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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Fractal Model for Drag Reduction on Multiscale Nonwetting Rough Surfaces

Rough surfaces in contact with a flow of fluid exhibit alternating no-slip and free shear boundary conditions at the solid–liquid and air–liquid interfaces, respectively, thereby potentially offering drag reduction benefits. The balance between the dynamic pressure in the flow and the restoring capillary pressure in the interasperity spaces determines the stability of the Cassie state of wettability and is a function of the relative extent of no-slip and free shear regions per unit surface area. In the present study, using a fractal representation of rough surface topography, an analytical model is developed to quantify the stability of the Cassie state of wettability as well as drag reduction and the friction factor for laminar flow in a rectangular channel between nonwetting multiscale rough surfaces. A systematic study is conducted to quantify the effects of fractal parameters of the surfaces and the flow Reynolds number on drag reduction and the friction factor. The studies are used to develop friction factor curves extending the classical Moody diagram to hydrophobic and superhydrophobic surfaces. On the basis of the studies, regime maps are derived for estimating the extent of drag reduction offered by hydrophobic and superhydrophobic surfaces, revealing that superhydrophobic surfaces do not always offer the best drag reduction performance. The application of the fractal model to practical topographies of nonwetting surfaces of copper, aluminum, and zinc oxide fabricated via electrodeposition and etching is also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation

In geoenergy applications, mudrocks prevent fluids to leak from temporary (H 2 , CH 4 ) or permanent (CO 2 , radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Skyrmion‐Excited Spin‐Wave Fractal Networks

Magnetic skyrmions exhibit unique, technologically relevant pseudo-particle behaviors which arise from their topological protection, including well-defined, 3D dynamic modes that occur at microwave frequencies. During dynamic excitation, spin waves are ejected into the interstitial regions between skyrmions, creating the magnetic equivalent of a turbulent sea. However, since the spin waves in these systems have a well-defined length scale, and the skyrmions are on an ordered lattice, ordered structures from spin-wave interference can precipitate from the chaos. This work uses small-angle neutron scattering (SANS) to capture the dynamics in hybrid skyrmions and investigate the spin-wave structure. Performing simultaneous ferromagnetic resonance and SANS, the diffraction pattern shows a large increase in low-angle scattering intensity, which is present only in the resonance condition. This scattering pattern is best fit using a mass fractal model, which suggests the spin waves form a long-range fractal network. The fractal structure is constructed of fundamental units with a size that encodes the spin-wave emissions and are constrained by the skyrmion lattice. Furthermore, these results offer critical insights into the nanoscale dynamics of skyrmions, identify a new dynamic spin-wave fractal structure, and demonstrate SANS as a unique tool to probe high-speed dynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Sea Ice Rheology Experiment (SIREx): 1. Scaling and Statistical Properties of Sea-Ice Deformation Fields

As the sea-ice modeling community is shifting to advanced numerical frameworks, developing new sea-ice rheologies, and increasing model spatial resolution, ubiquitous deformation features in the Arctic sea ice are now being resolved by sea-ice models. Initiated at the Forum for Arctic Modeling and Observational Synthesis, the Sea Ice Rheology Experiment (SIREx) aims at evaluating state-of-the-art sea-ice models using existing and new metrics to understand how the simulated deformation fields are affected by different representations of sea-ice physics (rheology) and by model configuration. Part 1 of the SIREx analysis is concerned with evaluation of the statistical distribution and scaling properties of sea-ice deformation fields from 35 different simulations against those from the RADARSAT Geophysical Processor System (RGPS). For the first time, the viscous-plastic (and the elastic-viscous-plastic variant), elastic-anisotropic-plastic, and Maxwell-elasto-brittle rheologies are compared in a single study. We find that both plastic and brittle sea-ice rheologies have the potential to reproduce the observed RGPS deformation statistics, including multi-fractality. Model configuration (e.g., numerical convergence, atmospheric representation, spatial resolution) and physical parameterizations (e.g., ice strength parameters and ice thickness distribution) both have effects as important as the choice of sea-ice rheology on the deformation statistics. It is therefore not straightforward to attribute model performance to a specific rheological framework using current deformation metrics. In light of these results, we further evaluate the statistical properties of simulated Linear Kinematic Features in a SIREx Part 2 companion paper.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A viscoelastic model for seismic attenuation using fractal mechanical networks

SUMMARY Seismic attenuation (quantified by the quality factor Q) has a significant impact on the seismic waveforms, especially in the fluid-saturated rocks. This dissipative process can be phenomenologically represented by viscoelastic models. Previous seismological studies show that the Q value of Earth media exhibits a nearly frequency-independent behaviour (often referred to as constant-Q in literature) in the seismic frequency range. Such attenuation can be described by the mathematical Kjartansson constant-Q model, which lacks of a physical representation in the viscoelastic sense. Inspired by the fractal nature of the pore fluid distribution in patchy-saturated rocks, here we propose two fractal mechanical network (FMN) models, that is, a fractal tree model and a quasi-fractal ladder model, to phenomenologically represent the frequency-independent Q behaviour. As with the classic viscoelastic models, the FMN models are composed of mechanical elements (spring and dashpots) arranged in different hierarchical patterns. A particular parametrization of each model can produce the same complex modulus as in the Kjartansson model, which leads to the constant-Q. Applying the theory to several typical rock samples, we find that the seismic attenuation signature of these rocks can be accurately represented by either one of the FMN models. Besides, we demonstrate that the ladder model in particular exhibits the realistic multiscale fractal structure of the saturated rocks. Therefore, the FMN models as a proxy could provide a new way to estimate the microscopic rock structure property from macroscopic seismic attenuation observation.

Geochemistry & Geophysics↗
DOE OSTI2020

Scaling Analysis of Two–Phase Flow in Fractal Permeability Fields

Fluid mixing in permeable media is essential in many practical applications. The mixing process is a consequence of velocity fluctuations owing to geological heterogeneities and mobility contrast of fluids. Heterogeneities in natural rocks are often spatially correlated, and their properties, such as permeability, may be described using fractal distributions. This work models the fractal characteristics of such permeability fields in which the covariance function is expressed as a power-law function. A generalized scaling relation is derived relating various fractal permeability fields using the magnitude of their fluctuations. Here, this relation reveals the self-similar behavior of two-phase flow in such permeable media. To that end, a recently developed, high-resolution numerical simulator is employed to validate the analytically derived scaling relations. Two flow problems are considered in which flow is governed by 1) a linear, and 2) a nonlinear transport equation. Due to the probabilistic representation of the fractal permeability fields, a sensitivity study is conducted for each flow scenario to determine the number of realizations required for statistical convergence. Scaling analysis is performed using ensemble averages of simulated saturation profiles and their mixing lengths. Results support the validity of the developed scaling relation across the range of investigated flow conditions at intermediate times. The dynamics of linear flow in the asymptotic regime is affected by the correlation structure of heterogeneity. In nonlinear flow, scaling behavior appears to be dominated by the degree of nonlinearity.

58 GEOSCIENCES↗
DOE OSTI2020

Kinetics Modeling for Design of Continuous Enzymatic Hydrolysis

Enzymatic hydrolysis of cellulose to monomeric sugars continues to be a limiting step in cost-effectively producing sugar and fermentation-based biofuels from biomass. In particular, the high cost of enzymes coupled with the long time-scale of reaction pose challenges to economic viability. Performing enzymatic hydrolysis in a continuous mode with enzyme recycle may provide a path towards substantially reduced costs for sugar production, but design and analysis are complicated by a lack of suitable kinetics models. Computationally attainable models, such as fractal-based models, require knowledge of the reaction-history of the biomass, and are thus only suitable for describing the batch reactions from which they are derived. Fundamental models, while potentially more generalizable, are often too computationally intensive to use in process or reactor modeling. In this work, a phenomenological rate model is proposed based on a two-phase substrate representation. Good agreement is seen between batch and continuous enzymatic hydrolysis (CEH) experiment data, which validates the model and enables us to solve for reactor design parameters, such as CEH reactor size and stream flow rates, based on process variables like yield. This model is integrated with techno-economic analysis software to explore economic sensitivities. Important design optimizations and tradeoffs are identified and quantified, including the relative cost imposed by rate slowdown from sugar inhibition versus the cost to remove and concentrate sugars at a lower concentration. It also identifies, high-leverage avenues for further exploration, such as increasing the maximum feasible solids concentration, and sustaining high membrane flux and reliability.

09 BIOMASS FUELS↗
DOE OSTI2025

Experimental Characterization of Hydrogen Diffusion in Shale Rocks for Geologic Storage Applications

As global energy systems undergo a transition to cleaner alternatives, geologic hydrogen storage has emerged as a promising solution for large-scale energy storage. A critical factor in determining the feasibility of this approach is the effectiveness of caprock formations, such as shale, in preventing hydrogen migration. This study investigates the diffusion behavior of hydrogen through shale to assess its suitability as a caprock for geologic hydrogen storage. Using a novel double-seal core holder design and a through-diffusion apparatus, hydrogen diffusion was measured through shale rock from the Eagle Ford and Wolfcamp Formations under dry conditions. These measurements were complemented by microstructural and mineralogical analyses using low-pressure nitrogen adsorption and X-ray diffraction. The effective diffusion coefficient of hydrogen in these shale caprocks ranged from 2.51 × 10 –8 to 9.85 × 10 –8 m 2 /s. Notably, we observed that the diffusion behavior was more related to the pore network structure and could not be attributed to differences in the total pore volume between shale types alone. Here, to further understand the role of pore network complexity, a fractal pore model was developed to correlate tortuosity with the fractal dimension of the pore structure (a measure of pore network complexity). The proposed model closely matched tortuosity values obtained from diffusion experiments, outperforming existing theoretical tortuosity–porosity correlations. These findings provide key quantitative parameters needed to assess the feasibility of geologic hydrogen storage as well as insights that can be applied to hydrogen storage in a range of geologic formations.

08 HYDROGEN↗
DOE OSTI2022

Fractionalization of subsystem symmetries in two dimensions

The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go arguments, we show that subsystem symmetry fractionalization is not possible in many cases due to the additional rigid geometric structure of the symmetries. However, we identify a mechanism that allows fractionalization, involving global relations between macroscopically many symmetry generators. We find that anyons can fractionalize such relations, meaning that the total charge carried under all generators involved in the global relation is nontrivial, despite the fact that these generators multiply to the identity. We first discuss the general algebraic framework needed to characterize this type of fractionalization, and then explore this framework using a number of exactly solvable models with Z 2 topological order, including models having line and fractal symmetries. These models all showcase another necessary property of subsystem symmetry fractionalization: Fractionalized anyons must have restricted mobility when the symmetry is enforced, such that they are confined to a single line or point in the case of line and fractal symmetries, respectively. Looking forward, we expect that our identification of the importance of global relations in fractionalization will hold significance for the classification of phases with subsystem symmetries in all dimensions.

2-dimensional systems↗
DOE OSTI2026

Analytical desmearing of Bonse–Hart ultra-small-angle neutron scattering data via truncated Abel inversion

A non-iterative analytical framework based on the truncated Abel inversion is developed for desmearing Bonse–Hart ultra-small-angle neutron scattering (USANS) data. The method directly inverts the slit-averaged intensity without empirical extrapolation or iterative regularization, establishing a closed-form relationship between the measured and intrinsic scattering profiles. Numerical benchmarks on representative models, including a rigid-line form factor, a Lorentzian function and a fractal structural model, demonstrate quantitative recovery of the ground-truth intensity across the full Q range. Application to a deuterated polystyrene/poly(2-vinylpyridine) blend further confirms that the approach yields smooth continuous profiles consistent with companion small-angle neutron scattering data. The truncated Abel inversion thus provides a stable, model-independent and physically transparent route for accurate desmearing of Bonse–Hart USANS measurements.

Huang, Guan-Rong [National Tsing Hua University, T↗
DOE OSTI2024

Fractal analysis on Ag 2 O thin film using a data-driven approach

The synthesis of fractal Ag oxide (Ag 2 O) on the surface of Ag thin film has been achieved at room temperature by using Synchrotron X-ray irradiation. We have performed an automated quantitative analysis of a batch of 1879 fractal Ag 2 O patterns in a scanning electron microscopy (SEM) image within a radius of 2000 mm outward from the center of the X-ray beam. The morphology is similar to that of the diffusion-limited cluster aggregation (DLCA) model. The fractal dimension (D) of Ag 2 O is between 1.7 and 1.5 from the center to the edge. The area distribution density of fractal Ag 2 O follows a quadratic function with radius R. It is found that the branches’ number of fractal Ag 2 O is a key factor affecting the fractal dimension. The more branches the fractal has, the greater the D is. This is the first time that Ag fractal has been investigated by combining automated data analysis methods with batch experimental data. This data-driven approach provides a new research perspective for rationally regulating materials’ fractal morphology and performance.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Soot-particle core-shell and fractal structures from small-angle X-ray scattering measurements in a flame

We have characterized soot particles measured in situ in a laminar co-flow ethylene-air diffusion flame using small-angle X-ray scattering (SAXS). The analysis includes temperature measurements made with coherent anti-Stokes Raman spectroscopy (CARS) and complements soot volume-fraction and maturity measurements made with laser-induced incandescence (LII). We compared the results of fits to the SAXS measurements using a unified model and a fractal core-shell model. Power-law parameters yielded by the unified model indicate that aggregates of primary particles are in the mass-fractal regime, whereas the primary particles are in the surface-fractal regime in the middle of the flame. Higher and lower in the flame, the primary-particle power-law parameter approaches 4, suggesting smooth primary particles. Furthermore, these trends are consistent with fits using the fractal core-shell model, which indicate that particles have an established core-shell structure in the middle of the flame and are internally homogeneous at higher and lower heights in the flame. Primary-particle size distributions derived using the fractal core-shell model demonstrate excellent agreement with distributions inferred from transmission electron microscopy (TEM) images in the middle of the flame. Higher in the flame, a second small mode appears in the size distributions, suggesting particle fragmentation during oxidation. Surface oxidation would explain (1) aggregate fragmentation and (2) loss of core-shell structure leading to smoother primary-particle surfaces by removal of carbon overlayers. SAXS measurements are much more sensitive to incipient and young soot particles than LII and demonstrate significant volume fraction from particles low in the flame where the LII signal is negligible.

42 ENGINEERING↗
DOE OSTI2021

Dynamics of a fractal set of first-order magnetic phase transitions in frustrated Lu 2 CoMnO 6

The axial next-nearest-neighbor Ising model predicts a fractal (infinite) set of phases with incommensurate wave vectors that are separated by first-order phase boundaries. This complexity results from a simple frustration condition between nearest- and next-nearest-neighbor interactions along a chain of Ising spins. Using x-ray photon correlation spectroscopy (XPCS), we investigate the surprising antiferromagnetic dynamics that emerge from such a complex phase diagram over a wide range of temperatures. In this work, we present XPCS measurements of the frustrated magnetic chain compound Lu 2 CoMnO 6 and Monte Carlo simulations. Incommensurate magnetic Bragg peaks slide towards commensurate “up-up-down-down” spin order with decreasing temperature and increasing time. Both simulation and experiment support a counterintuitive “upside-down” temperature dependence of the magnetic dynamics: at higher temperatures in the region of first-order phase boundaries, slower dynamics are observed where the speckle maintains its coherence. At the lowest temperatures, where part of the sample adopts commensurate order, the dynamics speed up and result in fast decoherence.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Incorporating long-range dependence and fractal features in turbulence spectra

We introduce an advanced turbulence spectrum model developed from mathematical foundations from a covariance function class and empirically validated using extensive field data. This model captures the complex dynamics of long-range dependence, and fractal characteristics prevalent in riverine and atmospheric boundary layer (ABL) flows that are ignored by classical spectrum models, such as IEC (International Electrotechnical Commission) von Kármán and Kaimal model. The model delineates scaling behaviors across distinct frequency bands and offers substantial flexibility through five well-defined parameters each characterizing a distinct physical aspect of the velocity time series. A detailed procedure for obtaining each parameter from time series data is outlined. The comprehensive validations with field data from tidal currents and ABL flows substantiate the model’s fidelity in accurately replicating observed phenomena. This validation establishes the reliability of the proposed model and, when incorporated into stochastic full-field simulators such as TurbSim, demonstrates its potential to advance the predictive modeling and analysis of turbulent flows in environmental science and engineering contexts.

Cheng, Shyuan [Univ. of Illinois at Urbana-Champai↗
DOE OSTI2020

Cellular Response to Proton Irradiation: A Simulation Study with TOPAS-nBio

The cellular response to ionizing radiation continues to be of significant research interest in cancer radiotherapy, and DNA is recognized as the critical target for most of the biologic effects of radiation. Incident particles can cause initial DNA damages through physical and chemical interactions within a short time scale. Initial DNA damages can undergo repair via different pathways available at different stages of the cell cycle. The misrepair of DNA damage results in genomic rearrangement and causes mutations and chromosome aberrations, which are drivers of cell death. This work presents an integrated study of simulating cell response after proton irradiation with energies of 0.5–500 MeV (LET of 60–0.2 keV/µm). A model of a whole nucleus with fractal DNA geometry was implemented in TOPAS-nBio for initial DNA damage simulations. The default physics and chemistry models in TOPAS-nBio were used to describe interactions of primary particles, secondary particles, and radiolysis products within the nucleus. The initial DNA double-strand break (DSB) yield was found to increase from 6.5 DSB/Gy/Gbp at low-linear energy transfer (LET) of 0.2 keV/µm to 21.2 DSB/Gy/Gbp at high LET of 60 keV/µm. A mechanistic repair model was applied to predict the characteristics of DNA damage repair and dose response of chromosome aberrations. It was found that more than 95% of the DSBs are repaired within the first 24 h and the misrepaired DSB fraction increases rapidly with LET and reaches 15.8% at 60 keV/µm with an estimated chromosome aberration detection threshold of 3 Mbp. The dicentric and acentric fragment yields and the dose response of micronuclei formation after proton irradiation were calculated and compared with experimental results.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

Analysis of convection heat transfer on multiscale rough superhydrophobic and liquid infused surfaces

Multiscale rough superhydrophobic or slippery liquid infused porous surfaces have gained much interest in recent years for their improved transport phenomena properties. While there have been several studies on drag reduction and condensation on non-wetting surfaces, convection heat transfer that is important in many thermal and thermochemical applications has not been addressed systematically. Here, this article utilizes a fractal description of rough surface topographies to develop analytical models for the Nusselt number and the thermal hydraulic factor for fluid flow and heat transfer inside a cylinder with non-wetting surfaces. For air-infused superhydrophobic surfaces, the model considers the dynamic stability of the air/fluid interface in the asperities. Using the analytical formulations and the stability criteria, systematic studies are presented on the effects of the fractal surface parameters, cylinder radius and Reynolds number on the convective heat transfer characteristics, from which surface texture design maps are developed for maximizing the convection heat transfer. It is shown that multiscale non-wetting surfaces are most effective in the range of lower Reynolds number and small cylinder radius for achieving the best convective heat transfer and thermal hydraulic performance. Applying the models to actual non-wetting surface topographies fabricated using electrodeposition and chemical etching, it is shown that contrary to prevailing notion, superhydrophobicity, characterized by the highest contact angles, does not always lead to the maximum convective heat transfer performance, and that under certain fluid flow conditions, hydrophobic surfaces may offer a greater thermal performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗