Surface Gradient Research Articles

Characterization of an Overlooked Kinematical Descriptor in the Second-Gradient Hyperelastic Theory for Thin Shells

In 1978, Murdoch presented a direct second-gradient hyperelastic theory for thin shells in which the strain-energy density associated with a deformation η of a surface S is allowed to depend constitutively on the three kinematical descriptors C, H, and F⊤G, where F=GradSη, C=F⊤F, H=F⊤LS′F is the covariant pullback of the curvature tensor LS′ of the deformed surface S′, and G=GradSF. On the other hand, in Koiter’s direct thin-shell theory, the strain-energy density depends constitutively on only C and H. Due to the popularity of Koiter’s theory, the second-order tensors C and H are well understood and have been extensively characterized. However, the third-order tensor F⊤G in Murdoch’s theory is largely overlooked in the literature. We address this gap, providing a detailed characterization of F⊤G. We show that for η twice continuously differentiable, F⊤G depends solely on C and its surface gradient GradSC and does not depend on LS′. For the special case of a conformal deformation, we find that a suitably defined strain measure corresponding to F⊤G depends only the conformal stretch and its surface gradient. For the further specialized case of an isometric deformation, this strain measure vanishes. An orthogonal decomposition of F⊤G reveals that it belongs to a ten-dimensional subspace of the space of third-order tensors and embodies two independent types of non-local phenomena: one related to the spatial variations in the stretching of S′ and the other to the curvature of S.

Transient Models of a Photophoretically Filtering Structure in the Stratosphere

The stratosphere has very little convection and tends to trap any dust and gases that enter this region from the atmosphere. This study suggests how dust and particles can be filtered from the stratosphere by a 2-plated parallel-walled infinite rotatable, levitating vertical/horizontal channel (preferably) perforated with holes which have pockets on the cooler upper wall for collecting particles. A movement of particles by light called photophoresis, is caused by the radiative warming layer of a sandwich structure. Collisions of gases with surface of structure and thermal gradients between the two thin plates will also deflect particles. Equations of momentum and energy are solved using an implicit finite difference scheme while exact solutions are presented for steady state dimensionless velocity, concentration and temperature for a fully developed flow. Heat and mass transfer characteristics of parameters like time are displayed graphically. Combined photophoretic and thermophoretic effect on water particles is negligible when compared to soot or dust particles Sc=600.

Fabricating High-Efficiency Sb2(S,Se)3 Solar Cells by Novel Additive-Assisted Longitudinal Component Engineering.

Antimony selenosulfide (Sb2(S,Se)3) solar cells have achieved an efficiency of over 10.0%. However, the uncontrollable hydrothermal process makes preparing high-quality Sb2(S,Se)3 thin films a bottleneck for efficient Sb2(S,Se)3 solar cell. To address this problem, triethanolamine (TEA) additive is innovatively utilized to regulate the reaction kinetic process of Sb2(S,Se)3 thin films in this work. The results show that TEA chelator can realize the time-domain control of the reaction process, optimizing the Se/(S+Se) elemental distribution of Sb2(S,Se)3 thin film and shrinking the bandgap offset of Sb2(S,Se)3 thin film. Meanwhile, the (021) and (061) crystal orientation of Sb2(S,Se)3 thin film are enhanced and the harmful VSe1 defects in Sb2(S,Se)3 solar cells are passivated. Interestingly, a uniform back surface gradient for Sb2(S,Se)3 thin film is formed to reduce the minority carrier recombination at the back contact, increase the photocurrent and decrease the diode current of Sb2(S,Se)3 solar cells. Finally, the Jsc and FF of Sb2(S,Se)3 solar cells are significantly improved by 8.6% and 5.5% respectively, and the open-circuit voltage deficit of the device is reduced by 44mV, which leads to an efficiency of 9.94% which is the highest values of Sb2(S,Se)3 solar cells by sodium selenosulfate system.

Influence of liquid–vapor phase change on the self-propelled motion of droplets on wettability gradient surfaces

Self-propelled motion of sessile droplets on gradient surfaces is key to the advancement of microfluidic, nanofluidic, and surface fluidic technologies. Precise control over droplet dynamics, which often involves liquid–vapor phase transitions, is crucial for a variety of applications, including thermal management, self-cleaning surfaces, biochemical assays, and microreactors. Understanding how specific phase changes like condensation and evaporation affect droplet motion is essential for enhancing droplet manipulation and improving transport efficiency. We use the thermal Navier–Stokes–Korteweg equations to investigate the effects of condensation and evaporation on the motion and internal dynamics of droplets migrating across a surface with a linear surface energy profile. The study focuses on the early dynamics of self-propelled motion of a phase changing droplet at sub-micron scale before viscous forces are comparable with the gradient forces. Our results demonstrate that phase change significantly affects the self-propelled motion of droplets by reshaping interfacial mass flux distributions and internal flow dynamics. Condensation increases droplet volume and promotes extensive spreading toward regions of higher wettability, while evaporation reduces both volume and spreading. These changes in droplet shape and size directly affect the driving forces of motion, augmenting self-propulsion through condensation and suppressing it during evaporation. Additionally, each phase change type generates distinct internal flow patterns within the droplet, with condensation and evaporation exhibiting unique circulatory movements driven by localized phase changes near the contact lines.

A numerical study of the effect of different geometrical parameters on the cooling processes in electrical transformer

Proper thermal control is one of the most important aspects that should be considered when utilizing electrical transformers. This research work offers a numerical analysis of the effect of changing the shape of transformer fins on the heat exchange process. Based on the results of CFD simulations, several types of fin shapes such as rectangular, triangular and wavy are discussed to describe the improvements of heat transfer. The study examines the shape of an electrical transformer, determining the optimal distance between fins, fin shapes, transformer shape, rib type, and rib number. The results are then applied to a special case, representing the best of all variables on the transformer. The study also considers the effect of increasing the surface area of the ribs on the fins, and the number of ribs used on the fins. The temperature gradient of a coil, oil, and transformer varies depending on the distance between fins, fin shape, rib type, and number of ribs. The coil temperature is 383 K when the fins are 7 cm apart, 381 K when the fins are 5 cm apart, and 381 K when the fins are 3cm apart. The temperature gradient also varies depending on the rib type, with triangular ribs increasing the surface area for heat energy transfer and reducing the temperature value. The oil temperature gradient varies depending on the fins, ribs type, and number of ribs. The heat transfer coefficient gradient of the transformer surface varies depending on the fins, ribs type, and number of ribs. The surface heat transfer coefficient reaches 1.5 W/m2. K when the fins are l shape, 1.6 W/m2. K when the fins are c shape, 1.7 W/m2. K when the fins are z shape, 1.4 W/m2. K when the ribs are rectangular, 1.6 W/m2. K when the ribs are triangular, and 1.4 W/m2. K when the ribs are 9 ribs.

Clickable Plastic Surfaces with Controllable Azide Surface Density

AbstractThis study investigates the surface functionalization of plastic substrates through dip‐coating in azide‐functionalized polymer solutions, followed by a click reaction (i.e., strain‐promoted azide–alkyne cycloaddition). Acrylic, poly(ethylene terephthalate) (PET), and nylon substrates are dip‐coated with a series of polymers containing various azide groups grafted onto the poly(methyl methacrylate‐co‐hydroxyethyl methacrylate) backbone to examine structural effects on the surface density of clickable azide groups. X‐ray photoelectron spectroscopy and fluorescence spectroscopy confirm the subsequent click‐immobilization of cycloalkyne‐tagged fluorescein, which is quantified to calculate the surface density of clickable azide groups. Further investigations demonstrate that the surface density of azide groups can be controlled by manipulating the polymer ratio during dip‐coating, thus enabling the preparation of a linear surface gradient in terms of azide group density. Finally, the microcontact printing (µCP) method is employed to pattern the functionalized surfaces and quantify the functional molecules immobilized on the surface by µCP. This study highlights the adaptability of click chemistry and polymer coating techniques for the advanced functionalization of plastic surfaces for materials science and engineering applications.

Emergence of Potential Anadromous Arctic Charr (Salvelinus alpinus) Habitats in the Svalbard Archipelago After the End of the Little Ice Age

AbstractGlaciers in the Svalbard Archipelago are retreating rapidly in response to climate change. This retreat leads to the alteration of the hydrological and thermal regimes of freshwater ecosystems. In this delicate context, existing anadromous Arctic charr (Salvelinus alpinus) populations are at severe risk and might disappear from the archipelago. However, the retreat of glaciers also promotes the formation of new lake systems that might be suitable for colonization by anadromous Arctic charr. These systems may provide a substantial opportunity for the establishment of new populations of anadromous charr, potentially buffering the decline in existing systems. To date, there is a lack of information on the number of recently deglaciated lake systems that have emerged since the end of the Little Ice Age (ca. 1920) that might be suitable for charr colonization. Therefore, the goal of this paper is to provide an initial assessment of the number of these lakes. To this end, and in accordance with previously published research, this study assesses whether a recently deglaciated lake system is potentially open to colonization based on gradient, river length, and lake surface area. Depending on the applied threshold (four in total), up to 24 lake systems are classified as potentially open to colonization by anadromous Arctic charr, with Spitsbergen emerging as a potential hotspot for colonization. The findings of this paper might serve as basis for new studies and for implementing proactive management and conservation strategies to protect anadromous charr populations.

Effects of ultrasonic shot peening process on the microstructure and mechanical properties of nickel-based superalloys formed by selective laser melting

Selective laser melting (SLM) is an attractive additive manufacturing technique for fabricating high-performance superalloys engineering components. Unfortunately, these as-built parts generally exhibit unsatisfied mechanical properties because of their natural thermal residual stress and non-equilibrium microstructures. Ultrasonic shot peening (USP) can effectively inhibit defect expansion and even close pores, thereby improving the mechanical properties of alloys. In this study, the internal defects, residual stress and microhardness redistribution, tensile properties, as well as microstructural response of the GH3230 alloy treated by different ultrasonic peening time are systematically studied. USP treatment induces a significant carbides fragmentation and synthesizes surface gradient heterogeneous structure, which displays a microstructure gradient in grain size, carbides size and dislocation density from surface to core. Long-time USP treatment induces work softening of GH3230 alloys. The work softening mechanism of the GH3230 alloys after long-time USP treatment is ascribed to the increase of surface temperature and high stored strain energy. Both the microhardness and residual compressive stress in the softened region of GH3230 alloys are reduced. Work softening effect increases the surface plasticity of the GH3230 sample, which induces deeper gradient structure. The various strengthening mechanisms of gradient heterogeneous structures, as well as the multiple effects of hetero deformation induced (HDI) hardening, and densification strengthening are responsible for achieving strength-ductility synergy. The research findings provide new insights based on USP for improving the mechanical properties of heterogeneous superalloys engineering components.

Exploring mechanisms of asymmetric droplet impact dynamics on roughness gradient surface

Droplet impact on surfaces with varying roughness and wettability is a common phenomenon in both natural and industrial environments. While previous studies have primarily examined asymmetric droplet rebound driven by impact velocity or Weber number, the influence of surface structure and associated impact mode transitions has received less attention. In this study, molecular dynamics simulations and detailed analyses are employed to investigate the mechanisms governing droplet rebound on nanopillar arrays with gradient distributions. Results reveal that nanopillar height significantly influences rebound direction, with two distinct directional transitions occurring as the height increases. Additionally, the effects of surface structure and Weber number on impact patterns, rebound velocity, and contact time are systematically evaluated, with contact angle calculations shedding light on the underlying force mechanisms. A phase diagram is developed to illustrate the relationship between rebound direction, Weber number, and nanopillar height. The study further extends the analysis to substrates with bidirectional gradient distributions, demonstrating consistency with single-directional gradient results and validating the broader applicability of the findings. This research provides critical insights into droplet dynamics on roughness gradient surfaces, emphasizing the role of nanopillar height and impact mode in controlling droplet behavior and highlighting potential applications in the design of structured array surfaces.

Synthesis, Crystal Structure, Intermolecular Interactions, HOMO-LUMO, MEP, NLO Properties, and DFT/TD-DFT Investigation of (Z)-5-(4-Nitrobenzylidene)-3-N(3-Chlorophenyl)-2-Thioxothiazolidin-4-One

A novel heterocyclic compound named (Z)-5-(4-nitrobenzylidene)-3-N(3-chlorophenyl)-2-thioxothiazolidin-4-one (NCTh) was synthesized and analyzed using various techniques, including single crystal X-ray diffraction, FT-IR, UV-Vis, NMR spectroscopy, and mass spectral data methods. NCTh was observed to crystallize in the triclinic crystal system P-1 space group. To validate the experimental findings, density functional theory (DFT) calculations were performed using the B3LYP functional with the 6-311 G(d,p) basis set. The results indicated good agreement in geometrical parameters between the experimental and theoretical outcomes. The study also calculated HOMO-LUMO energies, molecular electrostatic potential (MEP), and global chemical reactivity descriptors to evaluate the compound’s reactivity. Additionally, the study conducted reduced density gradient and Hirshfeld surface analyses to reveal attractive, repulsive, and van der Waals strong and weak interactions. The calculation of thermodynamic parameters was also included. The study focused on investigating the nonlinear optical (NLO) properties of NCTh, which were characterized through key parameters such as the electric dipole moment (µ), polarizability (α), first-order hyperpolarizability (β), and second-order hyperpolarizability (γ). These properties provide insights into the material’s potential applications in optical and photonic technologies. Additionally, a molecular docking study was performed to further explore the structure-activity relationship, particularly in a biological context. The docking results revealed a strong ligand-protein interaction, with a binding energy of −10.3 kcal/mol, indicating significant affinity. Moreover, the inhibition constant (Ki) was calculated to be 0.0281 μM, suggesting a highly potent interaction, which could be relevant for drug design or biochemical applications.

Shape optimization for high efficiency metasurfaces: theory and implementation

Complex non-local behavior makes designing high efficiency and multifunctional metasurfaces a significant challenge. While using libraries of meta-atoms provide a simple and fast implementation methodology, pillar to pillar interaction often imposes performance limitations. On the other extreme, inverse design based on topology optimization leverages non-local coupling to achieve high efficiency, but leads to complex and difficult to fabricate structures. In this paper, we demonstrate numerically and experimentally a shape optimization method that enables high efficiency metasurfaces while providing direct control of the structure complexity through a Fourier decomposition of the surface gradient. The proposed method provides a path towards manufacturability of inverse-designed high efficiency metasurfaces.

Investigation of Mechanical Properties and Microstructural Evolution in Pure Copper with Dual Heterostructures Produced by Surface Mechanical Attrition Treatment

Heterostructured materials consist of heterogeneous zones with dramatic variations in mechanical properties, and have attracted extensive attention due to their superior performance. Various heterostructured materials have been widely investigated in recent years. In the present study, a combination of two different types of heterogeneous structures, a surface bimodal structure and gradient structure, was designed using the traditional surface mechanical attrition treatment (SMAT) method in pure copper, and the mechanical properties and microstructural evolution of dual-heterostructure Cu were studied in depth. In total, 100 stainless steel balls with a diameter of 6 mm were utilized to impact the specimen surface at room temperature for a short period of time. In this work, the sample surface was divided into hard areas and soft areas, along with a roughly 90 μm gradient structure in the cross-sectional direction after 30 s of SMAT processing. After the partial SMAT processing, lasting 30 s, the strength increased to 158.0 MPa and a considerable ductility of 25.7% was sustained, which overcomes the strength–ductility trade-off. The loading–unloading–reloading (LUR) test was utilized to measure the HDI stress, and the result showed that the HDI stress of the partial SMAT sample was much higher than the annealed one, especially for the Cu-SMAT-30S specimen, the strength of which increased from 80.4 MPa to 153.8 MPa during the tensile test. An in situ digital image correlation (DIC) investigation demonstrated that the strain developed stably in the Cu-SMAT-10S specimen. Furthermore, electron backscatter diffraction (EBSD) was carried out to study the microstructural evolution after partial SMAT processing; the KAM value increased to 0.34 for the Cu-SMAT-10S specimen. This research provides insights for the effective combination of superior strength and good ductility in dual-heterostructure materials.

High-Efficiency Microwave Wireless Power Transmission via Reflective Phase Gradient Metasurfaces and Surface Wave Aggregation.

Microwave Wireless Power Transfer (MWPT) technology is crucial for emergency power supply during natural disasters and powering off-grid equipment. Traditional antenna arrays, however, suffer from low energy capture efficiency, difficult impedance matching, complex synthetic networks, and intricate manufacturing processes. This paper introduces a microwave energy receiver design utilizing Reflective Phase Gradient Metasurfaces (R-PGMs) and surface wave energy convergence technology. The design leverages the effective plane wave-to-surface wave conversion capability of R-PGMs to transform incident microwave energy into a surface wave mode, which is then efficiently harvested using a circular energy convergence array before being output to a coupling port. By optimizing R-PGM parameters, an ideal 60° phase gradient distribution is achieved, facilitating the focus of surface wave energy via dispersion characteristics. These components are integrated into a hybrid antenna array, complemented by a matched energy output port structure. Numerical simulations show that this array can efficiently convert microwave energy from plane waves to surface waves, achieving a conversion efficiency of 85.32% and a collection efficiency of 68.26%. Experimental results corroborate these findings, with peak energy collection efficiency reaching 64.68% at 5.8 GHz and an RF-DC conversion efficiency of 42%, confirming the design's efficacy. Compared to conventional methods, this design simplifies the system by avoiding complex combining networks and significantly enhances the efficiency of microwave MWPT.

Vertical heterogeneity enhances network complexity and stability of co-occurrence microbes in the eastern Indian Ocean

Microbes are core to driving biogeochemical cycles and differ between sun-drenched surface and relatively dark deep oceans. However, their distinct contributions to the organization and association of communities are still remaining elusive. Here, their assembly and co-occurrence stability are systematically researched along the surface and vertical gradients in the eastern Indian Ocean. The distribution of surface microbes was grouped tightly with closer phylogenetic distance and broader niche breadth, and separately from those vertical samples. Clear distance-decay of community similarity was observed in surface microbes with lower richness, while more diverse microeukaryotes and prokaryotes were observed in surface and vertical environments, respectively. Co-occurrence microbes along vertical gradients had a more complex network that was dominated by prokaryotes, while exhibited a lower modularity compared to the surface network. Microbial associations along vertical gradients were more stable and resilient, with lower robustness, higher vulnerability, and a relatively consistent fragmentation. Moreover, prokaryotes contribute greatly to the network topology and stability compared to microeukaryotes in surface environments, emphasizing their distinct functions and survival strategies in maintaining community stability across spatial variations. Environmental selection and community differentiation led to the divergence in organization and potential function of microbes. This study shed light on new perspectives on how marine microbes were associated with and influenced by spatial heterogeneity and their distinct roles in community organization in the face of environmental fluctuations.

Persistently active El Niño–Southern Oscillation since the Mesozoic

The El Niño-Southern Oscillation (ENSO), originating in the central and eastern equatorial Pacific, is a defining mode of interannual climate variability with profound impact on global climate and ecosystems. However, an understanding of how the ENSO might have evolved over geological timescales is still lacking, despite a well-accepted recognition that such an understanding has direct implications for constraining human-induced future ENSO changes. Here, using climate simulations, we show that ENSO has been a leading mode of tropical sea surface temperature (SST) variability in the past 250 My but with substantial variations in amplitude across geological periods. We show this result by performing and analyzing a series of coupled time-slice climate simulations forced by paleogeography, atmospheric CO2 concentrations, and solar radiation for the past 250 My, in 10-My intervals. The variations in ENSO amplitude across geological periods are little related to mean equatorial zonal SST gradient or global mean surface temperature of the respective periods but are primarily determined by interperiod difference in the background thermocline depth, according to a linear stability analysis. In addition, variations in atmospheric noise serve as an independent contributing factor to ENSO variations across intergeological periods. The two factors together explain about 76% of the interperiod variations in ENSO amplitude over the past 250 My. Our findings support the importance of changing ocean vertical thermal structure and atmospheric noise in influencing projected future ENSO change and its uncertainty.

Coherent turbulent flow structure under plunging breaker on movable grain bed simulated by 3D DEM-MPS method

ABSTRACT Breaking waves transport momentum, gas, and sediment vertically. Recent particle image velocimetry (PIV) measurements have elucidated the coherent vortex and turbulence structures under breaking waves. However, clarifying three-dimensional fluid motion under breaking waves with PIV remains challenging. Although particle methods have performed wave-breaking simulations, they have never been validated through velocity distributions for breaking waves above movable sediment beds. This study simulated the sediment transport process under plunging waves using a 3D Lagrangian fluid-particle mixture model. The investigation focuses on the first wave plunging for a fundamental investigation. Our simulation shows the instantaneous velocity distributions at different wave phases, which agree with the PIV measurement. A physically-based turbulence extraction method is introduced: a numerical filter based on the coherence between the water elevation and horizontal velocity. Visualized three-dimensional vortex and turbulence structures are consistent with previous studies. The transport equation of the kinetic turbulence energy investigates the turbulence budget near the bed surface and emphasizes the negative contribution of the fluid-particle interaction. Our findings show that a contribution of the pressure gradient to offshore sediment transport. The pressure gradient is difficult to correlate to the water surface gradient and is derived from the large vortex induced by the plunging wave.

Evolution of Graded Surface Microstructure and Property of Ti6Al4V Threads Processed by Surface Rolling

The surface rolling process is important for the forming property of titanium alloy bolts. This study systematically investigated the evolution of the surface microstructure and property of Ti6Al4V threads induced by surface rolling processes with different feeding times. Gradient surface microstructure and property, as characterized by the depth-dependent variations of refined and deformed grains and hardness, were revealed. A comparative analysis of the microstructure and property of the topmost and subsurface layers in different characteristic areas (root, flank, and crest) of the thread was specifically carried out. The surface microstructure and properties are highly heterogeneous in different areas of the rolled thread. Meanwhile, a gradient microstructure and hardness along the depth from the surface was revealed in the surface layer. Our results showed that the highly heterogeneous surface microstructure and property can be attributed to the close correlation between the different stress/strain levels at different depths from the surface and the different deformation mechanisms in the characteristic surface areas of the thread. The present study has indicated that the distinctive microstructure and property in the different characteristic areas of the rolled thread should be featured by those of surface layers at different depths.

Optimizing crucible geometry to improve the quality of AlN crystals by the physical vapor transport method

In the conventional crucible structure for AlN crystal growth by physical vapor transport, owing to the long molecular transport path of Al vapor and the disruption of the gas flow by the presence of a deflector, the Al vapor easily forms polycrystals in the growth domain. The result is increased internal stress in the crystals and increased difficulty in growing large-sized crystals. On this basis, with the help of finite element simulations, a novel crucible structure is designed. This crucible not only optimizes the gas transport but also increases the radial gradient of the AlN crystal surface, making the enhanced growth rate in the central region more obvious. The thermal stresses between the deflector and the crystal are also reduced. High-quality AlN crystals with an FWHM of 79 arcsec were successfully grown with this structure, verifying the accuracy of finite element simulation of the growth of AlN crystals. Our work has important guiding significance for the growth of high-quality AlN crystals.

Gradient Functionalization of Poly(lactic acid)-Based Materials with Polylysine for Spatially Controlled Cell Adhesion.

The development of biomaterials with gradient surface modification capable of spatially controlled cell adhesion and migration is of great importance for tissue engineering and regeneration. In this study, we proposed a method for the covalent modification of PLA-based materials with a cationic polypeptide (polylysine, PLys) via a thiol-ene click reaction carried out under a light gradient. With this aim, PLA-based films were fabricated and modified with 2-aminoethyl methacrylate (AEMA) as a double bond source. The latter was introduced by reacting pre-formed and activated surface carboxyl groups with the amino group of AEMA. The success of the modification was confirmed by 1H NMR, Raman and X-ray photoelectron spectroscopy data. A further photoinduced thiol-ene click reaction in the presence of a photosensitive initiator as a radical source was further optimized using cysteine. For grafting of PLys via the thiol-ene click reaction, PLys with a terminal thiol group was synthesized by ring-opening polymerization using Cys(Acm) as an amine initiator. Deprotection of the polypeptide resulted in the formation of free thiol groups of Cys-PLys. Successful gradient grafting of Cys-PLys was evidenced by covalent staining with the fluorescent dye Cy3-NHS. In addition, PLys gradient-dependent adhesion and migration of HEK 293 cells on PLys-PLA-based surfaces was confirmed.

Facilitating water droplet removal from surfaces using air flow and wettability gradients

A new method is proposed to mitigate ice accretions on wind turbine blades via the creation of a microstructural gradient surface geometry that facilitates spontaneous water droplet motion along the surface. The wettability gradients are formed by laser etching 35 μm wide, 35 μm deep channels into aluminum to form a surface with a gradually increasing solid area fraction. Different design variations are then proposed and systematically evaluated on the merits of their performance. An analytical model is also derived based on a balance of hysteresis and drag forces to predict the critical air speed necessary for droplet movement as a function of the droplet size and surface contact angle. Experimentation has shown good agreement with the model for both the baseline and fixed-pitch channel surfaces and has also demonstrated that, in certain cases, up to 70 % lower critical air speeds are needed to initiate droplet motion on these microstructured surfaces.