Small Length Scales Research Articles

A reduced-order model of concentration polarization in reverse osmosis systems with feed spacers

Feed spacers in reverse osmosis systems generate complex fluid flows that limit computational fluid dynamics (CFD) simulations to small length and time scales. That limits our ability to simulate mineral scaling and other membrane fouling phenomena, which occur over longer length and time scales. Thus motivated, we develop a reduced model that replaces the CFD simulation of the velocity field with an analytical model that mimics spacers. This focuses the remaining numerical effort on simulating the advection–diffusion equation governing solute transport. We motivate and validate the model with CFD simulations and bench-scale experiments of spacer filaments in three different arrangements, including cases of unsteady vortex shedding. We show that the model produces a roughly 10,000-fold speedup compared to CFD, and accurately reproduces CFD predictions of not only the average and maximum concentrations, but also the local concentration distribution along the membrane. We also demonstrate the model for simulating a feed channel with a length-to-height ratio of 200. The model provides a simple testbed for exploratory studies of multispecies transport, precipitation, and membrane fouling phenomena for which simulating spacers is often prohibitive.

Microphysics of liquid water in sub-10 nm ultrafine aerosol particles

Abstract. Ultrafine aerosol particles with sizes smaller than 50 nm have been shown in recent studies to serve as a large source of cloud condensation nuclei that can promote additional cloud droplet formation under supersaturation conditions. Knowledge of the microphysics of liquid water in these droplets remains limited, particularly in the sub-10 nm particle size range, due to experimental and theoretical challenges associated with the complexity of aerosol components and the small length scales of interest (e.g., difficulty of precisely sampling the liquid–air interface, questionable validity of mean-field theoretical representations). Here, we carried out molecular dynamics (MD) simulations of aerosol particles with diameters between 1 and 10 nm and characterized atomistic-level structure and water dynamics in well-mixed and phase-separated systems with different particle sizes, NaCl salinities, and pimelic acid (PML) organic surface loadings as a function of distance from the time-averaged Gibbs dividing interface or instantaneous water–air interface. We define a sphericity factor (ϕ) that can shed light on the phase-mixing state of nanodroplets, and we reveal an unexpected dependence of mixing state on droplet size. Our results also evidence an ion concentration enhancement in ultrafine aerosols, which should modulate salt nucleation kinetics in sub-10 nm droplets, and provide detailed characterization of the influence of droplet size on surface tension and on water self-diffusivity near the interface. Analysis of water evaporation free energy and water activity demonstrates the validity of the Kelvin equation and Köhler theory at droplet sizes larger than 4 nm under moderate salinities and organic loadings and the need for further extension to account for ion concentration enhancement in sub-10 nm aerosols, droplet-size-dependent phase separation effects, and a sharp decrease in the cohesiveness of liquid water in sub-4 nm droplets. Finally, we show that an idealized fractional surface coating factor (fs) can be used to categorize and reconcile water accommodation coefficients (α*) observed in MD simulations and experimental results in the presence of organic coatings, and we resolve the droplet size dependence of α*.

Hydrodynamic Characteristics of Textured Microchannel Flow

Abstract Microchannel flow is of great interest across many disciplines and applications, from biochemical diagnostics to thermal management systems. Nonetheless, such flow requires large pumping power due to its small cross-sectional length scale. Textured surfaces have shown encouraging results in terms of drag reduction in external flows and at larger scales (turbulent regime). However, there have been some discrepancies in the literature regarding the possibility of drag/friction reduction in microscale internal flows (laminar regime), which is believed to be due to the absence of a proper definition for the reference baseline. The main goal of this paper is to determine whether the (rectangular) textures lead to drag/friction reduction while comparing their results with the correct reference. The rectangular trenches have been introduced on the side walls of the microchannels/microgaps to understand the underlying frictional physics by conducting numerical simulations and experiments. The effect of geometrical parameters of the rectangular trenches as well as the Reynolds number has been investigated on characteristics of the flow. A thorough analysis has been performed using a neural network (NN) to evaluate the potential drag reduction in textured microchannels. The results showed that using the correct reference baseline, no drag reduction was observed in textured microchannels with rectangular trenches. Moreover, the width-to-depth aspect ratio of the trenches and roughness (texture size to mean microchannel dimension) are introduced to be critical parameters in the flow behavior inside textured microchannels.

Extended Isogeometric Analysis of Cracked Piezoelectric Materials in the Presence of Flexoelectricity

AbstractTo accurately analyze the fracture behavior of piezoceramics at small length scales, flexoelectricity must be considered along with piezoelectricity. Due to its dependence on size, flexoelectricity predominates at the micro‐ and nano‐length scales. Additionally, crack tips having the largest strain gradient state cause large flexoelectricity around them. Different approaches are employed in the past to model cracks computationally. However, extended isogeometric analysis (XIGA) is proven to be an accurate and efficient method. C1 continuity requirements for modeling gradients in flexoelectricity are met by non‐uniform rational B‐splines (NURBS) basis functions used in XIGA. In this work, XIGA‐based computational model is developed and implemented to study the fracture behavior of the piezoelectric‐flexoelectric domain. An in‐house MATLAB code is developed for the same. Several numerical examples are studied to ensure the efficacy and efficiency of the implemented model, and crack behavior is presented in the form of an electro‐mechanical J‐integral. The analysis is carried out to investigate how cracks behave for different flexoelectric coefficients under different electrical and mechanical loading combinations. J‐integral is also analyzed against crack parameters such as crack orientation and length. It is observed that boundary loads and flexoelectric material constants significantly influence J‐integral. Results also show a considerable amount of fracture toughening in the presence of flexoelectricity. The peak value of J‐integral is found to be reduced with an increase in the flexoelectric coefficient. A significant reduction in J‐integral, as much as 45%, is observed when the flexoelectric constant varied from 0.5 to 2 µCm−1.

Modeling of horizontal steam injection in a water pool

A comprehensive understanding of the direct contact condensation (DCC) phenomena of steam discharged into a subcooled water pool is essential for the nuclear engineering field. DCC is the most rapid and efficient way to condense high-pressure and high-temperature steam with simple engineering systems. However, the pressure oscillation due to the rapid condensation and small length and time scales of turbulent two-phase flow make the investigation of DCC phenomena challenging either by experiments or with numerical simulations.This paper presents the computational fluid dynamics (CFD) simulations of the small-scale separate effect test facility (SEF-POOL) experiment of Lappeenranta-Lahti University of Technology (LUT University). In the SEF-POOL test, the steam was injected using the orifice of a diameter of 16 mm. All simulations were performed by employing the compressible two-phase solver of OpenFOAM which was based on the Eulerian–Eulerian two-fluid approach. The interfacial heat transfer between steam and water was modeled by using the Nusselt number formulation of Coste (2004). The Rayleigh–Taylor interfacial (RTI) area model of Pellegrini et al. (2015) was applied for the interfacial area modeling. In this work, the formation and collapse of the steam bubbles are studied using the extended pattern recognition based image analysis algorithm. The pattern recognition (PR) algorithm is based on the video material recorded during the SEF-INF2 experiment of the SEF-POOL test facility.The presented study show that if the two-phase interface is rough and smear into the subgrid scale, the interfacial area density calculation solely with the volume fraction gradient is inadequate for predicting rapid condensation rates. Results indicate that rapid and high interfacial accelerations in DCC trigger interfacial instabilities which increased the interface roughness and total interfacial area consequently. Thus, interfacial area modeling with the RTI increased the total interfacial heat transfer rate in the simulations. The achieved results exhibit that the selected modeling approach captured the rapid bubbling condensation oscillation mode of the SEF-POOL test. Presented results demonstrate that image analysis and pattern recognition have great potential in thermal-hydraulic research that can be beneficial for direct contact condensation and phase-interface dynamics model development.

Significantly improved strength and plasticity of a refractory high-entropy alloy at small length scale

Refractory high-entropy alloy (RHEA) VNbMoTaW exhibits remarkably high strength in a much wide temperature range, whereas the brittle fracture behavior limits the applications. Here we show a significant size effect on the strength, plasticity and fracture behaviour of the VNbMoTaW RHEA. As sample size goes from millimeter to sub-micrometer scale, the brittle cracking behavior of the RHEA is greatly suppressed, along with a simultaneous enhancement of strength and plasticity. The improved mechanical properties can be attributed to the disappearance of crack initiation sites, the size-dependent dislocation plasticity at small length scale and the size-dependent competition in thermodynamics driving-force for cleavage cracking and plastic yielding. The results imply a promising potential of the RHEA for making microscale devices with high temperature environment.

Nonlocal antiplane shear interfacial waves

In this paper, non-local shear interfacial waves between two non-local elastic half-spaces in perfect contact along a common boundary are investigated. For the sake of simplicity, an anti-plane problem formulated through the framework of Eringen’s theory is considered. The non-locality is taken only in the transverse coordinate making the analysis of the problem easier than that of non-local problems of 2D. Effective boundary conditions are obtained, with the help of a small internal characteristic length scale, along the interface utilizing an asymptotic approach enabling one to write the non-local stresses through their local counterparts. Antiplane non-local shear interfacial waves are analysed by the derived formulation. Numerical results are presented for certain characteristic values of the problem parameters.

Revisiting RANS prediction of transitional flow on T3A flat plate subject to various freestream turbulences

A laminar–turbulent transition subject to a freestream turbulence involves highly complex flow mechanisms, which have received considerable interest in the past decades. Accurately predicting such complex physical phenomena is significantly challenging using computational fluid dynamics solvers, particularly in industrial engineering applications. In this study, the capability of two transitional turbulence models—k−kl−ω and k−ω−γ−Re˜θt—to predict a T3A plate transition scenario was revisited. First, the predicted boundary layer data was compared to ERCOFTAC experimental measurements. Subsequently, a transitional flow subject to constant and sinusoidal freestream turbulences was systematically investigated. Under a constant freestream turbulence, the two models exhibited opposite tendencies of the transition starting and ending positions with the increase in Refst. However, there were still some similarities between the results of the two models. When the length scale was fixed, the transition area moved upstream with increasing turbulence intensity. The transition zone was more sensitive to a small length scale than to a considerable length scale. The dynamic boundary layer under the sinusoidal combination condition was less disturbed than the sinusoidal turbulence intensity and the sinusoidal specific turbulence dissipation rate. Regardless of the type of sinusoidal freestream turbulence the boundary layer was exposed to, increasing the oscillation frequency significantly disturbed the transitional flow. It was observed that the inertia effect of the dynamic onset point was enhanced by increasing the oscillation frequency. Concurrently, a significant phase delay occurred, and the delay time was approximately proportional to the oscillation frequency. The extreme position of the transition onset close to the leading edge of the plate was not affected by the oscillation frequency, whereas it depended on the sinusoidal variable. However, the extreme downstream transition onset point was significantly affected by the oscillation frequency.

Quantifying microstructures of earth materials using higher-order spatial correlations and deep generative adversarial networks

The key to most subsurface processes is to determine how structural and topological features at small length scales, i.e., the microstructure, control the effective and macroscopic properties of earth materials. Recent progress in imaging technology has enabled us to visualise and characterise microstructures at different length scales and dimensions. However, one limitation of these technologies is the trade-off between resolution and sample size (or representativeness). A promising approach to this problem is image reconstruction which aims to generate statistically equivalent microstructures but at a larger scale and/or additional dimension. In this work, a stochastic method and three generative adversarial networks (GANs), namely deep convolutional GAN (DCGAN), Wasserstein GAN with gradient penalty (WGAN-GP), and StyleGAN2 with adaptive discriminator augmentation (ADA), are used to reconstruct two-dimensional images of two hydrothermally rocks with varying degrees of complexity. For the first time, we evaluate and compare the performance of these methods using multi-point spatial correlation functions—known as statistical microstructural descriptors (SMDs)—ultimately used as external tools to the loss functions. Our findings suggest that a well-trained GAN can reconstruct higher-order, spatially-correlated patterns of complex earth materials, capturing underlying structural and morphological properties. Comparing our results with a stochastic reconstruction method based on a two-point correlation function, we show the importance of coupling training/assessment of GANs with higher-order SMDs, especially in the case of complex microstructures. More importantly, by quantifying original and reconstructed microstructures via different GANs, we highlight the interpretability of these SMDs and show how they can provide valuable insights into the spatial patterns in the synthetic images, allowing us to detect common artefacts and failure cases in training GANs.

Perspective on Ferroelectric Devices: Lessons from Interfacial Chemistry

Ferroelectric fluorite-structured oxide thin films have attracted increased interest from both academia and industry because of their superior scalability─in which their ferroelectric properties can be maintained even below 10 nm thickness─and excellent compatibility with current complementary metal–oxide–semiconductor technology. Regarding recent efforts to downscale the technology node of semiconductor processing, the emergence of ferroelectric properties in fluorite-structured oxide thin films at small length scales is of particular interest. As the length scale of the fluorite-structured oxide thin films reaches the atomic scale, the contribution of the interfacial layer to the properties naturally increases. In particular, the quality and type of interfacial layer, as well as the reaction chemistry in response to the electric field, play a major role in determining the properties of the devices. Consequently, understanding the chemistry of ferroelectric–electrode and ferroelectric–semiconductor interfaces is crucial for their use in industrial applications in the near future. In this context, emerging semiconductor devices based on fluorite-structured oxide ferroelectrics, including ferroelectric field-effect transistors, ferroelectric random-access memories, and ferroelectric tunnel junctions, and the impact of interface chemistry in the devices are reviewed in detail.

Microfluidic techniques for mechanical measurements of biological samples.

The use of microfluidics to make mechanical property measurements is increasingly common. Fabrication of microfluidic devices has enabled various types of flow control and sensor integration at micrometer length scales to interrogate biological materials. For rheological measurements of biofluids, the small length scales are well suited to reach high rates, and measurements can be made on droplet-sized samples. The control of flow fields, constrictions, and external fields can be used in microfluidics to make mechanical measurements of individual bioparticle properties, often at high sampling rates for high-throughput measurements. Microfluidics also enables the measurement of bio-surfaces, such as the elasticity and permeability properties of layers of cells cultured in microfluidic devices. Recent progress on these topics is reviewed, and future directions are discussed.

Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials

Ductile materials, such as metal alloys, can undergo substantial deformation before failure. Additionally, these materials are usually of polycrystalline composition and exhibit strongly anisotropic behavior at small length scales. Previously developed fast Fourier transform (FFT)-based models can model ductile fracture of isotropic materials or the elastic–plastic behavior of anisotropic polycrystalline materials; however, there remains a need to couple both capabilities. This work extends a large-strain FFT-based crystal plasticity model to simulate ductile fracture of polycrystalline materials. A triaxiality-based continuum damage mechanics (CDM) formulation is incorporated into a large-strain elasto-viscoplastic FFT (LS-EVPFFT) framework. The CDM formulation is augmented with an integral-based nonlocal regularization approach that correctly handles gas-phase material necessary to model unconstrained surfaces. To validate the damage-enabled LS-EVPFFT framework, mesoscale copper tensile coupons were machined using microwire electrical discharge machining and experimentally characterized using electron backscatter diffraction. In-situ optical digital image correlation was performed during uniaxial testing to provide a side-by-side comparison of the experimental and computational strain fields and stress–strain responses. The damage-enabled LS-EVPFFT framework can simulate the complete macroscopic stress–strain response of ductile polycrystals to failure. The model reproduces necking behavior that qualitatively agrees with experimental observations. By leveraging the relatively low computational cost of the damage-enabled LS-EVPFFT framework, the framework presented here allows the ductile fracture response of 3D polycrystalline materials to be tractably predicted.

High Sensitivity Near-Infrared Imaging of Fluorescent Nanosensors.

Biochemical processes are fast and occur on small-length scales, which makes them difficult to measure. Optical nanosensors based on single-wall carbon nanotubes (SWCNTs) are able to capture such dynamics. They fluoresce in the near-infrared (NIR, 850-1700nm) tissue transparency window and the emission wavelength depends on their chirality. However, NIR imaging requires specialized indium gallium arsenide (InGaAs) cameras with a typically low resolution because the quantum yield of normal Si-based cameras rapidly decreases in the NIR. Here, an efficient one-step phase separation approach to isolate monochiral (6,4)-SWCNTs (880nm emission) from mixed SWCNT samples is developed. It enables imaging them in the NIR with high-resolution standard Si-based cameras (>50× more pixels). (6,4)-SWCNTs modified with (GT)10 -ssDNA become highly sensitive to the important neurotransmitter dopamine. These sensors are 1.7× brighter and 7.5× more sensitive and allow fast imaging (<50ms). They enable high-resolution imaging of dopamine release from cells. Thus, the assembly of biosensors from (6,4)-SWCNTs combines the advantages of nanosensors working in the NIR with the sensitivity of (Si-based) cameras and enables broad usage of these nanomaterials.

Taming the Pseudoelastic Response of Nitinol Using Ion Implantation

Implantation of Ni50.5Ti49.5 wire with 30 MeV Ni6+ ions at doses (< 0.1 DPA) typically smaller than employed in the literature is shown to systematically alter the pseudoelastic response, with extrema in Berkovich nanoindentation load (+50%), hysteresis (−60%), and recoverable displacement (−19%) occurring at ∼ 3.6 μm below the implantation surface. These extraordinary values are attributed to ∼ 10 to 20 nm amorphous clusters that constrain the stress-induced B2-B19′ phase transformation. This is substantiated by phase field simulations of crystalline-amorphous composites and molecular dynamics simulations of crystalline-vacancy cluster composites showing the spatial refinement of martensite caused by nm-scale defects. The results suggest that ion implantation may potentially expand the processing and performance space for NiTi, by creating amorphous defects at smaller length scales than dislocation substructures produced by conventional deformation processing.

Magnetically locked Janus particle clusters with orientation-dependent motion in AC electric fields.

Active particles, or micromotors, locally dissipate energy to drive locomotion at small length scales. The type of trajectory is generally fixed and dictated by the geometry and composition of the particle, which can be challenging to tune using conventional fabrication procedures. Here, we report a simple, bottom-up method to magnetically assemble gold-coated polystyrene Janus particles into "locked" clusters that display diverse trajectories when stimulated by AC electric fields. The orientation of particles within each cluster gives rise to distinct modes of locomotion, including translational, rotational, trochoidal, helical, and orbital. We model this system using a simplified rigid beads model and demonstrate qualitative agreement between the predicted and experimentally observed cluster trajectories. Overall, this system provides a facile means to scalably create micromotors with a range of well-defined motions from discrete building blocks.

Vibrational spectroscopy as a probe of heterogeneities within geochemical thin films on macro, micro, and nanoscales.

Minerals play a critical role in the chemistry occurring along the interface of different environmental systems, including the atmosphere/geosphere and hydrosphere/geosphere. In the past few decades, vibrational spectroscopy has been used as a probe for studying interfacial geochemistry. Here, we compare four different vibrational methods for probing physical and chemical features across different mineral samples and length scales, from the macroscale to nanoscale. These methods include Attenuated Total Reflection - Fourier Transform Infrared (ATR-FTIR), Optical Photothermal Infrared (O-PTIR), Atomic Force Microscopy-Infrared (AFM-IR) and micro-Raman spectroscopy. The emergence of these micro-spectroscopic probes has offered new insights into heterogeneities within geochemical thin films and particles. These developments represent an important step forward for analyzing environmental interfaces and thin films as often these are assumed to be physically and chemically homogeneous. By comparing and integrating data across these measurement techniques, new insights into sample differences and heterogeneities can be gained. For example, interrogation of the various mineral samples at smaller length scales is shown to be particularly informative in highlighting unique chemical environments, including for chemically complex, multicomponent samples such as Arizona Test Dust (AZTD), as well as differences due to crystal orientation.

Potential of environmental scanning electron microscopy and SAXS to determine structural insights of plant-based emulsions with increasing dry matter content

Plant-based emulsions with increasing dry matter content show a large range of structural features from atomic to macroscopic length scales, which may be examined with scattering techniques in reciprocal space and microscopic techniques in real space. In this contribution, we focus on plan-based emulsions in terms of mesoscopic structure, and report on the impact of temperature and humidity on the structure measured via environmental scanning electron microscopy (ESEM) in real space. Small angle x-ray scattering in reciprocal space extends the knowledge on structural properties on smaller length scales at different temperature. Decreasing the humidity for the ESEM experiments revealed structural properties of different products. Temperature decrease from room temperature to 5 °C showed emerging crystalline peaks during SAXS measurements.

Hypertemperature effects in heterogeneous media and thermal flux at small-length scales

&lt;abstract&gt;&lt;p&gt;We propose an enriched microscopic heat conduction model that can account for size effects in heterogeneous media. Benefiting from physically relevant scaling arguments, we improve the regularity of the corrector in the classical problem of periodic homogenization of linear elliptic equations in the three-dimensional setting and, while doing so, we clarify the intimate role that correctors play in measuring the difference between the heterogeneous solution (microscopic) and the homogenized solution (macroscopic). Moreover, if the data are of form $ f = {\rm div}\; {\boldsymbol{F}} $ with $ {\boldsymbol{F}} \in {\rm L}^{3}(\Omega, {\mathbb R}^3) $, then we recover the classical corrector convergence theorem.&lt;/p&gt;&lt;/abstract&gt;

Dielectric polarization-based separations in an ionic solution.

A novel non-electrophoretic, electric field-based separation mechanism capable of transporting ions based on their dielectric properties is presented here for the first time. Though this polarization-based mechanism behaves similarly to dielectrophoresis, the separation mechanism is remarkably very efficient at small length scales compared to any dielectrophoretic separation mechanism for particles. For an applied electric field of strength as low as ∼0.75 MV m-1 across a 100 μm channel, the working solute - sodium fluorescein - is shown to decrease in its concentration by ≈20% in electric field region relative to the non electric field region. The existing macroscopic theoretical models like electrohydrodynamics and equilibrium thermodynamics are shown to underestimate the concentration change by two orders of magnitude for the same electric field strength. This surprisingly large difference between theory and experimental results suggests that the electric field-based equilibrium thermodynamic model lacks a key physics.

Patchy particle insights into self-assembly of transparent, graded index squid lenses.

Squids have spherical, gradient index lenses that maximize optical sensitivity while minimizing light scattering and geometric aberration. Previous studies have shown that the constituent lens proteins behave like patchy particles, and that a density gradient of packing fraction ∼0.01 to 1 assembles from a gradient of average particle valence, 〈M〉 ≈ 2.1 to 〈M〉 > 6. A priori, transparency requires that all regions within the larger gradient must minimize density fluctuations at length scales close to the wavelength of visible light. It is not known how a material can achieve this at all possible packing fractions via attractive interactions. We also observe that the set of proteins making the lens is remarkably polydisperse (there are around 40 isoforms expressed). Why does nature employ so many geometrically similar isoforms when theory suggests a few would suffice, and what, if any, is the physical role of the polydispersity? This study focuses on answering these questions for the sparsest regions of the lens, where the patchy nature of the system will have the largest influence on the final structure. We first simulated mixtures of bi- and trivalent patchy particles and found a strong influence of patch angle on the percolation and gel structure of the system. We then investigated the influence of the interaction polydispersity on the structure of the M = 2.1 system. We find that increasing the variance in patch energies and single-patch angle appears to decrease the length scale of density fluctuations while also moving the percolation line to lower temperature. S-Crystallin geometry and polydispersity appear to promote regular percolation of a gel structure while also limiting density fluctuations to small length scales, thereby promoting transparency in the annealed structure.