Re-entrant Angles Research Articles

Dual Superlyophobic Aliphatic Polyketone Membranes for Highly Efficient Emulsified Oil-Water Separation: Performance and Mechanism.

Efficient treatment of difficult emulsified oil-water wastes is a global challenge. Membranes exhibiting unusual dual superlyophobicity (combined underwater superoleophobicity and underoil superhydrophobicity) are intriguing to realize high-efficiency separation of both oil-in-water and water-in-oil emulsions. For the first time, a robust polymeric membrane demonstrating dual superlyophobicity to common apolar oils was facilely fabricated via a simple one-step phase separation process using an aliphatic polyketone (PK) polymer, thanks to a conjunction of intermediate hydrophilicity and re-entrant fibril-like texture upon the prepared PK membrane. Further chemical modification to improve surface hydrophilicity slightly can enable dual superlyophobicity to both apolar and polar oils. It is found that a nonwetting composite state of oil against water or water against oil was obtainable on the membrane surfaces only when the probe liquids possess an equilibrium contact angle (θow or θwo) larger than the critical re-entrant angle of the textured surfaces (73°), which can explain the existences of dual superlyophobicity and also the nonwetting to fully wetting transitions. A simple design chart was developed to map out the operational windows of material hydrophilicity and re-entrant geometry, that is, a possible zone, to help in the rational design of similar interfacial systems from various materials. Switchable filtrations of oil-in-water and water-in-oil nanoemulsions were achieved readily with both high flux and high rejection. The simplicity and scalability of the membrane preparation process and the well-elucidated underlying mechanisms illuminate the great application potential of the PK-based superwetting membranes.

An analytical model for star-shaped re-entrant lattice structures with the orthotropic symmetry and negative Poisson's ratios

A new analytical model is developed for three types of 2-D periodic star-shaped re-entrant lattice structures that possess the orthotropic symmetry and exhibit negative Poisson's ratios. Contributions from both the re-entrant and connection struts are considered using an energy method based on Castigliano's second theorem. Each re-entrant strut is treated as a Timoshenko beam, and stretching, transverse shearing and bending deformations are all incorporated in the formulation. Unlike existing studies, the overlapping of struts at joints is included in determining the relative density, which is analytically expressed for each lattice type. Closed-form formulas are derived for the effective Young's moduli and Poisson's ratios of each type of lattice structure, which contain three non-dimensional length ratios, two re-entrant angles, one shear correction factor, and Young's modulus and Poisson's ratio of the strut material. The new analytical model is validated against finite element simulations conducted in the current study and two existing analytical models for simpler square lattice structures without re-entrant struts. To illustrate the newly developed analytical model, a parametric study is conducted to quantitatively show the effects of the five geometrical parameters on the effective properties of each type of lattice structure. It is found that for the effective Poisson's ratios the key controlling parameters are the two re-entrant angles, while for the effective Young's moduli all of the geometrical parameters can have significant effects except for the external connection length ratio. It is demonstrated that through a proper selection of the geometrical parameters, vertex connections and strut material, it is possible to tailor the effective Poisson's ratios and Young's moduli of each type of lattice structure over wide ranges to satisfy different needs in various applications.

The manufacture and characterization of composite three-dimensional re-entrant auxetic cellular structures made from carbon fiber reinforced polymer

In recent years, three-dimensional auxetic structures have attracted great interest. Generally, three-dimensional auxetic structures are of complicate geometries which make them difficult to fabricate, benefiting from the development of additive manufacturing technologies, many three-dimensional auxetic structures can be made from metals or polymers. However, to the authors' knowledge, the additive manufacturing technology of fiber reinforced polymer is not fully developed, and none three-dimensional auxetic structure made from fiber reinforced polymer has been reported before. To integrate the high specific stiffness, high specific strength, and light weight merits of high-performance fiber reinforced polymer composites into three-dimensional auxetic structures with unique properties, research on composite three-dimensional auxetic structures made from fiber reinforced polymer should be conducted. This paper presents the composite three-dimensional re-entrant auxetic structures made from carbon fiber reinforced polymer laminates using an interlocking assembly method. The auxetic nature of the composite structure has been verified by experimental testing and finite element simulations. Based on the finite element models, the dependences of the Poisson's ratio and effective compression modulus of the composite auxetic three-dimensional re-entrant structure on the re-entrant angle have been studied and compared to metal three-dimensional re-entrant structure. A comparative study of the Poisson's ratio and specific stiffness of carbon fiber reinforced polymer composite auxetic structure with the three-dimensional printed polymer and metal auxetic structures in literature has also been conducted.

Compressive property of Al-based auxetic lattice structures fabricated by 3-D printing combined with investment casting

Auxetic lattice structures are a new kind of structures that show unique mechanical performance, particularly negative Poisson's ratio behavior. In the present study, an Al-based auxetic lattice structure has been fabricated by 3-D printing and investment casting, and the compressive mechanical behavior was studied. It is shown that increasing the length of re-entrant struts or re-entrant angle leads to decreased compression strength but increased Poisson's ratio. If the relative density of the structures keeps constant, the elastic modulus and compression strength will be enhanced as the Poisson's ratio increases owing to the auxetic effect.

3D Printed Auxetic Mechanical Metamaterial with Chiral Cells and Re-entrant Cores

By combining the two basic deformation mechanisms for auxetic open-cell metamaterials, re-entrant angle and chirality, new hybrid chiral mechanical metamaterials are designed and fabricated via a multi-material 3D printer. Results from mechanical experiments on the 3D printed prototypes and systematic Finite Element (FE) simulations show that the new designs can achieve subsequential cell-opening mechanism under a very large range of overall strains (2.91%–52.6%). Also, the effective stiffness, the Poisson’s ratio and the cell-opening rate of the new designs can be tuned in a wide range by tailoring the two independent geometric parameters: the cell size ratio {{boldsymbol{c}}}_{{bf{0}}}{boldsymbol{/}}{{boldsymbol{b}}}_{{bf{0}}}, and re-entrant angle θ. As an example application, a sequential particle release mechanism of the new designs was also systematically explored. This mechanism has potential application in drug delivery. The present new design concepts can be used to develop new multi-functional smart composites, sensors and/or actuators which are responsive to external load and/or environmental conditions.

Three dimensional modeling of warp and woof periodic auxetic cellular structure

This paper presents a novel periodic auxetic cellular structure (PACS) whose cells were spanned as warp and woof. Warp and woof periodic auxetic cellular structure (WWPACS) is compressed in two transverse directions when quasi-static compressive loading is applied. In this paper, among different available manufacturing processes of auxetic structures, interlocking assembly method was used to fabricate the periodic cellular structure. To this end, the effects of NPR and mechanical behavior of auxetic structure were investigated and results compared with 3D finite element simulation. Good agreements were found between the experimental and FE results. The total energy and specific energy absorbed for experimental works and FE simulation were calculated. Furthermore, the effect of re-entrant angle on NPR was also obtained. The results show that the NPR increases and reaches to maximum value and then, due to overlaying the cellular, decreases. FE simulations show that the effect of structural geometry on NPR is more important than that of the materials used in the structure.

Micromechanical modeling of 3D printable interpenetrating phase composites with tailorable effective elastic properties including negative Poisson's ratio

3D printable two-phase interpenetrating phase composites (IPCs) are designed by embedding a 3D periodic re-entrant lattice structure (as the reinforcing phase) in a matrix phase. These IPCs display the cubic or tetragonal symmetry. A micromechanical model is developed to evaluate effective elastic properties of the IPCs. Effective Young's moduli, shear moduli and Poisson's ratios (PRs) of each IPC are determined from the effective stiffness and compliance matrices of the composite, which are obtained through a homogenization analysis using a unit cell-based finite element (FE) model incorporating periodic boundary conditions. The FE simulation results are also compared with those based on various analytical bounding techniques in micromechanics, including the Voigt–Reuss, Hashin–Shtrikman, and Tuchinskii bounds. The effective properties of the IPC can be tailored by adjusting five geometrical parameters, including two strut lengths, two re-entrant angles and one strut diameter, and elastic properties of the two constituent materials. The numerical results reveal that IPCs with a negative PR can be generated by using a compliant matrix material and large re-entrant angles. In addition, it is found that the two re-entrant angles can greatly affect other effective elastic properties of the IPC: the effective shear modulus can be enhanced, while the effective Young's modulus can be enhanced or compromised with the increase of the re-entrant angles. Furthermore, it is seen that by adjusting one of the two re-entrant angles or one of the two strut lengths, the material symmetry exhibited by the IPC can be changed from cubic to tetragonal.

Formation and evolution of air–water interfaces between hydrophilic structures in a microchannel

Air–water interfaces play an important role in the superhydrophobicity for the surface, which is always made of hydrophobic materials. In the present study, microstructures made of hydrophilic material with different topologies were fabricated on the sidewalls of a microchannel, and the detailed formation processes of air–water interfaces were captured by a microscope and a high-speed camera. The current study found that doubly reentrant structures, even made of wettable material, can capture and sustain the air–water interface. Considering Laplace equation and the geometry restrictions, critical pressure difference in the channel was estimated, and the influences of the structure parameters (the structure spacing and the reentrant angle) were investigated.

Computing ultra-precise eigenvalues of the Laplacian within polygons

The classic eigenvalue problem of the Laplace operator inside a variety of polygons is numerically solved by using a method nearly identical to that used by Fox, Henrici, and Moler in their 1967 paper. It is demonstrated that such eigenvalue calculations can be extended to unprecedented precision, often to well over a hundred digits, or even thousands of digits. To work well, geometric symmetry must be exploited. The de-symmetrized fundamental domains (usually triangular) considered here have at most one non-analytic vertex. Dirichlet, Neumann, and periodic-type edge conditions are independently imposed on each symmetry-reduced polygon edge. The method of particular solutions is used whereby an eigenfunction is expanded in an N-term Fourier-Bessel series about the non-analytic vertex and made to match at a set of N points on the boundary. Under the right conditions, the so-called point-matching determinant has roots that approximate eigenvalues. A key observation is that by increasing the number of terms in the expansion, the approximate eigenvalue may be made to alternate above and below, while approaching what is presumed to be the exact eigenvalue. This alternation effectively provides a new method to bound eigenvalues, by inspection. Specific examples include Dirichlet and Neumann eigenvalues within polygons with re-entrant angles (L-shape, cut-square, 5-point star) and the regular polygons. Thousand-digit results are reported for the lowest Dirichlet eigenvalues of the L-shape, and regular pentagon and hexagon.

Structural optimization of re-entrant negative Poisson's ratio structure fabricated by selective laser melting

In this paper, a quantitative optimization of a modified re-entrant negative Poisson's ratio (NPR) structure whose overhanging struts were replaced with inclined ones to avoid the support structures which were generally required in the selective laser melting (SLM) process was carried out using finite element analysis (FEA) method. Poisson's ratios of models with inclined links of different strut inclination angles were calculated. The optimal simulated inclination angle of struts was 9° and the corresponding optimum re-entrant angle was 79° while the thickness of the strut was 0.9mm. The influence of fillet radii on Poisson's ratio and stress concentration was also discussed and the Poisson's ratio decreased and the stress concentration phenomenon remitted to some extent with increased fillet radii. In order to verify the improvement of the manufacturability of structures with inclined links, AlSi10Mg specimens were fabricated by SLM process using different scanning speeds and compression tests were also developed. Experimentally obtained results and simulation predicted ones were in good agreement. Therefore, the custom-tailor service could be accomplished in this way and the modified NPR structure with better surface quality could be obtained.

A statistical model for the wettability of surfaces with heterogeneous pore geometries

We describe a new approach to modeling the wetting behavior of micro- and nano-textured surfaces with varying degrees of geometrical heterogeneity. Surfaces are modeled as pore arrays with a Gaussian distribution of sidewall reentrant angles and a characteristic wall roughness. Unlike conventional wettability models, our model considers the fraction of a surface’s pores that are filled at any time, allowing us to capture more subtle dependences of a liquid’s apparent contact angle on its surface tension. The model has four fitting parameters and is calibrated for a particular surface by measuring the apparent contact angles between the surface and at least four probe liquids. We have calibrated the model for three heterogeneous nanoporous surfaces that we have fabricated: a hydrothermally grown zinc oxide, a film of polyvinylidene fluoride (PVDF) microspheres formed by spinodal decomposition, and a polytetrafluoroethylene (PTFE) film with pores defined by sacrificial polystyrene microspheres. These three surfaces show markedly different dependences of a liquid’s apparent contact angle on the liquid’s surface tension, and the results can be explained by considering geometric variability. The highly variable PTFE pores yield the most gradual variation of apparent contact angle with probe liquid surface tension. The PVDF microspheres are more regular in diameter and, although connected in an irregular manner, result in a much sharper transition from non-wetting to wetting behavior as surface tension reduces. We also demonstrate, by terminating porous zinc oxide with three alternative hydrophobic molecules, that a single geometrical model can capture a structure’s wetting behavior for multiple surface chemistries and liquids. Finally, we contrast our results with those from a highly regular, lithographically-produced structure which shows an extremely sharp dependence of wettability on surface tension. This new model could be valuable in designing and evaluating processes for manufacturing liquid-repellent surfaces on an industrial scale.

Three-Dimensional Soft Material Micropatterning via Direct Laser Lithography of Flexible Molds.

Three-dimensionally micropatterned surfaces are attracting increasing interest in soft robotics owing to the potential of mimicking natural morphologies at the micro/nanoscale. We employ direct laser lithography to fabricate molds with complex three-dimensional (3D) micrometric features, in a positive photoresist on flexible substrates, to pattern curved macroscopic soft surfaces with shapes not achievable with standard methods (e.g., reentrant angles). We present several 3D intricate microstructures in poly(dimethylsiloxane) (PDMS) and show a soft cylinder patterned with 3D microstructures with one molding process. Finally, we deform PDMS-based 3D architectures and show soft microgripping capability, indicating the potentiality of this approach for future application in soft robotics.

Experimental and numerical analysis of a novel three-dimensional auxetic metamaterial

An innovative three-dimensional (3D) auxetic structure based on 2D re-entrant honeycombs was developed in this article. A sample of the proposed structure made of acrylonitrile–butadiene–styrene (ABS) was fabricated through 3D printing technology, and a compression test was performed on it. Meanwhile, the unit cell required for the finite-element (FE) analysis was determined to simulate the auxetic behavior of the proposed structure. Both experimental and numerical results showed that the 3D structure can achieve a negative Poisson's ratio (NPR) in two principal orthogonal coordinate directions when it was compressed along the other principal axis. A systematic numerical simulation was performed through the experimentally validated finite element models to analyze the effects of structural parameters (i.e., top-view re-entrant angle and lateral-view re-entrant angle) and deformation on the auxetic behavior. Numerical results revealed that this structure can achieve a negative Poisson's ratio (NPR) under large deformation and the structural parameters and compression strain have significant effects on the auxetic behavior. Our structure, with large flexibility in design, is based on very simple initial geometric shapes. This analysis can provide useful information for the design, fabrication of this kind of 3D auxetic structure, which is promising in some technical applications.

Interlocking assembled 3D auxetic cellular structures

As promising metamaterials, 3D periodic auxetic cellular structures (PACSs) have attracted great interest. However, they usually consist of intricate geometries which make their fabrication a significant challenge. The present paper is focused on introducing the interlocking assembly concept into the fabrication of 3D PACSs. There are distinct advantages of the interlocking assembly method compared with the additive manufacturing methods mainly used before. Based on the interlocking assembly method, the dependences of mechanical properties mainly including the Poisson's ratio and the Young's modulus of the structure on the re-entrant angle were investigated through a combination of uniaxial compression experiments and numerical simulations, excellent qualitative and quantitative agreement was found. Using the experimentally verified numerical model, the effects of the strut thickness and the ratio of the vertical strut length to oblique strut length on the mechanical properties of the structure were investigated. Results show that the compression modulus of the structure will increase with the structure becomes more re-entrant, but there exists an extreme value for Poisson's ratio with the re-entrant angle around 45° which differs from former studies. With the thickening of the struts the compression modulus of the structure monotonously increases and the Poisson's ratio of the structure will gradually changes from negative to positive then gradually approaches to the Poisson's ratio of the parent material. The vertical strut length to oblique strut length ratio plays fewer roles on the mechanical properties compared with the re-entrant angle and the strut thickness.

Superhydrophobic Textiles: Review of Theoretical Definitions, Fabrication and Functional Evaluation

Engineering of superhydrophobic textile surfaces has gained significant scientific and industrial interest for its potential applications in outdoor wear and protective textiles, resulting in many publications especially on theoretical models and fabrication methods. In this review, progress in theoretical definitions to explain the wetting behavior and realization techniques for superhydrophobic textile surfaces is discussed. Firstly, theoretical models from Young, Wenzel, and Cassie-Baxter to the more recent re-entrant angle model are overviewed to understand the design strategy for superhydrophobic surfaces. Secondly, major surface manipulation techniques to produce superhydrophobic textiles were reviewed for: modification of surface energy, addition of surface roughness by depositing or growing nanoparticles either in spherical form or in high aspect ratio, etching by plasma or caustic chemicals. Particular attention is paid to evaluation methods to measure the level of hydrophobicity for superhydrophobic textile surfaces, as a limitation of static water contact angle (WCA) on differentiating superhydrophobic surfaces has been reported elsewhere. The challenges in application of superhydrophobic textiles to clothing materials in terms of comfort properties and durability are discussed with the suggestion of further research opportunities to expand the application.

Experimental and numerical investigation of a shaped microchannel evaporator for a micro Rankine cycle application

In the present study, numerical analysis and experimental observations have been conducted to investigate the heat and mass transfer behavior in a shaped microchannel evaporator and to determine its ability to provide high quality steam for micro Rankine cycle application. The micro evaporator is designed to prevent the presence of liquid droplets at the exit by incorporating re-entrant wall angles for capillary flow stabilization and a stream wise temperature gradient to allow a range of wall temperatures along its length. Meniscus evaporation, periodic bubbly evaporation and boiling regimes were observed based on experiments at different mass flow rates and working temperatures. Experimental results show that the meniscus evaporation and periodic bubbly evaporation regimes provide fully evaporated steam without droplets at the exit. Thus they are successful operating regimes for the micro evaporator in micro Rankine cycle application. One dimensional conjugate heat transfer was considered along the microchannel evaporator with thin film theory used to model the evaporation rate. The numerical results are in good agreement with experimental observation for the meniscus evaporation regime. This kind of micro evaporator achieves the objective of providing a constant flow of fully evaporated steam without the presence of mixed flow at the exit, but only up to a limit flow rate.

Analyses on the In-Plane Impact Resistance of Auxetic Double Arrowhead Honeycombs

Double arrowhead honeycombs (DAHs) are a type of auxetic materials, i.e., showing negative Poisson's ratio (NPR), and are promising for energy absorption applications. Their in-plane impact responses are theoretically and numerically explored. Theoretical models for the collapse stress under quasi-static, low-velocity, and high-velocity impacts are developed, based upon the corresponding microstructural deformation modes. Obtained results show that the collapse stress under quasi-static and low velocity impacts depends upon the two re-entrant angles responsible for NPR, while it is insensitive to them under high-velocity impact. The developed theoretical models are employed to analyze the energy absorption capacity of DAHs, showing the absorbed energy under high-velocity impact approximately proportional to the second power of velocity. Extension of the high-velocity impact model to functionally graded (FG) DAHs is also discussed. Good agreement between the theoretical and finite element (FE) predictions on the impact responses of DAHs is obtained.

Pinning and wetting stability of liquids on superoleophobic textured surfaces

Super water/oil repellency has been a very active research field and could be achieved via combination of surface texturing and chemical treatment. When a droplet is deposited on a superhydrophobic/superoleophobic surface, its contact line can be pinned somewhere on the structured surface instead of fully wetting the substrate, forming a solid–liquid–air composite interface. The focus of this article is to understand the effect of pinning and wetting stability through energy analysis and force balance. Textured surfaces with straight sidewall pillar, wavy sidewall pillar and hoodoo structures are discussed in detail. For the straight sidewall structure, it was found that the top pillar edge is a stable pinning site for water. Meanwhile, hexadecane fully wets the structure without any pinning. On the wavy sidewall structure, the protruding and concave corners are pinning sites for both water and hexadecane. However, the dominant breakthrough pressure comes from the energy barrier against contact line advancing along the re-entrant slope of the wave. On the hoodoo structure, there are two pinning sites (top and bottom corner of the hoodoo cap) for water, but only one pinning site (bottom corner) for hexadecane. The effects of solid area fraction and re-entrant angles on pinning stability are studied with the wavy sidewall structure. This study suggests that Gibbs energy analysis can be a viable approach in designing robust superoleophobic surfaces by enhancing the pinning stability and breakthrough pressure, which is strongly correlated to design parameters, for example solid area fraction, geometrical re-entrant angle and dimensions. This article contains supporting information that is available online.

LEM for twisted re-entrant angle sections

In this paper an innovative numerical method named as line element-less method, LEM, for finding solution of torsion problem has been extended to all shaped sections, including sections possessing re-entrant angles at their boundary. The response solution in terms of shear stress field or Prandtl function or warping function in all domain and for any kind of domain with arbitrary contour, may be performed quickly, calculating line integrals only. The method takes full advantage of the theory of analytic complex function and is robust in the sense that returns exact solution if this exists. Numerical implementation of LEM has been developed using Mathematica software without resorting to any discretization neither in the domain nor in the boundary. The latter means that you can use the same program for all sections just by changing the first few lines of program where you declare the geometry of the section. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.

Facies and geochemistry of non-marine gypsum, EMISAL, Egypt

Diverse gypsum facies in terms of crystal size and morphology are deposited in a shallow, non-marine, sulfate-enriched, semi-closed, perennial evaporite basin. These gypsum facies were deposited in intimate association with cyanobacterial mats. Facies analyses and geochemistry revealed two distinct primary facies, based on gypsum fabric; massive selenite, and laminated gypsum varieties. The massive selenite facies is composed of clusters of single and twinned crystals along (100), with upward pointing re-entrant angle. The laminated gypsum varies from rhythmically laminated grass-like selenite to gypsum microbialite (stromatolite). The change from massive selenite to laminated gypsum facies implies fluctuation in lateral and vertical salinity profiles, seasonal brine concentrations and wind action. Post-depositional changes in the form of dissolution, slight to moderate crystal deformation and recrystallization to anhydrite are evaluated. We develop a qualitative model for the depositional basin and facies distribution in order to simulate ancient analogues.