angle hysteresis, and sliding angles for water and ethanol droplets on flat, microscale, nanoscale, and hierarchically textured surfaces subjected to various spinning rates (from 100 to 10,000 rpm), we show that lubricant-infused textured surfaces with uniform nanofeatures provide the most shear-tolerant liquid-repellent behavior, unlike lotus leaf-inspired superhydrophobic surfaces, which generally favor hierarchical structures for improved pressure stability and low contact angle hysteresis. On the basis of these findings, we present generalized, low-cost, and scalable methods to manufacture uniform or regionally patterned nanotextured coatings on arbitrary materials and complex shapes. After functionalization and lubrication, these coatings show robust, shear-tolerant omniphobic behavior, transparency, and nonfouling properties against highly contaminating media.

Boundary layer flow dynamics at a cold-water coral reef

The Tisler cold-water coral reef is a 2km long reef in the north-eastern Skagerrak, Norway. The reef is comprised principally of Lophelia pertusa at depths between 70 and 160m. Velocity shear and boundary layer shear stresses have been measured at Tisler Reef to quantify the effect of the reef structure on the benthic boundary layer (BBL) dynamics.Two different approaches to estimating the magnitude of the near seabed stress were employed: using a logarithmic (constant stress) boundary layer approach and direct Reynolds stress measurements. Resultant estimates of near seabed stresses using both methods were comparable.Using the logarithmic layer approach to estimate seabed stresses both inside and out of the reef structure demonstrated that, for any particular impinging flow strength, higher shear stresses were observed within the live coral region than in the dead coral rubble region with no live coral stands. Bottom shear stresses of up to 3.5Nm−2 were measured within the reef complex and 1.2Nm−2 in the rubble region outside the live reef. This difference is due to large roughness length scales inside the rough living coral area relative to the smaller scales in the coral rubble.Low frequency acoustic backscatter data, used as a proxy for relative suspended particulate matter concentrations, suggested that both local re-suspension and advection of suspended material most likely occur at, and through, the reef system. The high stresses measured inside the living reef may favour corals by increasing the degree of re-suspension for a given current speed and providing more particulates to the filter feeding polyps.

Frictional forces between hydrophilic and hydrophobic particle coated nanostructured surfaces

Friction forces have long been associated with the famous Amontons' rule that states that the friction force is linearly dependent on the applied normal load, with the proportionality constant being known as the friction coefficient. Amontons' rule is however purely phenomenological and does not in itself provide any information on why the friction coefficient is different for different material combinations. In this study, friction forces between a colloidal probe and nanostructured particle coated surfaces in an aqueous environment exhibiting different roughness length scales were measured by utilizing the atomic force microscope (AFM). The chemistry of the surfaces and the probe was varied between hydrophilic silica and hydrophobized silica. For hydrophilic silica surfaces, the friction coefficient was significantly higher for the particle coated surfaces than on the flat reference surface. All the particle coated surfaces exhibited similar friction coefficients, from which it may be concluded that the surface geometry, and not the roughness amplitude per se, influenced the measured friction. During measurements with hydrophobic surfaces, strong adhesive forces related to the formation of a bridging air cavity were evident from both normal force and friction force measurements. In contrast to the frictional forces between the hydrophilic surfaces, the friction coefficient for hydrophobic surfaces was found to depend on the surface structure and we believe that this dependence is related to the restricted movement of the three-phase line of the bridging air cavity. For measurements using a hydrophobic surface and a hydrophilic probe, the friction coefficient was significantly smaller compared to the two homogeneous systems. A layer of air or air bubbles on the hydrophobic surface working as a lubricating layer is a possible mechanism behind this observation.

Superfast Nonlinear Diffusion: Capillary Transport in Particulate Porous Media

The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this Letter, we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime, the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of nonlinear diffusion described by a superfast diffusion equation for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by superfast diffusion equation that robustly convey a time power law of spreading as seen in our experiments.

Effects of contact angle hysteresis on ice adhesion and growth on superhydrophobic surfaces under dynamic flow conditions

In this paper, the icephobic properties of superhydrophobic surfaces are investigated under dynamic flow conditions using a closed-loop low-temperature wind tunnel. Superhydrophobic surfaces were prepared by coating aluminum and steel substrate plates with nano-structured hydrophobic particles. The superhydrophobic plates, along with uncoated controls, were exposed to a wind tunnel air flow of 12 m/s and −7 °C with deviations of ±1 m/s and ±2.5 °C, respectively, containing micrometer-sized (∼50 μm in diameter) water droplets. The ice formation and accretion were observed by CCD cameras. Results show that the superhydrophobic coatings significantly delay ice formation and accretion even under the dynamic flow condition of highly energetic impingement of accelerated supercooled water droplets. It is found that there is a time scale for this phenomenon (delay in ice formation) which has a clear correlation with contact angle hysteresis and the length scale of the surface roughness of the superhydrophobic surface samples, being the highest for the plate with the lowest contact angle hysteresis and finest surface roughness. The results suggest that the key for designing icephobic surfaces under the hydrodynamic pressure of impinging droplets is to retain a non-wetting superhydrophobic state with low contact angle hysteresis, rather than to only have a high apparent contact angle (conventionally referred to as a “static” contact angle).

Roughness of fault surfaces over nine decades of length scales

We report on the topographic roughness measurements of five exhumed faults and thirteen surface earthquake ruptures over a large range of scales: from 50 μm to 50 km. We used three scanner devices (LiDAR, laser profilometer, white light interferometer), spanning complementary scale ranges from 50 μm to 10 m, to measure the 3‐D topography of the same objects, i.e., five exhumed slip surfaces (Vuache‐Sillingy, Bolu, Corona Heights, Dixie Valley, Magnola). A consistent geometrical property, i.e., self‐affinity, emerges as the morphology of the slip surfaces shows at first order, a linear behavior on a log‐log plot where axes are fault roughness and spatial length scale, covering five decades of length‐scales. The observed fault roughness is scale dependent, with an anisotropic self‐affine behavior described by four parameters: two power law exponents H, constant among all the faults studied but slightly anisotropic (H∥ = 0.58 ± 0.07 in the slip direction and H⊥ = 0.81 ± 0.04 perpendicular to it), and two pre‐factors showing variability over the faults studied. For larger scales between 200 m and 50 km, we have analyzed the 2‐D roughness of the surface rupture of thirteen major continental earthquakes. These ruptures show geometrical properties consistent with the slip‐perpendicular behavior of the smaller‐scale measurements. Our analysis suggests that the inherent non‐alignment between the exposed traces and the along or normal slip direction results in sampling the slip‐perpendicular geometry. Although a data gap exists between the scanned fault scarps and rupture traces, the measurements are consistent within the error bars with a single geometrical description, i.e., consistent dimensionality, over nine decades of length scales.

A colloidal route to fabricate hierarchical sticky and non-sticky substrates

We present a facile and inexpensive bottom-up colloidal route to prepare sticky superhydrophobic surfaces and non-sticky ones. Either spin coating to assemble silica microspheres into random multilayered arrays or irreversible adsorption of gold nanoparticles is used to manufacture substrates with a single length scale roughness. Hierarchical roughness with multiple length scales is achieved by decorating the silica spheres with gold nanoparticles. The surface chemistry of the silica surfaces is modified by the adsorption of fluoroalkylsilane self-assembled monolayers, while gold nanoparticles are hydrophobized by dodecanethiol. The wetting properties, both static and dynamic, of surfaces in relation to the morphology of the substrates are addressed. We demonstrate the role of hierarchy in the roughness in converting a sticky into a non-sticky superhydrophobic surface and discuss the results in terms of existing models describing wetting characteristics.

Influence of Surface Topography on the Interactions between Nanostructured Hydrophobic Surfaces

Nanostructured particle coated surfaces, with hydrophobized particles arranged in close to hexagonal order and of specific diameters ranging from 30 nm up to 800 nm, were prepared by Langmuir-Blodgett deposition followed by silanization. These surfaces have been used to study interactions between hydrophobic surfaces and a hydrophobic probe using the AFM colloidal probe technique. The different particle coated surfaces exhibit similar water contact angles, independent of particle size, which facilitates studies of how the roughness length scale affects capillary forces (previously often referred to as "hydrophobic interactions") in aqueous solutions. For surfaces with smaller particles (diameter < 200 nm), an increase in roughness length scale is accompanied by a decrease in adhesion force and bubble rupture distance. It is suggested that this is caused by energy barriers that prevent the motion of the three-phase (vapor/liquid/solid) line over the surface features, which counteracts capillary growth. Some of the measured force curves display extremely long-range interaction behavior with rupture distances of several micrometers and capillary growth with an increase in volume during retraction. This is thought to be a consequence of nanobubbles resting on top of the surface features and an influx of air from the crevices between the particles on the surface.

Influence of Surface Properties of Coated Papers on Printed Electronics

Thin and narrow conductive patterns of metal (silver) and organic polymer (polyaniline) were printed on various coated paper samples. A detailed characterization of the physical properties (i.e., short length scale roughness, surface energy, and air permeability) of the paper samples was conducted. These properties were correlated with print quality (print resolution and edge waviness) and electrical performance (resistance) of the printed wires. A plastic film was used as a reference substrate. The print resolution and the magnitude of the edge waviness were affected by the complex interplay of different physical properties of both the substrate and the ink. On the other hand, the resistance of the printed wires was found to correlate linearly with the short length scale roughness of the print substrate. The electrical performance of the paper substrates showing the highest conductivity for the printed patterns was comparable to that of the plastic film. The paper substrate on which the printed wires showed the best electrical performance was used as a substrate for fabrication of an organic transistor with low operating voltage.

Atmospheric stability of surface boundary layer in coastal region of the Wol–Ryong site

In order to provide statistically reliable information of a wind energy site, accurate analysis on the atmospheric stability and climate characteristics in a certain area is a prerequisite. Two 2-D ultrasonic anemometers and one cup anemometer, located perpendicular to the prevailing wind direction, were used to measure the atmospheric wind environment at a height of 4.5 m in coastal region of the Wol–Ryong, Jeju, South Korea. The study is aiming to understand the atmospheric stability about a coastal region, and the effect of roughness length. We calculate the Monin–Obukhov length for division of atmospheric stability about unstable regime, neutral regime and stable regime. The distribution of diurnal Monin–Obukhov length is highly sporadic in the coastal region due to the effect of radiant heat from the surface or other environmental effects. In order to calculate the roughness length in coastal region, three different methods are applied in terms of the surface roughness, flow fluctuation and gust wind, which are called logarithmic profile, standard deviation and gust factor methods. In the study, the atmospheric stability was insignificant when applying these three methods. In the results, three different roughness length scales sufficiently showed the effect of obstacle and surface conditions around the measurement position. On the basis of an overall analysis of the short-term data measured in the Wol–Ryong area, Jeju Island, it is concluded that for the development of future wind energy resources, the Wol–Ryong site could be a good candidate for a future wind energy site.

Dissipation of wave energy and turbulence in a shallow coral reef lagoon

Simultaneous in situ measurements of waves, currents and turbulence are presented to describe dissipation rates of wave energy and turbulent kinetic energy in the windward coral reef‐lagoon system at Lady Elliot Island (LEI), Australia. The dissipation of wave energy in the lagoon is tidally modulated and strongly correlates with frictional dissipation due to the presence of the extremely rough bottom boundary. The observed turbulent kinetic energy (TKE) dissipation rate, ε, in this wave‐dominated lagoon is much larger than recently reported values for unidirectional flows over natural fringing coral reefs. The correlation between the wave dissipation and ε is examined. The average rate of dissipation induced by the rough turbulent flow was estimated directly from the observed ε coupled with both a depth‐integrated approach and with a bottom boundary layer scaling. Rates of TKE dissipation estimated using the two approaches approximate well, within a factor of 1.5 to 2.4, to the surface‐wave energy dissipation rate. The wave dissipation and friction factor in the lagoon can be described by a spectral wave‐frictional model with a bottom roughness length scale that is approximately constant across the lagoon. We also present estimates of dissipation induced by the canopy drag force of the coral heads. The dissipation in this case is enhanced and becomes more significant for the total energy dissipation when the water depth in the lagoon is comparable to the height of the coral heads.

How nanorough is rough enough to make a surface superhydrophobic during water condensation?

Nanostructured surfaces which manifest superhydrophobic properties during water condensation have a potential to dramatically enhance energy efficiency in power generation and desalination systems. Although various such surfaces have been reported, their development has been fortuitous, not driven by an understanding of the underlying physical processes. In this work, we perform a comprehensive study of microscale water condensation dynamics on nanostructured superhydrophobic surfaces made using a variety of synthetic methods. We demonstrate that the growth mechanism of individual water microdroplets on these surfaces is universal and independent of the surface architecture. The key role of the nanoscale topography is confinement of the base area of forming droplets, which allows droplets to grow only through contact angle increase. The nearly spherical droplets formed in this fashion become highly mobile after coalescence. By comparing experimentally observed drop growth with interface free energy calculations, we show that the minimum observed confined microdroplet base diameter depends directly on the nanoscale surface roughness and degree of interfacial wetting. Specifically, we show that the microscale condensation mechanism depends on the height of a liquid film with volume equal to the fill volume between the nanostructures. This introduced roughness length scale is a universal metric that allows for facile comparison of arbitrarily complex surface architectures. We use this new fundamental insight to develop quantitative design guidelines for superhydrophobic surfaces intended for condensation applications.

Decorative, hydrophobic sol–gel coatings densified using near-infrared radiation

Decorative, hydrophobic coatings were generated using sols synthesized from hydrolysis and condensation of methyltriethoxy silane, tetraethoxy silane and 1H,1H,2H,2H-perfluorooctyltriethoxysilane, in combination with nanosized and submicron-sized inorganic black pigment particles. Coatings were densified at 250 °C using near-infrared radiation as well as by a conventional curing method. The densified coatings were characterized for their thickness, roughness, contact angles and adhesion. The properties of the near-infrared radiation cured pigmented coatings were found to be comparable with those of the conventionally cured coatings. The pigmented coatings generated using nanosized pigments, whether near-infrared radiation cured or conventionally cured were seen to exhibit improved hydrophobicity with contact angles ranging from 130 to 145° when compared to their transparent unpigmented counterparts, that showed water contact angles from 93 to 97°. The improved hydrophobicity was explained on the basis of presence of a possible double length scale roughness of the coatings.

Tailoring the frictional properties of granular media

A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning interparticle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains are systematically investigated. The surface roughness of the grains is measured using white-light interferometry and characterized by the lateral and vertical roughness length scales. The underwater angle of repose is measured to characterize the bulk frictional behavior. We observe that the coefficient of friction depends on the vertical roughness length scale.