Macroscopic Length Scales Research Articles

Flexible polymer networks: rubber elasticity and segmental orientation

Abstract Thermoreversible networks are very attractive materials because of a large variety of suitable thermoreversible chemical bonds which can be used for crosslinking. In future, to certain extent, they may replace so far used irreversibly crosslinked networks and contribute to more sustainable material concepts also in the field of crosslinked elastomers. This paper gives some theoretical basis for understanding the elastic deformation properties of crosslinked polymers and presents some experimental tools for studying deformation behavior not only on a macroscopic length scale but also on a segmental scale. Basic knowledge of these two topics is useful for chemists and material scientists when designing new sustainable elastomeric polymer networks.

DNA Cryogels with Anisotropic Mechanical and Responsive Properties for Specific Cell Capture and Release.

Due to their programmable stimuli-responsiveness, excellent biocompatibility, and water-rich and soft structures similar to biological tissues, smart DNA hydrogels hold great promise for biosensing and biomedical applications. However, most DNA hydrogels developed to date are composed of randomly oriented and isotropic polymer networks, and the resulting slow response to biotargets and lack of anisotropic properties similar to those of biological tissues have limited their extensive applications. Herein, anisotropic DNA hydrogels consisting of unidirectional void channels internally oriented up to macroscopic length scales were constructed by a directional cryopolymerization method, as exemplified by a DNA-incorporated covalently cross-linked DNA cryogel and a DNA duplex structure noncovalently cross-linked DNA cryogel. Results showed that the formation of unidirectional channels significantly improved the responsiveness of the gel matrix to biomacromolecular substances and further endowed the DNA cryogels with anisotropic properties, including anisotropic mechanical properties, anisotropic swelling/shrinking behaviors, and anisotropic responsiveness to specific biotargets. Moreover, the abundant oriented and long macroporous channels in the gel matrix facilitated the migration of cells, and through the introduction of aptamer structures and thermosensitive polymers, an anisotropic DNA cryogel-based platform was further constructed to achieve the highly efficient capture and release of specific cells. These anisotropic DNA hydrogels may provide new opportunities for the development of anisotropic separation and biosensing systems.

Red-light-controlled supramolecular assemblies of indigo amphiphiles at multiple length scales

Amphiphilic molecules functionalized with photoresponsive motifs have attractive prospects for applications in smart functional bio-material ranging from cell-material interfaces to drug delivery systems owing to the precisely controllable functionality of self-assembled hierarchical supramolecular structures in aqueous media by a non-invasive light stimulation with high temporal- and spatial-resolution. However, most of reported photoresponsive amphiphiles are triggered by bio-damaging UV-light, which greatly limits the potential in bio-related applications. Herein, we present newly designed red-light controlled N,N’-diaryl-substituted indigo amphiphiles (IA), exhibiting excellent photoswitchablity and photostability with dual red-/green-light in organic media. Meanwhile, aqueous solutions of IA assembled into supramolecular structures in both microscopic and macroscopic length-scale, though the photoresponsiveness of IA is slightly compromised in aqueous media. At macroscopic length-scale, morphological changes of IA macroscopic scaffold prepared by a shear-flow method can be fine adjusted upon red-light irradiation. Moreover, the preferential attachment of live h-MSCs to IA macroscopic scaffold surface also indicates a good biocompatibility of IA macroscopic scaffold. These results provide the potential for developing the next generation of red-light controlled soft functional materials with good biocompatibility.

Tuning the order of poly(3-alkylthiophene) derivatives ultrathin films through side-chain polarity: From a short-range ordered monolayer to a highly crystalline bilayer

In order to pave the way for the formation of ultrathin electronically conductive organic films, we explored the structure and morphology of polythiophene derivatives in situ on the water surface. By changing the side chain end-group of poly(3-hexylthiophene) (P3HT) from methyl to carboxylic acid potassium salt, we showed that the film structure is drastically changed from a highly ordered bilayer to a short-range organized monolayer. Using a comprehensive experimental approach from macroscopic length scale to molecular organization as well as simulations of diffraction patterns, the detailed structure of the crystalline P3HT bilayer was determined. Some similarities with the structure measured on thicker films deposited on solid substrates were evidenced such as the π-stacking distance, the interlayer spacing, and the edge-on conformation. Some differences were also pointed out, in particular the in-plane packing along the polymer backbones and the shift of the upper monolayer with respect to the bottom one in this direction. Such observations highlighted the influence of both the forced two-dimensional confinement and the nature of the substrate (water) on the P3HT film structure. The presence of a carboxylic acid potassium salt at the end of the side chain induced completely different behavior. Indeed, high pressures were necessary to observe a π-stacking of the thiophene units, but only short-range, and although the polymer keeps a monolayer organization independently of the pressure, a deep change in the polymer conformation was evidenced with the pressure.

(Invited) Neutrons as a Powerful Tool for Better Understanding Electrochemistry on Various Length and Time Scales

Today, sophisticated methods are applied to gain a deeper understanding of processes in in-situ electrochemistry. There are few ways to study electrochemically relevant processes on different length and/or time scales without affecting the processes themselves. Probes that cover a sufficient volume of the sample non-destructively and are sensitive to the important charge carriers are in great demand. For such purposes, neutrons are an ideal candidate to perform this task because they have relatively high sensitivity to the light chemical elements, can distinguish neighboring elements of the periodic table, have a large beam cross-section, and possess high penetration depth for many types of materials.Therefore, many open questions are addressed to unique neutron techniques tailored to solve the open problems. This article gives an overview of some examples to show the advantages of using neutrons for special questions on different length and time scales [1]. For surface investigations of electrodes, the neutron depth profiling method (NDP) is suitable for characterizing the Li distribution up to the nano range [2]. Neutron diffraction is a powerful tool to better understand cylindrical cells at the atomic level, e.g. during the intercalation process [3]. Another strong field of neutrons is the monitoring of the wetting process during the electrolyte filling of prismatic hard case cells on the macroscopic length scale using the neutron imaging technique [4].

Measurements of stresses in β‐(Y,Yb)2Si2O7 environmental barrier coating layers using Raman spectroscopy

AbstractResidual stress measurements in environmental barrier coatings (EBCs) can help in understanding coating durability and potential damage mechanisms. We demonstrate the capability of Raman spectroscopy to measure average residual stresses in two different β‐RE2Si2O7 (RE = rare earth or Y3+, denoted as REDS) EBCs with a nominal (Yb,Y)2Si2O7 composition, focusing on macroscopic residual stresses acting at macroscopic length scales. Uniaxial compression measurements of dense β‐(Yb,Y)2Si2O7 ceramics are used for calibration curves for applied stress versus Raman peak shift. We use these calibration curves to evaluate the macroscopic thermoelastic residual stress in the (Yb,Y)2Si2O7 layers from coefficient of thermal expansion (CTE) mismatch of two different (Yb,Y)2Si2O7‐based EBCs on SiC‐based substrates. Microscopic stress contributions to Raman peak shifts are subtracted using reference free‐standing coatings and analytic estimates for inclusion stresses when (Yb,Y)2Si2O7 coatings have a high, variable volume fraction of (Yb,Y)2SiO5. The macroscopic thermal residual stress in these (Yb,Y)2Si2O7 EBCs is compressive, as expected from the smaller CTE of β‐REDS versus SiC. These thermal residual stresses can vary between different YbYDS EBC coatings by more than a factor of three with a measured layer residual stress of approximately –180 MPa (compressive) for a high modulus, low CTE coating, and our measured values generally agree with calculated estimates.

The effect of shape, polydispersity, charge, and fraction of crystallite bundles on the cholesteric pitch of cellulose nanocrystal suspensions

Using Onsager–Straley’s second-virial theory, we investigate the cholesteric pitch of cellulose nanocrystal (CNC) suspensions. We model the CNCs as hard chiral bundles of microfibrils and examine the effect of the shape of these chiral bundles, characterized by aspect ratio and chirality, on the cholesteric pitch. Additionally, we explore the impact of length polydispersity and surface charge on the cholesteric phase of CNCs. Furthermore, we consider binary mixtures of twisted bundles and achiral primary crystallites to provide a more realistic representation of CNC suspensions. Our findings reveal that the degree of bundle twisting significantly affects the helical twisting of the cholesteric phase. We also observe that the average particle length and length polydispersity have substantial effects on strongly twisted bundles but minimal effects on weakly twisted ones. Finally, our study indicates that as the range of electrostatic interactions increases, the transfer of chirality from the microscopic to macroscopic length scales becomes masked, resulting in an increase in the cholesteric pitch. In the case of binary mixtures, the bundles act as chiral dopants, and an increasing fraction of bundles progressively enhances the helical twisting of the cholesteric phase.

Laminar flow in a channel bounded by porous/rough walls: Revisiting Beavers-Joseph-Saffman

The fully developed, steady, incompressible, laminar flow in a channel delimited by rough and/or permeable walls is considered. The influence of the micro-structured bounding surfaces on the channel flow behavior is mimicked by imposing high-order effective boundary conditions which stem from homogenization theory and do not contain empirical parameters. A closed-form solution of the Navier–Stokes equations is found for the flow in the channel, with conditions at each virtual boundary linking the slip velocities to shear stress and streamwise pressure gradient. The boundary condition for the longitudinal velocity coincides with a little-noticed extension of the so-called Beavers-Joseph condition, first derived by Saffman (1971); it applies to both permeable and rough surfaces, including the case of separated flow (Couette-Poiseuille motion with adverse pressure gradient). The analytical solution obtained for the velocity distribution in the channel is validated against full feature-resolving simulations of the flow for either highly ordered or random textures, highlighting the accuracy and the applicability range of the model. The Stokes-based model used to identify slip and interface permeability coefficients in the effective boundary conditions is found to be reliable and accurate up to ϵReτ≈10, with ϵ ratio of microscopic to macroscopic length scales and Reτ the shear-velocity Reynolds number. Above this threshold, the coefficients must account for advective effects: a new upscaling procedure, based on an Oseen’s approximation, is thus proposed and validated, extending considerably beyond the Stokes regime.

Multiscale mechanical analysis of the elastic modulus of skin

The mechanical properties of the skin determine tissue function and regulate dermal cell behavior. Yet measuring these properties remains challenging, as evidenced by the large range of elastic moduli reported in the literature—from below one kPa to hundreds of MPa. Here, we reconcile these disparate results by dedicated experiments at both tissue and cellular length scales and by computational models considering the multiscale and multiphasic tissue structure. At the macroscopic tissue length scale, the collective behavior of the collagen fiber network under tension provides functional tissue stiffness, and its properties determine the corresponding elastic modulus (100–200 kPa). The compliant microscale environment (0.1–10 kPa), probed by atomic force microscopy, arises from the ground matrix without engaging the collagen fiber network. Our analysis indicates that indentation-based elasticity measurements, although probing tissue properties at the cell-relevant length scale, do not assess the deformation mechanisms activated by dermal cells when exerting traction forces on the extracellular matrix. Using dermal-equivalent collagen hydrogels, we demonstrate that indentation measurements of tissue stiffness do not correlate with the behavior of embedded dermal fibroblasts. These results provide a deeper understanding of tissue mechanics across length scales with important implications for skin mechanobiology and tissue engineering. Statement of SignificanceMeasuring the mechanical properties of the skin is essential for understanding dermal cell mechanobiology and designing tissue-engineered skin substitutes. However, previous results reported for the elastic modulus of skin vary by six orders of magnitude. We show that two distinct deformation mechanisms, related to the tension–compression nonlinearity of the collagen fiber network, can explain the large variations in elastic moduli. Furthermore, we show that microscale indentation, which is frequently used to assess the stiffness perceived by cells, fails to engage the fiber network, and therefore cannot predict the behavior of dermal fibroblasts in stiffness-tunable fibrous hydrogels. This has important implications for how to measure and interpret the mechanical properties of soft tissues across length scales.

Spin-mediated shear oscillators in a van der Waals antiferromagnet.

Understanding how microscopic spin configuration gives rise to exotic properties at the macroscopic length scale has long been pursued in magnetic materials1-5. One seminal example is the Einstein-de Haas effect in ferromagnets1,6,7, in which angular momentum of spins can be converted into mechanical rotation of an entire object. However, for antiferromagnets without net magnetic moment, how spin ordering couples to macroscopic movement remains elusive. Here we observed a seesaw-like rotation of reciprocal lattice peaks of an antiferromagnetic nanolayer film, whose gigahertz structural resonance exhibits more than an order-of-magnitude amplification after cooling below the Néel temperature. Using a suite of ultrafast diffraction and microscopy techniques, we directly visualize this spin-driven rotation in reciprocal space at the nanoscale. This motion corresponds to interlayer shear in real space, in which individual micro-patches of the film behave as coherent oscillators that are phase-locked and shear along the same in-plane axis. Using time-resolved optical polarimetry, we further show that the enhanced mechanical response strongly correlates with ultrafast demagnetization, which releases elastic energy stored in local strain gradients to drive the oscillators. Our work not only offers the first microscopic view of spin-mediated mechanical motion of an antiferromagnet but it also identifies a new route towards realizing high-frequency resonators8,9 up to the millimetre band, sothe capability of controlling magnetic states on the ultrafast timescale10-13 can be readily transferred to engineering the mechanical properties of nanodevices.

On the Asymmetry in Photo-Induced Motion of Graphene-Oxide Paper

We report on the photo-mobility properties of a free standing large area graphene oxide (GO) paper (GOP). The thickness of the film is ≈20 μm. GOP is made by drop casting an aqueous suspension of GO on a microscope glass slide placed on a hot plate kept at the temperature of 70 °C. The film is peeled-off from the glass substrate and irradiated under different coherent and incoherent light sources. The film bends up to ≈55° when the irradiation is made using a near infra-red (NIR) incoherent incandescent lamp and returns back to the initial position when the NIR lamp is switched-off. The bending mechanism is attributed to the asymmetry of the GOP film obtained during the film formation process. We characterize the film morphology and structure using a Scanning Electron Microscopy (SEM) imaging and X-ray Diffraction (XRD) measurements, respectively. Remarkable differences between the two surfaces of the GOP are evidenced, both on a macroscopic length scale (surface roughness) and on a microscopic one (GO interlayer distance). This asymmetry results in different (negative) thermal expansion coefficients for the two film surfaces and hence in the bending of the film when the film temperature is increased by light absorption.

A combined ensemble-volume average homogenization method for lattice structures with defects under dynamic and static loading

In the study of lattices structures, both experiments and numerical simulations are often conducted with small samples. Using combined ensemble and volume averaging, this work introduces a method to extract a macroscopic constitutive response of a lattice material from numerical simulations performed in periodic domains. The domain size needed to obtain statistically accurate results is investigated. Similar to molecular dynamics, the concept of the virial stress is introduced after homogenized equations are derived using the ensemble averaging method. Under static conditions, the virial stress is shown to agree with the volume averaged solid stress.Using the homogenization method, constitutive relations for this stress can be obtained from systems with uniform strains. Application of such obtained constitutive relations to more general cases results in an error proportional to the square of the ratio between the lattice length scale and the macroscopic length scale. Taking advantage of this property, numerical simulations are performed in systems with a uniform gradient of the average velocity. The volume average method is then used to accelerate convergence when studying lattices with defects. To avoid the artificial numerical time scale from the size of a representative volume element divided by the wave speed, a numerical scheme is developed to enforce a spatially uniform velocity gradient within the computational domain while allowing fluctuations of the velocity or displacement to develop naturally. To account for probability distribution of lattice defects, the stress is calculated as the ensemble-volume averaged value. For dynamic systems, energy dissipation properties are also studied.

Evidence for ferroelastic switching and nanoscopic domains in polycrystalline Si-doped hafnium oxide films

The mechanism of nanoscopic domain switching in ferroelectric hafnium oxide and its implications for antiferroelectric-like behavior as well as for the wake-up effect is still widely discussed. Understanding this mechanism is of vital importance for a multitude of applications like piezoelectric actuators, pyroelectric sensors, and nonvolatile memory devices. In this article, electrical and physical analysis methods are used to characterize ferroelectric hafnium oxide on the nanoscopic as well as the macroscopic length scale. Evidence for nanoscopic domains is found using transmission Kikuchi diffraction. In combination with macroscopic Preisach density measurements, strong evidence is found that antiferroelectric-like behavior and wake-up are governed by ferroelastic switching, i.e., a 90° domain wall motion. Based on these insights, the material stack can be optimized to further improve microelectronic applications based on HfO2.

Non-Covalent Free-Standing Monolayer Nanoarchitectonics of Heterocoronene-Based Discotic Liquid Crystal Molecules

With excellent charge carrier mobility, tendency to form long-range assembly with self-healing ability, and remarkable chemical and mechanical stability, highly conjugated discotic molecules constitute an important class of materials for electronic applications. Here, we report formation of the stable free-standing molecular film of heterocoronene-based discotic liquid crystal (DLC) molecules, held solely by supra-molecular non-covalent interactions. The films of monolayer thickness (∼4 nm) were lifted from Langmuir trough directly onto a circular ring of diameter up to 2 mm as well as onto TEM grids. Films remain free-standing up to a macroscopic length scale, as revealed by optical and secondary electron microscopy, presumably due to the synergistic effect of intermolecular π–π interactions and the dispersion forces between the peripheral alkyl chains as well as their interdigitation. The monolayer is more than 97% transparent in the visible range. Further, resistive switching measurements carried out on the monolayer DLC film transferred on a silver substrate revealed electrochemical metallization to be the governing process. The switching time was found to decrease exponentially with voltage indicating nucleation to be a possible rate-limiting step. We anticipate that the method presented here will facilitate utilization of such non-covalent free-standing films in flexible memristor and nano-electromechanical systems.

Multiscale Monte Carlo simulations of gold nanoparticle dose-enhanced radiotherapy I: Cellular dose enhancement in microscopic models.

The introduction of Gold NanoParticles (GNPs) in radiotherapy treatments necessitates considerations such as GNP size, location, and quantity, as well as patient geometry and beam quality. Physics considerations span length scales across many orders of magnitude (nanometer-to-centimeter), presenting challenges that often limit the scope of dosimetric studies to either micro- or macroscopic scales. To investigate GNP dose-enhanced radiation Therapy (GNPT) through Monte Carlo (MC) simulations that bridge micro-to-macroscopic scales. The work is presented in two parts, with Part I (this work) investigating accurate and efficient MC modeling at the single cell level to calculate nucleus and cytoplasm Dose Enhancement Factors (n,cDEFs), considering a broad parameter space including GNP concentration, GNP intracellular distribution, cell size, and incident photon energy. Part II then evaluates cell dose enhancement factors across macroscopic (tumor) lengthscales. Different methods of modeling gold within cells are compared, from a contiguous volume of either pure gold or gold-tissue mixture to discrete GNPs in a hexagonal close-packed lattice. MC simulations with EGSnrc are performed to calculate n,cDEF for a cell with radius µm and nucleus µm considering 10to 370keV incident photons, gold concentrations from 4 to 24mgAu /gtissue , and three different GNP configurations within the cell: GNPs distributed around the surface of the nucleus (perinuclear) or GNPs packed into one (or four) endosome(s). Select simulations are extended to cells with different cell (and nucleus) sizes: 5µm (2, 3, and 4µm), 7.35µm (4 and 6µm), and 10µm (7, 8, and 9µm). n,cDEFs are sensitive to the method of modeling gold in the cell, with differences of up to 17% observed; the hexagonal lattice of GNPs is chosen (as the most realistic model) for all subsequent simulations. Across cell/nucleus radii, source energies, and gold concentrations, both nDEF and cDEF are highest for GNPs in the perinuclear configuration, compared with GNPs in one (or four) endosome(s). Across all simulations of the (rcell , rnuc ) = (7.35, 5)µm cell, nDEFs and cDEFs range from unity to 6.83 and 3.87, respectively. Including different cell sizes, nDEFs and cDEFs as high as 21.5 and 5.5, respectively, are observed. Both nDEF and cDEF are maximized at photon energies above the K- or L-edges ofgold by 10 to 20 keV. Considering 5000 unique simulation scenarios, this work comprehensively investigates many physics trends on DEFs at the cellular level, including demonstrating that cellular DEFs are sensitive to gold modeling approach, intracellular GNP configuration, cell/nucleus size, gold concentration, and incident source energy. These data should prove especially useful in research as well as treatment planning, allowing one to optimize or estimate DEF using not only GNP uptake, but also account for average tumor cell size, incident photon energy, and intracellular configuration of GNPs. PartII will expand the investigation, taking the PartI cell model and applying it in cm-scalephantoms.

Multiscale Structural Insight into Dairy Products and Plant-Based Alternatives by Scattering and Imaging Techniques.

Dairy products and plant-based alternatives have a large range of structural features from atomic to macroscopic length scales. Scattering techniques with neutrons and X-rays provide a unique view into this fascinating world of interfaces and networks provided by, e.g., proteins and lipids. Combining these scattering techniques with a microscopic view into the emulsion and gel systems with environmental scanning electron microscopy (ESEM) assists in a thorough understanding of such systems. Different dairy products, such as milk, or plant-based alternatives, such as milk-imitating drinks, and their derived or even fermented products, including cheese and yogurt, are characterized in terms of their structure on nanometer- to micrometer-length scales. For dairy products, the identified structural features are milk fat globules, casein micelles, CCP nanoclusters, and milk fat crystals. With increasing dry matter content in dairy products, milk fat crystals are identified, whereas casein micelles are non-detectable due to the protein gel network in all types of cheese. For the more inhomogeneous plant-based alternatives, fat crystals, starch structures, and potentially protein structures are identified. These results may function as a base for improving the understanding of dairy products and plant-based alternatives, and may lead to enhanced plant-based alternatives in terms of structure and, thus, sensory aspects such as mouthfeel and texture.

A cure kinetics investigation of amine-cured epoxy by Rheo-Raman spectroscopy

In a companion paper, fluorescence lifetime imaging revealed a heterogeneous morphology at macroscopic and molecular length scales in a bis-epoxide blend composed of diglycidyl ether of bisphenol-A (DGEBA) and diglycidyl ether of 1,4-butanediol (DGEBD) cured with meta-phenylenediamine (m-PDA) with a strategically integrated mechanophore. This macroscopic heterogeneity most likely originates during the crosslinking process, which motivates measurements of both the reaction progress and the mechanical properties under controlled cure schedules. Rheo-Raman spectroscopy provides simultaneous measurements of Raman spectra to monitor vibrational modes relevant to the crosslinking process and rheology to track the viscoelastic shear modulus during crosslinking. Here, rheo-Raman measurements confirm that the molecular level heterogeneity is influenced by reaction kinetics differences of the two miscible bis-epoxides with m-PDA. In the companion paper the macroscopic heterogeneity was linked to the self-association of oligomers in DGEBD through interchain hydroxyl-hydroxyl hydrogen bonding. Rheo-Raman studies also revealed that this self-association slows down the overall cure-kinetics of the DGEBD/m-PDA and DGEBA/DGEBD/m-PDA curing reaction, thereby supporting the link between the macroscopic heterogeneity and oligomers in DGEBD.

Conjugate natural convection along regularly ribbed vertical surfaces: A homogenization-based study

Natural convection heat transfer from periodically ribbed vertical surfaces is targeted for upscaling, incorporating the analysis of thermal conduction through the microscale ribs. Asymptotic homogenization theory is employed, considering the steady conjugate heat transfer problem, to formulate second-order accurate effective conditions for velocity and temperature at a fictitious plane surface, beyond which the macroscale behavior of the flow is computed. This allows to avoid the numerically expensive resolution of fields within and through the microstructured corrugations. For the streamwise velocity component, the no-slip boundary condition is corrected at first order (in terms of a small parameter ϵ , ratio of microscopic to macroscopic length scales) by the classical Navier-slip condition plus a buoyancy term, while the gradient of the normal stress appears at second order together with a temperature-gradient term. The temperature at the virtual boundary deviates from the uniform value at the baseplate; the thermal slip is described via a first-order temperature-gradient term with a coefficient depending on rib geometry and thermal conductivity. Different case studies are conducted on the case of transverse square ribs, varying the density of the pattern and the rib-to-fluid thermal conductivity ratio, to provide extensive validation of the model against full feature-resolving simulations. Beyond the validation phase, a better understanding of the effects of different parameters on the heat transfer performance is pursued. The presence of ribs is found to decrease the overall heat transfer rate from the surface, and this deterioration is only partially alleviated by raising the thermal conductivity of the ribs. Increasing the number of conducting ribs on the hot surface has a complex, non-monotonic effect on the heat transfer rate, unlike the case of adiabatic ribs where the average Nusselt number decays monotonically. The performance of low-thermal-conductivity elements (e.g. wooden ribs) may considerably differ from that of perfectly adiabatic ones.

Fast calculation of scattering patterns using hypergeometric function algorithms

The scattering of light, X-rays, electrons or neutrons by matter is used widespread for structural characterization from atomic to macroscopic length scales. With the advent of high-brilliance beam sources and the development fast, large area pixelated detectors, scattering patterns are now acquired at unprecedented frame rates and frame sizes. The slow analysis of these scattering patterns has evolved into a severe bottleneck retarding scientific insight. Here we introduce an algorithm based on the use of hypergeometric functions providing gains in computational speed of up to 105 compared to present numerical integration algorithms. Hypergeometric functions provide analytical descriptions of geometrical shapes, can be rapidly computed as series and asymptotic expansions, and can be efficiently implemented in GPUs. The algorithm provides the necessary computational speed to calculate scattering patterns on timescales required for real-time experiment feedback, the analysis of large volumes of scattering data, and for the generation of training data sets for machine learning.

Investigation of cavitation bubble dynamics near a solid wall by high-resolution numerical simulation

We investigate dynamics of a single cavitation bubble in the vicinity of a horizontal wall throughout expansion and collapse using a sharp–interface level-set method. The numerical scheme is based on a finite-volume formulation with low-dissipation high-order reconstruction schemes. Viscosity and surface tension are taken into account. The simulations are conducted in three-dimensional axi-symmetric space. A wide range of initial bubble wall standoff distances is covered. We focus, however, on the near-wall region where the distance between the bubble and the wall is small. We reproduce three jetting regimes: needle, mixed, and regular jets. The needle jets impose a significant load on the solid wall, exceeding the force induced by the collapse of the pierced torus bubble. For intermediate standoff distances, the large delay time between jet impact and torus bubble collapse leads to a significant decrease in the imposed maximum wall pressure. A liquid film between bubble and wall is observed whenever the bubble is initially detached from the wall. Its thickness increases linearly for very small standoff distances and growths exponentially for intermediate distances leading to a significant increase in wall-normal bubble expansion and bubble asymmetry. For configurations where the torus bubble after jet impact reaches maximum size, the collapse time of the cavitation bubble also is maximal, leading to a plateau in the overall prolongation of the cycle time of the bubble. Once the initial bubble is attached to the solid wall, a significant drop of all macroscopic time and length scales toward a hemispherical evolution is observed.