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17 pages, 12837 KB  
Article
The Geometric Effect on the Two-Fluid Mixing in Planetary Centrifugal Mixer During Spin-Up: A Numerical Study
by Liang Qin, Huan Han, Xiaoxia Lu, Lei Li, Jianghai Liu, Xiaofang Yan and Yinze Zhang
Processes 2025, 13(3), 874; https://doi.org/10.3390/pr13030874 - 16 Mar 2025
Cited by 2 | Viewed by 1148
Abstract
In this paper, the geometric effect on flow structure and mixing performance of two miscible fluids (deionized water and glycerol) in a planetary centrifugal mixer (PCM) during the spin-up is numerically evaluated, using the OpenFOAM interMixingFoam solver. Six different aspect ratios, specifically 0.5, [...] Read more.
In this paper, the geometric effect on flow structure and mixing performance of two miscible fluids (deionized water and glycerol) in a planetary centrifugal mixer (PCM) during the spin-up is numerically evaluated, using the OpenFOAM interMixingFoam solver. Six different aspect ratios, specifically 0.5, 1, 1.25, 1.5, 2, and 2.5, are considered. The flow structure in each geometric configuration is illustrated by the liquid interface and vorticity isosurface represented by the Q criterion, while the mixing performance is evaluated in terms of a mixing index MI. As the aspect ratio increases from small to large, MI first increases and then decreases. The peak MI at the end of spin-up reaches 0.196 for the aspect ratio of 1.25, rather than the other five aspect ratios in our study. The mechanism analysis shows that under an aspect ratio of 1.25, the vortex structure is most violently dissipated, the interface collapse degree is the largest, and the low-velocity region volume is the smallest, which enhances the chaotic convection mixing. Full article
(This article belongs to the Special Issue Multi-Phase Flow and Heat and Mass Transfer Engineering)
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17 pages, 2442 KB  
Article
On the Aerodynamic Performance of a Blended-Wing-Body, Low-Mach Number Unmanned Aerial Vehicle
by Nikolaos Lampropoulos, Alexandros Vouros, Ioannis Templalexis and Theodoros Lekas
Fluids 2025, 10(3), 54; https://doi.org/10.3390/fluids10030054 - 20 Feb 2025
Cited by 2 | Viewed by 3878
Abstract
A study on aerodynamic design studies of a blended wing–body (BWB) unmanned aerial vehicle (UAV) operating at low Mach numbers is presented. First, a parametric investigation based on analytical equations is carried out to identify the range of the necessary wetted area for [...] Read more.
A study on aerodynamic design studies of a blended wing–body (BWB) unmanned aerial vehicle (UAV) operating at low Mach numbers is presented. First, a parametric investigation based on analytical equations is carried out to identify the range of the necessary wetted area for the UAV to maximize endurance at a Mach number close to 0.1. A base-of-reference configuration is designed, and its aerodynamic performance is evaluated by utilizing a panel method in Xflr5. An optimization algorithm is then incorporated to trim the UAV and produce the ‘clean’ configuration. Computational fluid dynamics (CFD) simulations are performed within the OpenFoam environment to produce first the updated drag polars, and then, to analyze the integration of the nacelle and the pair of electric ducted fans (EDFs) used for the propulsion system. In particular, when examining the integration of the nacelle with a spinning electric ducted fan (EDF) standing as the propulsion system of the vehicle, a rotating, sliding mesh computational approach is adopted. Results indicate that the clean configuration is characterized by strong longitudinal stability so that the UAV has the potential to fly trimmed at very low speeds. Mounting EDFs on the back of the fuselage is conducive to higher loading with minimal drag penalty. An increased lift-to-drag ratio is achieved. Reduced wake mixing due to the EDF’s jet flow is observed. The spanwise flow that is conducive to pitch brake and loss of stability is also weak, as the suction produced by the EDF diverts the flow inboard. Full article
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46 pages, 13796 KB  
Review
Measurement Techniques for Interfacial Rheology of Surfactant, Asphaltene, and Protein-Stabilized Interfaces in Emulsions and Foams
by Ronald Marquez and Jean-Louis Salager
Colloids Interfaces 2025, 9(1), 14; https://doi.org/10.3390/colloids9010014 - 14 Feb 2025
Cited by 5 | Viewed by 7458
Abstract
This work provides a comprehensive review of experimental methods used to measure rheological properties of interfacial layers stabilized by surfactants, asphaltenes, and proteins that are relevant to systems with large interfacial areas, such as emulsions and foams. Among the shear methods presented, the [...] Read more.
This work provides a comprehensive review of experimental methods used to measure rheological properties of interfacial layers stabilized by surfactants, asphaltenes, and proteins that are relevant to systems with large interfacial areas, such as emulsions and foams. Among the shear methods presented, the deep channel viscometer, bicone rheometer, and double-wall ring rheometers are the most utilized. On the other hand, the main dilational rheology techniques discussed are surface waves, capillary pressure, oscillating Langmuir trough, oscillating pendant drop, and oscillating spinning drop. Recent developments—including machine learning and artificial intelligence (AI) models, such as artificial neural networks (ANN) and convolutional neural networks (CNN)—to calculate interfacial tension from drop shape analysis in shorter times and with higher precision are critically analyzed. Additionally, configurations involving an Atomic Force Microscopy (AFM) cantilever contacting bubble, a microtensiometer platform, rectangular and radial Langmuir troughs, and high-frequency oscillation drop setups are presented. The significance of Gibbs–Marangoni effects and interfacial rheological parameters on the (de)stabilization of emulsions is also discussed. Finally, a critical review of the recent literature on the measurement of interfacial rheology is presented. Full article
(This article belongs to the Special Issue Rheology of Complex Fluids and Interfaces)
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19 pages, 5688 KB  
Article
Dynamic Instability Investigation of the Automotive Driveshaft’s Forced Torsional Vibration Using the Asymptotic Method
by Mihai Bugaru and Ovidiu Vasile
Appl. Sci. 2024, 14(17), 7681; https://doi.org/10.3390/app14177681 - 30 Aug 2024
Cited by 2 | Viewed by 1437
Abstract
This paper aims to investigate using FOAM to analyze the dynamic instability in the APPR for ADFTV based on a dynamic model (DMADFTV). The DMADFTV considers the following aspects: AD kinematic nonuniformity (ADKN), AD geometric nonuniformity (ADGN) of inertial characteristics for the spinning [...] Read more.
This paper aims to investigate using FOAM to analyze the dynamic instability in the APPR for ADFTV based on a dynamic model (DMADFTV). The DMADFTV considers the following aspects: AD kinematic nonuniformity (ADKN), AD geometric nonuniformity (ADGN) of inertial characteristics for the spinning movements (ICSM) of the AD elements (ADE), and the excitations induced by the gearbox–internal combustion engine modulations. The DMADFTV is considered the already-designed dynamic model developed by the first author of the ADFTV in a previous publication. This DMADFTV was used to compute the stationary frontiers of instability and the nonstationary spectral velocity amplitude (NSVA) versus nonstationary spectral amplitude (NSA) in the configuration space in transition through APPR, using the FOAM. The use of FOAM is much more versatile, from the analytical point of view, than the method of multiple scales and allows the computation of the NSA and the NSVA in the APPR. In contrast, these computations cannot be performed using the harmonic balance method. MATLAB Software R 2017 was developed based on DMADFTV and used the FOAM to compute the stationary frontiers of instability and the NSVA versus the NSA in transition through APPR for the ADFTV. The numerical results were compared with the experimental and numerical data published in the literature, finding agreements. The computation of the NSVA versus NSA in the configuration space using FOAM represents a method of detection of the chaotic manifestation of ADFTV. Full article
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27 pages, 7130 KB  
Article
Enhancing Tennis Practice: Sensor Fusion and Pose Estimation with a Smart Tennis Ball
by Yu Kit Foo, Xi Li and Rami Ghannam
Sensors 2024, 24(16), 5306; https://doi.org/10.3390/s24165306 - 16 Aug 2024
Cited by 2 | Viewed by 4405 | Correction
Abstract
This article demonstrates the integration of sensor fusion for pose estimation and data collection in tennis balls, aiming to create a smaller, less intrusive form factor for use in progressive learning during tennis practice. The study outlines the design and implementation of the [...] Read more.
This article demonstrates the integration of sensor fusion for pose estimation and data collection in tennis balls, aiming to create a smaller, less intrusive form factor for use in progressive learning during tennis practice. The study outlines the design and implementation of the Bosch BNO055 smart sensor, which features built-in managed sensor fusion capabilities. The article also discusses deriving additional data using various mathematical and simulation methods to present relevant orientation information from the sensor in Unity. Embedded within a Vermont practice foam tennis ball, the final prototype product communicates with Unity on a laptop via Bluetooth. The Unity interface effectively visualizes the ball’s rotation, the resultant acceleration direction, rotations per minute (RPM), and the orientation relative to gravity. The system successfully demonstrates accurate RPM measurement, provides real-time visualization of ball spin and offers a pathway for innovative applications in tennis training technology. Full article
(This article belongs to the Section Intelligent Sensors)
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34 pages, 17795 KB  
Article
Lorentzian Quantum Cosmology from Effective Spin Foams
by Bianca Dittrich and José Padua-Argüelles
Universe 2024, 10(7), 296; https://doi.org/10.3390/universe10070296 - 13 Jul 2024
Cited by 18 | Viewed by 2335
Abstract
Effective spin foams provide the most computationally efficient spin foam models yet and are therefore ideally suited for applications, e.g., to quantum cosmology. Here, we provide the first effective spin foam computations of a finite time evolution step in a Lorentzian quantum de [...] Read more.
Effective spin foams provide the most computationally efficient spin foam models yet and are therefore ideally suited for applications, e.g., to quantum cosmology. Here, we provide the first effective spin foam computations of a finite time evolution step in a Lorentzian quantum de Sitter universe. We will consider a setup that computes the no-boundary wave function and a setup describing the transition between two finite scale factors. A key property of spin foams is that they implement discrete spectra for the areas. We therefore study the effects that are induced by the discrete spectra. To perform these computations, we had to identify a technique to deal with highly oscillating and slowly converging or even diverging sums. Here, we illustrate that high-order Shanks transformation works very well and is a promising tool for the evaluation of Lorentzian (gravitational) path integrals and spin foam sums. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2024—'Cosmology')
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18 pages, 10677 KB  
Article
Monitoring the Geopolymerization Reaction of Geopolymer Foams Using 29Si and 27Al MAS NMR
by Ghizlane Moutaoukil, Isabel Sobrados, Saliha Alehyen and M’hamed Taibi
Minerals 2024, 14(5), 516; https://doi.org/10.3390/min14050516 - 16 May 2024
Cited by 6 | Viewed by 2773
Abstract
This study aims to investigate the geopolymerization reaction of geopolymer foams produced with three different foaming agents: aluminum powder, zinc powder, and hydrogen peroxide. The geopolymerization reaction of geopolymer foam was monitored using the 27Al and 29Si magic angle spinning (MAS) [...] Read more.
This study aims to investigate the geopolymerization reaction of geopolymer foams produced with three different foaming agents: aluminum powder, zinc powder, and hydrogen peroxide. The geopolymerization reaction of geopolymer foam was monitored using the 27Al and 29Si magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy technique. 27Al MAS-NMR was used to monitor the reaction at an early stage, while 29Si and 27Al MAS-NMR analyses were employed at specific time intervals of 3, 6, 10, 15, and 28 days to examine the changes that occurred in the formed gel over time. We discussed in detail how the type of foaming agent used and the duration of the reaction both influence the quantity of gel formed and the amount of remnant fly ash. Our findings indicate that the type of foaming agent used affects the formation and structure of the gel, with aluminum powder leading to the highest gel formation. Additionally, the duration of the reaction plays a significant role in determining the quantity of remnant fly ash, with longer reaction times resulting in decreased fly ash content. This study sheds light on the relevance of understanding the role of foaming agents in the geopolymerization reactions of geopolymer foams and the influence of reaction time on the formed gel properties. Full article
(This article belongs to the Special Issue NMR Spectroscopy in Mineralogy and Crystal Structures: 2nd Edition)
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27 pages, 662 KB  
Article
Causal Structure in Spin Foams
by Eugenio Bianchi and Pierre Martin-Dussaud
Universe 2024, 10(4), 181; https://doi.org/10.3390/universe10040181 - 14 Apr 2024
Cited by 2 | Viewed by 2755
Abstract
The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin foam models of quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality [...] Read more.
The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin foam models of quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin foam model and discuss the role of the causal structure in the reconstruction of a semiclassical space–time geometry. Full article
(This article belongs to the Special Issue Loop Quantum Gravity: A Themed Issue in Honor of Prof. Abhay Ashtekar)
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19 pages, 9175 KB  
Article
Nonwoven Fabrics from Agricultural and Industrial Waste for Acoustic and Thermal Insulation Applications
by Aravin Prince Periyasamy
Textiles 2023, 3(2), 182-200; https://doi.org/10.3390/textiles3020013 - 30 Apr 2023
Cited by 12 | Viewed by 5232
Abstract
Natural fibers are increasingly being used to make nonwoven fabrics, substituting synthetic materials for environmental and economic reasons. In this study, a series of needle-punched nonwoven fabrics were made by extracting fibers from coffee husks and blending them with a proportion of spinning [...] Read more.
Natural fibers are increasingly being used to make nonwoven fabrics, substituting synthetic materials for environmental and economic reasons. In this study, a series of needle-punched nonwoven fabrics were made by extracting fibers from coffee husks and blending them with a proportion of spinning waste consisting of cotton fibers and another five different natural fibers. This work investigates the coefficient of sound absorption, thermal conductivity, areal density, thickness, and air permeability. Overall, the sound absorption properties of the produced nonwoven fabric depend on the blend proportion and the number of layers. The results from the fabric containing nettle and banana fibers demonstrate a much-improved sound absorption coefficient. These results have been compared with those of commercially available nonwoven fabrics that are manufactured from polyester and polyurethane foam. The thermal conductivities of the fabrics made with nettle and coir were the highest and lowest, respectively. This is because of the fiber linear density, but all in all, fibers extracted from coffee husks show significantly promising potential for scaling up to replace existing synthetic fibers. Full article
(This article belongs to the Special Issue Fibrous Materials (Textiles) for Functional Applications II)
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18 pages, 8285 KB  
Article
Lightweight and High Impact Toughness PP/PET/POE Composite Foams Fabricated by In Situ Nanofibrillation and Microcellular Injection Molding
by Junwei Sun, Qian Li, Yufan Jiang, Jing Jiang, Lian Yang, Caiyi Jia, Feng Chen and Xiaofeng Wang
Polymers 2023, 15(1), 227; https://doi.org/10.3390/polym15010227 - 1 Jan 2023
Cited by 15 | Viewed by 4415
Abstract
Polypropylene (PP) has become the most promising and candidate material for fabricating lightweight products. Microcellular injection molding (MIM) is a cost-effective technology for manufacturing porous plastic products. However, it is still challenging to fabricate high-performance PP microcellular components. Herein, we reported an efficient [...] Read more.
Polypropylene (PP) has become the most promising and candidate material for fabricating lightweight products. Microcellular injection molding (MIM) is a cost-effective technology for manufacturing porous plastic products. However, it is still challenging to fabricate high-performance PP microcellular components. Herein, we reported an efficient strategy to produce lightweight and high impact toughness foamed PP/polyethylene terephthalate (PET)/polyolefin-based elastomer (POE) components by combining in situ fibrillation (INF) and MIM technologies. First, the INF composite was prepared by integrating twin-screw compounding with melt spinning. SEM analysis showed PET nanofibrils with a diameter of 258 nm were achieved and distributed uniformly in the PP due to the POE’s inducing elaboration effect. Rheological and DSC analysis demonstrated PET nanofibrils pronouncedly improved PP’s viscoelasticity and crystal nucleation rate, respectively. Compared with PP foam, INF composite foam showed more stretched cells in the skin layer and refined spherical cells in the core layer. Due to the synergistic toughening effect of PET nanofibrils and POE elastic particles, the impact strength of INF composite foams was 295.3% higher than that of PP foam and 191.2% higher than that of melt-blended PP/PET foam. The results gathered in this study reveal potential applications for PP based INF composite foams in the manufacturing of lightweight automotive products with enhanced impact properties. Full article
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16 pages, 8336 KB  
Article
Spectroscopic Characterization of the Binding and Release of Hydrophilic, Hydrophobic and Amphiphilic Molecules from Ovalbumin Supramolecular Hydrogels
by Ana Vesković, Danica Bajuk-Bogdanović, Vladimir B. Arion and Ana Popović Bijelić
Gels 2023, 9(1), 14; https://doi.org/10.3390/gels9010014 - 26 Dec 2022
Cited by 7 | Viewed by 3906
Abstract
Protein-based hydrogels have attracted growing attention for pharmaceutical and biomedical applications. Ovalbumin (OVA), the hen egg white albumin, possessing good foaming and gelling properties and being widely used in the food industry, has recently been indicated as a potential pharmaceutical vehicle. In this [...] Read more.
Protein-based hydrogels have attracted growing attention for pharmaceutical and biomedical applications. Ovalbumin (OVA), the hen egg white albumin, possessing good foaming and gelling properties and being widely used in the food industry, has recently been indicated as a potential pharmaceutical vehicle. In this study, the binding and release properties of pure OVA hydrogels were investigated by electron paramagnetic resonance (EPR) spin labeling. The comparative analysis between OVA and serum albumin (SA) hydrogels revealed the same release kinetics of hydrophilic 3-carbamoyl-proxyl and 3-carboxy-proxyl, suggesting the diffusion-dominated release of small probes from both hydrogel types. The results obtained with the amphiphilic 16-doxylstearate (16-DS) indicate that OVA, unlike SAs, does not possess a specific fatty acid binding site. However, the OVA hydrogels were able to accommodate a two-fold excess of 16-DS, resulting from protein thermally induced conformational changes, as confirmed by Raman spectroscopy. Similarly, the hydrophobic modified paullone ligand HL, which was initially free in the OVA solution, was bound in the hydrogel. The hydrogels were found to retain a significant amount of 16-DS and HL after 7-day dialysis in physiological saline. The observed facilitated binding of amphiphilic/hydrophobic molecules in OVA hydrogels compared to the solution, and their sustained release, demonstrate the applicability of OVA hydrogels in pharmaceutics. Full article
(This article belongs to the Special Issue Women’s Special Issue Series: Gels)
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26 pages, 4060 KB  
Review
Multiple Functions of Malpighian Tubules in Insects: A Review
by Priscilla Farina, Stefano Bedini and Barbara Conti
Insects 2022, 13(11), 1001; https://doi.org/10.3390/insects13111001 - 31 Oct 2022
Cited by 52 | Viewed by 12197
Abstract
The Malpighian Tubules (MTs) are the main excretory organs in most insects. They play a key role in the production of primary urine and osmoregulation, selectively reabsorbing water, ions, and solutes. Besides these functions conserved in most insects, MTs can serve some specialized [...] Read more.
The Malpighian Tubules (MTs) are the main excretory organs in most insects. They play a key role in the production of primary urine and osmoregulation, selectively reabsorbing water, ions, and solutes. Besides these functions conserved in most insects, MTs can serve some specialized tasks at different stages of some species’ development. The specialized functions include the synthesis of mucopolysaccharides and proteins for the building of foam nests, mucofibrils for the construction of dwelling tubes, adhesive secretions to help the locomotion, and brochosomes for protection as well as the usage of inorganic salts to harden the puparia, eggs chorion, and pupal cells’ closing lids. MTs are also the organs responsible for the astonishing bioluminescence of some Diptera glowworms and can go through some drastic histological changes to produce a silk-like fiber utilized to spin cocoons. The specialized functions are associated with modifications of cells within the entire tubules, in specific segments, or, more rarely, modified secretory cells scattered along the MTs. In this review, we attempted to summarize the observations and experiments made over more than a century concerning the non-excretive functions of insects’ MTs, underlying the need for new investigations supported by the current, advanced technologies available to validate outdated theories and clarify some dubious aspects. Full article
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27 pages, 3819 KB  
Article
Development of Multifunctional Nano-Graphene-Grafted Polyester to Enhance Thermal Insulation and Performance of Modified Polyesters
by Shih-Hsiung Chen, Naveed Ahmad and Chung-Feng Jeffrey Kuo
Polymers 2022, 14(18), 3821; https://doi.org/10.3390/polym14183821 - 13 Sep 2022
Cited by 9 | Viewed by 2878
Abstract
Nano-graphene materials have improved many thermal properties based on polymer systems. The additive polymers’ thermal insulation cannot be significantly increased for use as a reinforcement in multifunctional thermally insulating polymer foam. Herein, we present the development of far-infrared emissivity and antistatic properties using [...] Read more.
Nano-graphene materials have improved many thermal properties based on polymer systems. The additive polymers’ thermal insulation cannot be significantly increased for use as a reinforcement in multifunctional thermally insulating polymer foam. Herein, we present the development of far-infrared emissivity and antistatic properties using multifunctional nano-graphene polyester fibers. Nano-graphene far-infrared thermal insulation polyester was synthesized with 2% nano-graphene and dispersant polypropylene wax-maleic anhydride (PP wax-MA) using the Taguchi method combined with grey relational analysis (GRA) to improve the thermal properties and the performance of the polymer composite. The thermogravimetric analysis (TGA) shows that the pyrolysis temperature of spinning-grade polyester was increased when the nano-graphene powder was added to the polyester. The differential scanning calorimeter (DSC) analysis confirmed the modification of polyester by nano-graphene, showing the effect of the nucleating agent, which ultimately improved the performance of the polyester. The physical properties of the optimized polyester fibers were improved with a yarn count of 76.5 d, tensile strength of 3.3 g/d, and an elongation at break increased from 23.5% to 26.7% compared with unmodified polymer yarn. These far-infrared emission rates increased from 78% to 83%, whereas the far-infrared temperature increased from 4.0 °C to 22 °C, and the surface resistance increased to 108 Ω. The performance of the optimized modified polyester yarn is far better than single-polypropylene-grafted maleic anhydride yarn. The performance of optimized modified polyester yarn, further confirmed using grey correlation analysis (GRA), can improve the yarns’ mechanical properties and far-infrared functions. Our findings provide an alternative route for developing nano-graphene polyester fabrics suitable for the fabric industry. Full article
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38 pages, 14001 KB  
Review
Recent Advances in the Interfacial Shear and Dilational Rheology of Polymer Systems: From Fundamentals to Applications
by Younes El Omari, Mohamed Yousfi, Jannick Duchet-Rumeau and Abderrahim Maazouz
Polymers 2022, 14(14), 2844; https://doi.org/10.3390/polym14142844 - 13 Jul 2022
Cited by 19 | Viewed by 7117
Abstract
The study of the viscoelastic properties of polymer systems containing huge internal two-dimensional interfacial areas, such as blends, foams and multilayer films, is of growing interest and plays a significant role in a variety of industrial fields. Hence, interfacial rheology can represent a [...] Read more.
The study of the viscoelastic properties of polymer systems containing huge internal two-dimensional interfacial areas, such as blends, foams and multilayer films, is of growing interest and plays a significant role in a variety of industrial fields. Hence, interfacial rheology can represent a powerful tool to directly investigate these complex polymer–polymer interfaces. First, the current review summarizes the theoretical basics and fundamentals of interfacial shear rheology. Particular attention has been devoted to the double-wall ring (DWR), bicone, Du Noüy ring and oscillating needle (ISR) systems. The measurement of surface and interfacial rheological properties requires a consideration of the relative contributions of the surface stress arising from the bulk sub-phases. Here, the experimental procedures and methodologies used to correct the numerical data are described considering the viscoelastic nature of the interface. Second, the interfacial dilational rheology is discussed, starting with the theory and underlying principles. In particular, the Langmuir trough method, the oscillating spinning drop technique and the oscillating pendant drop technique are investigated. The major pioneering studies and latest innovations dedicated to interfacial rheology in both shear and dilatation–compression are highlighted. Finally, the major challenges and limits related to the development of high-temperature interfacial rheology at the molten state are presented. The latter shows great potential for assessing the interfaces of polymer systems encountered in many high-value applications. Full article
(This article belongs to the Special Issue Rheology and Processing of Polymer-Based Materials)
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31 pages, 1521 KB  
Tutorial
How-to Compute EPRL Spin Foam Amplitudes
by Pietro Donà and Pietropaolo Frisoni
Universe 2022, 8(4), 208; https://doi.org/10.3390/universe8040208 - 26 Mar 2022
Cited by 23 | Viewed by 4326
Abstract
Spin foam theory is a concrete framework for quantum gravity where numerical calculations of transition amplitudes are possible. Recently, the field became very active, but the entry barrier is steep, mainly because of its unusual language and notions scattered around the literature. This [...] Read more.
Spin foam theory is a concrete framework for quantum gravity where numerical calculations of transition amplitudes are possible. Recently, the field became very active, but the entry barrier is steep, mainly because of its unusual language and notions scattered around the literature. This paper is a pedagogical guide to spin foam transition amplitude calculations. We show how to write an EPRL-FK transition amplitude, from the definition of the 2-complex to its numerical implementation using sl2cfoam-next. We guide the reader using an explicit example balancing mathematical rigor with a practical approach. We discuss the advantages and disadvantages of our strategy and provide a novel look at a recently proposed approximation scheme. Full article
(This article belongs to the Special Issue Probing the Quantum Space-Time)
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