Small Length Scales Research Articles

An adaptive numerical method for simulating diffusion flame jets

In this paper, we present an adaptive numerical methodology for a reacting three-dimensional low-Mach number flow. This computational strategy combines an adaptive mesh refinement (AMR), an implicit–explicit time stepping strategy (IMEX), an extension of increment-pressure projection method, and a mixture fraction to model the chemistry combustion dynamics. To accurately resolve sharp gradients, vorticity shedding, and localized small length scale flow features, dynamic adaptive mesh refinement (given by hierarchical nested Cartesian grid patches) is employed. That spatial dynamic adaptation is used in conjunction with a variable time step, second-order, linearly implicit time integration scheme. The capabilities of the present numerical method are demonstrated by numerical verification and simulation of two classical diffusion flame examples from literature.

Electric current-assisted manipulation of liquid metals using a stylus at micro-and nano-scales

A novel methodology, based on wetting and electromigration, for transporting liquid metal, over long distances, at micro-and nano-scale using a stylus is reported. The mechanism is analogous to a dropper that uses ‘suction and release’ actions to ‘collect and dispense’ liquid. In our methodology, a stylus coated with a thin metal film acts like the dropper that collects liquid metal from a reservoir upon application of an electric current, holds the liquid metal via wetting while carrying the liquid metal over large distances away from the reservoir and drops it on the target location by reversing the direction of electric current. Essentially, the working principle of the technique relies on the directionality of electromigration force and adhesive force due to wetting. The working of the technique is demonstrated by using an Au-coated Si micropillar as the stylus, liquid Ga as the liquid metal to be transported, and a Kleindiek-based position micro-manipulator to traverse the stylus from the liquid reservoir to the target location. For demonstrating the potential applications, the technique is utilized for closing a micro-gap by dispensing a minuscule amount of liquid Ga and conformally coating the desired segment of the patterned thin films with liquid Ga. This study confirms the promising potential of the developed technique for reversible, controlled manipulation of liquid metal at small length scales.

Size Dependent Buckling Analysis of a FG-CNTRC Microplate of Variable Thickness under Non-Uniform Biaxial Compression

This paper combines third-order shear deformation theory (TSDT) and modified couple stress theory (MCST) with the principle of total potential energy to analyze the size-dependent buckling behavior of a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular microplate of variable thickness subject to non-uniform biaxial compression when resting on an elastic medium. To determine the thickness qualities of the material, the extended rule of mixture was applied. In the context of microplate buckling in the presence of small length scale effects, the three kinds of Carbon Nanotube (CNT) distribution—(a) UD, (b) FG-O, and (c) FG-X—were used and compared. The equations governing various combinations of simply supported or clamped boundary conditions have been solved using the differential quadrature method (DQM). The correctness and precision of the solutions have been compared to another study. A numerical study was conducted to examine the dependence of buckling load on several parameters, including percentage change of thickness, length scale parameter, nonuniform edge loads, boundary conditions, volume percentage of the CNTs, CNT distribution, and elastic medium parameter. The results of their effects are presented in this paper.

Dispersion of Molecular Patterns Written in Turbulent Air.

We study the dispersion of tiny molecular clouds in turbulence by writing patterns in turbulent air and following their deformation in time. The writing is done by fusing O_{2} and N_{2} molecules into NO in the focus of a strong ultraviolet laser beam. By crossing several of these laser beams, patterns that have both small and large scales can be painted. The patterns are visualized a while later by inducing fluorescence of the NO molecules with a second UV laser and registering the image. The width of the lines that make the pattern is approximately 50 μm, a few times the Kolmogorov length η, the smallest length scale in turbulence, while the overall size of the patterns (≈4 mm) is inside the inertial range of the used turbulent jet flow. At small scales molecular clouds disperse under the joint action of molecular diffusion and turbulence. The experiments reveal for the first time this subtle, yet very important interaction. At macroscales (≈200 η) we verify the Batchelor dispersion of objects whose size is inside the inertial range; however, the expected influence of molecular diffusion is smaller than the accuracy of the experiments.

Propagation of vortex symmetric Airy beam in the turbulent link

The vortex symmetric Airy beam (VSAB) which couples the autofocusing symmetric Airy beam (SAB) and topological charge can provide new possibilities for the optical carrier of free space optical communication (FSOC). This paper focuses on the performance of VSAB propagating through turbulent link. Based on the wave optics simulation, the model of VSAB propagating in atmospheric turbulence is constructed. By using the model, the evaluation parameters light intensity and aperture averaged scintillation of VSAB are calculated. The influence of different beam parameters on the characteristics of VSAB propagation in turbulent link is investigated. The results show that the VSAB with small decaying factor, small transverse length scales and less topological charge has more advantage in turbulence resistance.

Rapid nanometer-precision autocorrelator.

The precise measurement of a target depth has applications in biophysics and nanophysics, and non-linear optical methods are sensitive to intensity changes on very small length scales. By exploiting the high sensitivity of an autocorrelator's dependency on path length, we propose a technique that achieves ≈30 nm depth precision for each pixel in 30 seconds. Our method images up-converted pulses from a non-linear crystal using a sCMOS (scientific Complementary Metal-Oxide-Semiconductor) camera and converts the intensity recorded by each pixel to a delay. By utilising statistical estimation theory and using the data from a set of 32×32 pixels, the standard error (SE) of the detected delay falls below 1 nm after 30 seconds of measurement. Numerical simulations show that this result is extremely close to what can be achieved with a shot-noise-limited source and is consistent with the precision that can be achieved with a sCMOS camera.

Structural Chirality of Polar Skyrmions Probed by Resonant Elastic X-Ray Scattering.

An escalating challenge in condensed-matter research is the characterization of emergent order-parameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.

Multi-Defect Detection in Additively Manufactured Lattice Structures Using 3D Electrical Resistance Tomography

Cellular lattice structures possess high strength-to-weight ratios suitable for advanced lightweight engineering applications. However, their quality and mechanical performance can degrade because of defects introduced during manufacturing or in-service. Their complexity and small length scale features make defects difficult to detect using conventional nondestructive evaluation methods. Here we propose a current injection-based method, electrical resistance tomography (ERT), that can be used to detect damaged struts in conductive cellular lattice structures with their intrinsic electromechanical properties. The reconstructed conductivity distributions from ERT can reveal the severity and location of damaged struts without having to probe each strut. However, the low central sensitivity of ERT may result in image artifacts and inaccurate localization of damaged struts. To address this issue, this study introduces an absolute, high throughput, conductivity reconstruction algorithm for 3D ERT. The algorithm incorporates a strut-based normalized sensitivity map to compensate for lower interior sensitivity and suppresses reconstruction artifacts. Numerical simulations and experiments on fabricated representative cellular lattice structures were performed to verify the ability of ERT to quantitatively identify single and multiple damaged struts. The improved performance of this method compared with classical ERT was observed, based on greatly decreased imaging and reconstructed value errors.

Using mesoporous thin films as nano-micro-fluidic tools

Achieving active control on small amounts of liquids represents a substantial challenge in both scientific and engineering aspects. Imbibition of fluids in bodies with nanoscale dimensions enables the spontaneous propelling of nano-flows because of the powerful capillarity at small-length scales. Peculiarities of nanopore imbibition at the thin film level lead to distinctive capillary transport phenomena of fluids across the nanopore matrix. This particular imbibition also impacts on the behavior of the in-contact liquid micro-volumes. These both features add versatile alternatives to the high interest in the management of femtolitre to microlitres amounts of liquids. Herein, we show a brief discussion-outlook based on recent advances in the design of versatile tools to attain programmable nano/microfluidics using mesoporous thin film platforms. Cited as: Berli, C. L. A., Bellino, M. G. Using mesoporous thin films as nano-micro-fluidic tools. Capillarity, 2022, 5(6): 123-127. https://doi.org/10.46690/capi.2022.06.03

Atomic-to-Continuum Multiscale Modeling of Defects in Crystals With Nonlocal Electrostatic Interactions

Abstract This work develops a multiscale modeling framework for defects in crystals with general geometries and boundary conditions in which ionic interactions are important, with potential application to ionic solids and electric field interactions with materials. The overall strategy is posed in the framework of the quasicontinuum multiscale method; specifically, the use of a finite element inspired kinematic description enables a significant reduction in the large number of degrees-of-freedom to describe the atomic positions. The key advance of this work is a method for the efficient and accurate treatment of nonlocal electrostatic charge–charge interactions without restrictions on the geometry or boundary conditions. Electrostatic interactions are long range with slow decay and hence require consideration of all pairs of charges making a brute-force approach computationally prohibitive. The method proposed here accounts for the exact charge–charge interactions in the near-field and uses a coarse-grained approximation in the far-field. The coarse-grained approximation and the associated errors are rigorously derived based on the limit of a finite body with a small periodic lengthscale, thereby enabling the errors in the approximation to be controlled to a desired tolerance. The method is applied to a simple model of gallium nitride, and it is shown that electrostatic interactions can be approximated with a desired level of accuracy using the proposed methodology.

Structure functions for optical waves in a complex medium of turbulent biological tissues.

Although optical wave propagation is investigated based on the absorption and scattering in biological tissues, the turbulence effect can also not be overlooked. Here, the closed-form expressions of the wave structure function (WSF) and phase structure function (PSF) of plane and spherical waves propagating in biological tissue are obtained to help with future research on imaging, intensity, and coherency in turbulent biological tissues. This paper presents the effect of turbulent biological tissue on optical wave propagation to give a perception of the performance of biomedical systems that use optical technologies. The behavior of optical waves in different types of turbulent biological tissues such as a liver parenchyma (mouse), an intestinal epithelium (mouse), a deep dermis (mouse), and an upper dermis (human) are investigated and compared. It is observed that turbulence becomes more effective with an increase in the characteristic length of heterogeneity, propagation distance, and the strength of the refractive index fluctuations. However, an increase in the fractal dimension, wavelength, and small length scale factor has a smaller turbulence effect on the propagating optical wave. We envision that our results may be used to interpret the performance of optical medical systems operating in turbulent biological tissues.

Bicontinuous Nanoporous Metals with Self-Organized Functionalities

The functional applications of bicontinuous nanoporous metals have been rapidly growing along with the fabrication methods of the materials. Besides the most common routes of electrochemical dealloying, liquid-metal dealloying, vapor-phase dealloying, and reduction-induced decomposition, all via similar mechanisms of interface-controlled self-organization have created a broad range of nanoporous structures made of noble metals (e.g., Au and Pt), refractory metals (e.g., Ti and Ta), and reactive metals (e.g., Al and Zn). They in turn enable new applications in catalysis, sensing, actuation, and electrochemical energy storage. Underlying the burgeoning development is the close connection between the functionalities and the structural evolution mechanism. In this perspective, I will dissect the structural complexity of bicontinuous nanoporous metal into three key features: the bicontinuity, the small length scale, and the compositional heterogeneity. I will discuss their roots in the self-organization process and their ties to properties such as mechanical strength, conductivity, and catalytic activity. The analysis will be centered around two aspects of the dealloying theory, namely, percolation and surface diffusion, showing how they can be applied to quantitatively understand the self-organized functionalities. In the end, I will also highlight emerging opportunities for structural designs to further advance the functional applications of the materials.

Elongational viscosity of poly(propylene carbonate) melts: tube-based modelling and primitive chain network simulations

In fast elongational flows, linear polymer melts exhibit a monotonic decrease of the viscosity with increasing strain rate, even beyond the contraction rate of the polymer defined by the Rouse time. We consider two possible explanations of this phenomenon: (a) the reduction of monomeric friction and (b) the reduction of the tube diameter with increasing deformation leading to an Enhanced Relaxation of Stretch (ERS) on smaller length scales. (Masubuchi et al. (2022) reported Primitive Chain Network (PCN) simulations using an empirical friction reduction model depending on segmental orientation and could reproduce the elongational viscosity data of three poly(propylene carbonate) melts and a polystyrene melt. Here, we show that the mesoscopic tube-based ESR model (Wagner and Narimissa 2021) provides quantitative agreement with the same data set based exclusively on the linear-viscoelastic characterization and the Rouse time. From the ERS model, a parameter-free universal relation of monomeric friction reduction as a function of segmental stretch can be derived. PCN simulations using this friction reduction relation are shown to reproduce quantitatively the experimental data even without any fitting parameter. The comparison with results of the earlier PCN simulation results with friction depending on segmental orientation demonstrates that the two friction relations examined work equally well which implies that the physical mechanisms of friction reduction are still open for discussion.

Asymptotic behaviour of rotating convection-driven dynamos in the plane layer geometry

Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ( $E$ ), magnetic Prandtl number ( $Pm$ ) and Rayleigh number ( $Ra$ ). The primary purpose of the investigation is to compare results of the simulations with previously developed asymptotic theory that is applicable in the limit of rapid rotation. We find that all of the simulations are in the quasi-geostrophic regime in which the Coriolis and pressure gradient forces are approximately balanced at leading order, whereas all other forces, including the Lorentz force, act as perturbations. Agreement between simulation output and asymptotic scalings for the energetics, flow speeds, magnetic field amplitude and length scales is found. The transition from large-scale dynamos to small-scale dynamos is well described by the magnetic Reynolds number based on the small convective length scale, $\widetilde {Rm}$ , with large-scale dynamos preferred when $\widetilde {Rm} \lesssim O(1)$ . The magnitude of the large-scale magnetic field is observed to saturate and become approximately constant with increasing Rayleigh number. Energy spectra show that all length scales present in the flow field and the small-scale magnetic field are consistent with a scaling of $E^{1/3}$ , even in the turbulent regime. For a fixed value of $E$ , we find that the viscous dissipation length scale is approximately constant over a broad range of $Ra$ ; the ohmic dissipation length scale is approximately constant within the large-scale dynamo regime, but transitions to a $\widetilde {Rm}^{-1/2}$ scaling in the small-scale dynamo regime.

Wind tunnel research, dynamics, and scaling for wind energy

The interaction of wind turbines with turbulent atmospheric boundary layer (ABL) flows represents a complex multi-scale problem that spans several orders of magnitudes of spatial and temporal scales. These scales range from the interactions of large wind farms with the ABL (on the order of tens of kilometers) to the small length scale of the wind turbine blade boundary layer (order of a millimeter). Detailed studies of multi-scale wind energy aerodynamics are timely and vital to maximize the efficiency of current and future wind energy projects, be they onshore, bottom-fixed offshore, or floating offshore. Among different research modalities, wind tunnel experiments have been at the forefront of research efforts in the wind energy community over the last few decades. They provide valuable insight about the aerodynamics of wind turbines and wind farms, which are important in relation to optimized performance of these machines. The major advantage of wind tunnel research is that wind turbines can be experimentally studied under fully controlled and repeatable conditions allowing for systematic research on the wind turbine interactions that extract energy from the incoming atmospheric flow. Detailed experimental data collected in the wind tunnel are also invaluable for validating and calibrating numerical models.

Dependency of Mesoscale Organization on Grid Anisotropy in Large‐Eddy Simulations of Convective Boundary Layers at Gray Zone Resolutions

AbstractA new generation of operational atmospheric models operating at horizontal resolutions in the range 200 m ∼ 2 km is becoming increasingly popular for operational use in numerical weather prediction and climate applications. Such grid spacings are becoming sufficiently fine to resolve a fraction of the turbulent transports. Here we analyze Large‐eddy simulation results of a convective boundary layer obtained by coarsening horizontal grid spacings up to 800 m. The aim is to explore the dependency of the mean state and turbulent fluxes on the grid resolution. Both isotropic and anisotropic eddy diffusion approaches are evaluated, where in the latter case the horizontal and vertical eddy diffusivities differ in accord with their horizontal and vertical grid spacings. For coarsening horizontal grid sizes entrainment at the top of the boundary layer tends to get slightly enhanced for isotropic diffusion, whereas for the anisotropic diffusion approach the vertically well‐mixed boundary‐layer structure becomes severely degraded. An analysis of the energy spectrum shows that anisotropic diffusion causes relatively more dissipation of variance at smaller length scales. This leads, in turn, to a shift of spectral energy toward larger length scales that also becomes apparent from a rather different kind of spatial organization of convection. The present study therefore suggests that details with regards to the representation of processes at small scales might impact the organization at length scales much larger than the smallest scales that can be resolved by the model.

Probing horizon scale quantum effects with Love

Future gravitational wave (GW) detectors have been projected to be able to probe the nature of compact objects in great detail. In this work, we study the potential observability of the small length scale physics near black hole horizon with the tidal deformability of the compact objects in an inspiraling binary. We find that it is possible to probe them with extreme mass ratio inspirals. We discuss how the quantum effects can affect the GW observables. This as a consequence is bound to shape our understanding of the quantum scale near the horizon.

Upscaling the Poisson–Nernst–Planck equations for ion transport in weakly heterogeneous charged porous media

The Poisson–Nernst–Planck (PNP) equations govern the continuum level description of ions in electrolytes and especially the impact of charged surfaces. In numerous applications such surfaces are complex, varying on a small lengthscale compared to the overall scale of the system, often prohibiting the direct prediction of the osmotic swelling pressures induced by ion behaviours in Debye layers near surfaces. With periodicity, upscaling techniques can be readily used to determine the behaviour of the swelling pressure on large lengthscales without solving the PNP equations on the complex domain, though generalising to cases where the periodicity is only approximate is more challenging. Here, we generalise a method by Bruna and Chapman (2015) for upscaling a non-periodic diffusion equation to the PNP equations. After upscaling, we find a rational derivation of the swelling pressure closely resembling the classical, though phenomenological, use of Donnan membrane theory predictions for the swelling pressure in cartilage, together with a novel contribution driven by heterogeneous fixed (surface) charges. The resulting macroscale model is also shown to be thermodynamically consistent, though its comparison with a recent upscaled models for swelling pressure in cartilage mechanics emphasises the need to understand how macroscale models depend on differing upscaling techniques, especially in the absence of perfect periodicity.

Nucleation and growth of crystals inside polyethylene nano-droplets.

Polymer crystallization is a long-standing interesting problem both in fundamental polymer physics and in polymer manufacturing. Fundamentally, the connectivity of the macromolecules provides a unique feature for the study of nucleation and growth of crystals in contrast to the crystallization of smaller molecules. In addition, understanding the crystallization in polymers is industrially important due to the necessity of its control to achieve mechanically durable plastic materials. Molecular dynamics simulations offer a suitable way of studying this phenomenon due to their capability to probe the small time and length scales that are characteristic of nucleation. In this paper, we use a long alkane chain model to study nucleation and the growth of polyethylene crystals both within bulk and nano-droplets whose diameters range from about 6 to 11nm. It is found that the droplets approach being more spherical during the nucleation whereas they deviate from this shape during the growth regime. Strikingly, a mean first passage time analysis indicates that the nucleation rate per unit volume decreases as the droplet size is increased. Finally, visual inspection of the simulation snapshots suggests that nuclei majorly emerged from the surface of the droplets.

Editorial: theme issue on complex rheology in biological systems

Editorial: theme issue on complex rheology in biological systems