Global Volume Fraction Research Articles

Microstructure-based prediction of hydrodynamic forces in stationary particle assemblies

In this work, we derive novel hydrodynamic force models to describe the interaction of a flow with particles in an assembly when only an averaged resolution of the flow is available. These force models are able to predict the average drag on the particle assembly, as well as the deviations from the average drag force and the lift force for each individual particle in the assembly. To achieve this, PR-DNS of various particle assemblies and flow regimes are carried out, varying the particle volume fraction up to 0.6, and the mean particle flow Reynolds number up to 300. To characterize the structure of the particles in the assembly, a Voronoi tessellation is carried out, and a number of scalars, vectors and tensors are defined based upon this tessellation. The microstructure informed hydrodynamic force models are based on symbolic regressions of these quantities derived from the Voronoi tessellation, the global particle volume fraction of the particle assembly and the flow regime represented by the Reynolds number, and the forces on the individual particles in the assembly.The resulting hydrodynamic force models are single expressions and can be directly employed in a Lagrangian particle tracking (LPT) or computational fluid dynamics/discrete element model (CFD/DEM) framework. By comparing the results of the newly proposed hydrodynamic force models with an averaged force model, as is usually adopted in Lagrangian particle tracking simulations, we show that, potentially, a significant increase in accuracy can be achieved, with only a relatively small increase in computational cost, compared to the cost of the CFD/DEM simulation.

Probabilistic fatigue strength assessment of cross-ply laminates: Exploring effects of manufacturing defects through a two-scale modeling approach

The study presents a two-scale modeling approach allowing for an efficient fatigue strength evaluation on a macro scale considering a micro-mechanical defect characterization of a Carbon Fiber Reinforced Polymer (CFRP) material. The modeling approach integrates a macro model with the effective elastic properties from micro-mechanical simulations considering voids. This enables the analysis of defects’ influence on material fatigue strength using a probabilistic weakest link approach. A CFRP laminate with a cross-ply layup was investigated. Two simulation case studies demonstrate the effect of void content and size on the characteristic fatigue strength. An experimental investigation was conducted testing the laminates in tension–tension fatigue verifying the predicted numerical behavior. The numerical models identify a difference in the characteristic fatigue strength consistent with the fatigue test results. It is numerically concluded that the investigated CFRP material’s fatigue strength is affected by the presence of voids and even with only a slight difference in the global void volume fraction a scatter in fatigue strength is identified.

Left ventricular cellular regression occurs without matrix changes at two months post aortic valve replacement in severe aortic stenosis

Abstract Funding Acknowledgements Type of funding sources: Foundation. Main funding source(s): British Heart Foundation Background Increased left ventricular mass (LVM) in severe aortic stenosis (AS) is a result of the combined expansion of myocardial cellular and extracellular compartments in response to chronic pressure overload. Upon relief of pressure overload by aortic valve replacement (AVR), LVM regresses significantly however patients remain at risk of post-AVR heart failure and mortality. T1 mapping, by cardiovascular magnetic resonance (CMR), can quantify the proportion of cellular and extracellular volume. Purpose We sought to determine the relative contributions of cellular and extracellular remodelling early after AVR to gain insight into potential post-AVR mechanisms of heart failure. Methods Patients with severe symptomatic AS underwent CMR (volumes, function, pre- and post-contrast T1 mapping using 0.1mmol/kg Dotarem) prior to and 8-weeks after surgical or transcatheter AVR. Global extracellular volume fraction (ECV%) was quantified from pre- and post-contrast T1 mapping and synthetic haematocrit. ECV% was used to calculate cellular compartment volume (CellVol) and extracellular volume (ECVol) from total LV volume (LVM/1.05[specific gravity of myocardium]). Segments with focal LGE were excluded from ECV% calculation. Statistical analysis was via paired t-test denoted by standard deviations (SD), or Wilcoxon signed-rank test with reported interquartile ranges (IQR). Results 27 patients (age 71.2 SD±9.8, male 70.3%) returned for repeat investigation at median 8.5 [IQR 7.1–11.6] weeks post-AVR (surgical: 16 / transcatheter: 11). Aortic valve peak velocity significantly improved (4.5 SD±0.5m/s to 2.4 SD±0.4m/s; p<0.001) alongside median NYHA class (2 [IQR 0] to 1 [IQR 0.5]; p<0.001). LVM regressed 10.3% (170.8 SD±36.6g to 153.2 SD±39g; P<0.001), which comprised of a 13.8% reduction in CellVol (134.8 SD±29.4mL to 116.2 SD±30.5mL; P<0.001). However, ECVol remained unchanged (44.4 SD±10.2mL to 44.7 SD±11.2mL; P=0.78) resulting in an ECV% increase of 3.1% (24.8 SD±2.4% to 27.9 SD±2.1%; P<0.001). Summary We show for the first time that the rapid early LVM reduction after AVR is driven entirely by regression of cardiomyocyte hypertrophy. The extracellular compartment volume is unchanged at two months post-AVR. This relative increase in the ratio of fibrosis and cell volume may result in early worsening myocardial stiffness and could be a contributing factor to post-AVR diastolic dysfunction and heart failure.

False diffusion, asymmetrical interface, and equilibrious state for pure solid-gallium phase change modeling by enthalpy-porosity methodology

Literature survey showed that three important and key scientific problems including: i) the mechanisms or underlying causes of the discrepant sources, especially at the top phase interfaces, are yet to be investigated, which are crucial to recognize the validation of the numerical technology for metal isothermal phase-change applications. Moreover, revisiting the well-known experiments in literature, they did ii) not display the interface shape under the conditions of aspect ratio = 0.714 & Stefan number = 0.0391 at the dimensionless time of 0.0184, but also iii) not discuss the equilibrium state of pure solid‑gallium phase change. Therefore, it is a fascinating and interesting concern that what happened for these two kinds of important problems or key questions ii) and iii). Here, all above-mentioned three problems i) to iii) are explored and addressed by finite-volume-based enthalpy-porosity methodology. The core findings in this work are that: i) The novel mechanisms of convective false diffusion are revealed and clarified for enthalpy-porosity modeling solid-liquid interface of pure solid‑gallium melting; ii) The novel phenomena of asymmetrical solid-liquid interface are found and explained for a large aspect ratio of 0.714; iii) The innovative findings and fitting correlations are discussed by extended literature’s study to phase-change equilibrium state, and it is comprehensively demonstrated that the dimensionless correlation of mean liquid layer thickness is equivalent to that of global liquid volume fraction.

Myocardial Tissue Characterization in Danon Disease.

HomeRadiologyVol. 307, No. 2 PreviousNext Reviews and CommentaryFree AccessImages in RadiologyMyocardial Tissue Characterization in Danon DiseaseFei Chen, Mao Chen Fei Chen, Mao Chen Author AffiliationsFrom the Department of Cardiology, Laboratory of Heart Valve Disease, West China Hospital, Sichuan University, No. 37 Guoxue Alley, Chengdu 610041, PR China.Address correspondence to M.C. (email: [email protected]).Fei ChenMao Chen Published Online:Jan 17 2023https://doi.org/10.1148/radiol.222333MoreSectionsPDF ToolsImage ViewerAdd to favoritesCiteTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked In A 14-year-old boy was referred for cardiac MRI, which showed mild left ventricular (LV) wall thickening to 13 mm (Figure, A). No edema signal or late gadolinium enhancement (LGE) was observed (Figure, A, B). Native myocardial T1 was elevated (1331 msec; reference, 1114–1290 msec), but extracellular volume (ECV) fraction (25%) and myocardial T2 (38 msec) were normal (Figure, C–E). LV hypertrophy associated with storage disorders was suspected.Baseline and follow-up cardiac MRI scans in a young boy with Danon disease. (A–E) Cardiac MRI scans at age 14 years show (A) mild left ventricular (LV) hypertrophy (maximum thickness, 13 mm; LV mass index, 93 g/m2) with no edema, (B) late gadolinium enhancement (LGE), (C) abnormal global native T1 value of 1331 msec (reference, 1114–1290 msec), (D) normal global extracellular volume (ECV) fraction of 25% (reference, 21%–33%), and (E) normal global T2 value of 38 msec (reference, 33–44 msec). (F–J) Cardiac MRI scans at age 19 years show (F) extreme LV hypertrophy (maximum thickness, 43 mm; LV mass index, 476 g/m2) with extensive midwall-dominant edema, (G) LGE, and (H-J) increased global tissue characterization metrics ([H] native T1 value [1478 msec], [I] extracellular volume fraction [44%], and [J] T2 value [51 msec]). CE-bSSFP = contrast-enhanced balanced steady-state free precession.Download as PowerPointOpen in Image Viewer At age 19 years, a repeated cardiac MRI showed a marked increase in LV wall thickness to 43 mm (Figure, F). LGE manifested in a nonischemic pattern of midwall-dominant involvement, sparing the basal septum, and with a base-to-apex increasing tendency (Figure, G). Myocardial T1 had increased (1478 msec) since the last examination, as had ECV fraction (44%) (Figure, H, I). T2 imaging showed myocardium edema signals and increased myocardial T2 (51 msec) (Figure, F, J).Genetic testing was indicated and identified a pathogenic mutation in the lysosome-associated membrane protein 2 (LAMP2) gene (c.190_191delGT), suggesting the diagnosis of Danon disease (1). Danon disease, or LAMP2 deficiency (glycogen type 2b storage disease), predominantly affects cardiac and skeletal muscles and also includes neurologic manifestations. It may be underrecognized as a cause of hypertrophic cardiomyopathy in childhood and early adulthood (2,3). Cardiac MRI could reveal cardiomyocyte injury, edema, and fibrosis in the progression of Danon disease, as well as isolated intracellular autophagic vacuoles accumulation during the early stage.Disclosures of conflicts of interest: F.C. No relevant relationships. M.C. No relevant relationships.

Analytical simulation of effects of local mechanisms on tensile response of ceramic matrix minicomposites

A micromechanics-based method based on a fiber shear lag analysis was developed to analyze the fast-fracture response of uncoated ceramic matrix minicomposites. The model was applied to two SiCf/SiC fiber minicomposite systems that were fabricated by Rolls-Royce High Temperature Composites, Inc., and the University of Connecticut. The analysis approach accounts for the fact that on average, the cracks in an actual minicomposite often have an irregular geometry. The effects of local variations in the fiber volume ratio on the composite response were also investigated. Parametric studies were performed to investigate the effects of the interfacial shear stress, global fiber volume fraction, and percentage of the composite that remains uncracked on the proportional limit stress and the composite secondary modulus. This work will facilitate an increased understanding of the key material mechanisms that take place during fast-fracture loading.

An Aggregation-Free Local Volume Fraction Formulation for Topological Design of Porous Structure.

Cellular structure can possess superior mechanical properties and low density simultaneously. Additive manufacturing has experienced substantial progress in the past decades, which promotes the popularity of such bone-like structure. This paper proposes a methodology on the topological design of porous structure. For the typical technologies such as the p-norm aggregation and implicit porosity control, the violation of the maximum local volume constraint is inevitable. To this end, the primary optimization problem with bounds of local volume constraints is transformed into unconstrained programming by setting up a sequence of minimization sub-problems in terms of the augmented Lagrangian method. The approximation and algorithm using the concept of moving asymptotes is employed as the optimizer. Several numerical tests are provided to illustrate the effectiveness of the proposed approach in comparison with existing approaches. The effects of the global and local volume percentage, influence radius and mesh discretization on the final designs are investigated. In comparison to existing methods, the proposed method is capable of accurately limiting the upper bound of global and local volume fractions, which opens up new possibilities for additive manufacturing.

Method to minimize polymer degradation in drag-reduced non-Newtonian turbulent boundary layers

Polymer solutions are often used to produce drag-reduced fluid flows, in which the drag reduction is achieved due to the solutions’ non-Newtonian shear-thinning and viscoelastic properties. However, experiments using polymer solutions are typically challenging due to the tendency of the polymer to degrade when subjected to intense shearing. The degradation reduces the amount of drag reduction as the experiment progresses, which limits the experiment duration and the accuracy of the results. Here we introduce a method to avoid the degradation of the polymer solution by driving the flow with a paddlewheel instead of a conventional pump. The solution is shown to undergo very little degradation during the paddlewheel’s operation. The method is then applied to perform novel measurements of a drag-reduced turbulent boundary layer at two different Reynolds numbers, both with and without a suspended particle phase. The effects of carrier fluid rheology and Reynolds number on the particle concentration and velocity profiles are explored, as well as the effect on total drag of the flow. For a given fluid type and Reynolds number, the drag is found to be nearly constant with the global particle volume fraction, suggesting that the particles have a limited ability to modulate the drag. Remarkably, the particle velocity fluctuations are greater in the non-Newtonian cases, possibly due to enhanced collisions in the near-wall region.

A lesson from earthquake engineering for selectively damaging cancer cell structures

The progressive falling of barriers among disciplines is opening unforeseen scenarios in diagnosis and treatment of cancer diseases. By sharing models and mature knowledge in physics, engineering, computer sciences and molecular biology, synergistic efforts have in fact contributed in the last years to re-think still unsolved problems, shedding light on key roles of mechanobiology in tumors and envisaging new effective strategies for a precise medicine. The use of ultrasounds for altering cancer cells’ program is one of the most attracting grounds to be explored in oncophysics, although how to administer mechanical energy to impair selected cell structures and functions simultaneously overcoming the critical trade-off between the impact of the cure and the patient risk still remains an open issue. Within this framework, by starting from the theoretical possibility of selectively attacking malignant cells by exploiting the stiffness discrepancies between tumor and healthy single cells, first proposed by Fraldi et al. (2015), we here investigate the in-frequency response of an overall spherical close-packing of geometrically equal polyhedral cells to gain insights into how mechanical resonance and vibration-induced failure phenomena can be oriented to destroy specific target units when both the cell populations coexist, as it happens for in vivo cases. Inspired by the dynamic action of earthquakes – which fracture only selected elements among adjacent ones in the same structure or damage individual constructions in contiguous buildings – we study the harmonic response of hierarchically architectured cell agglomerates, inhabited by both tumor and healthy cells that interact mutually throughout the extra-cellular matrix and whose cytoskeleton is modeled as a nonlinear soft-tensegrity structure. Numerical Finite Element results show that, at frequencies compatible with low intensity therapeutic ultrasounds, mechanical resonance and possible fatigue cycles of the pre-stressed actin filaments and microtubules can be selectively induced in cancer cells as a function of the global volume fraction of the cell species, paving the way for future engineered treatment protocols.

Progressive myocardial injury in myotonic dystrophy type II and facioscapulohumeral muscular dystrophy 1: a cardiovascular magnetic resonance follow-up study

AimMuscular dystrophy (MD) is a progressive disease with predominantly muscular symptoms. Myotonic dystrophy type II (MD2) and facioscapulohumeral muscular dystrophy type 1 (FSHD1) are gaining an increasing awareness, but data on cardiac involvement are conflicting. The aim of this study was to determine a progression of cardiac remodeling in both entities by applying cardiovascular magnetic resonance (CMR) and evaluate its potential relation to arrhythmias as well as to conduction abnormalities.Methods and results83 MD2 and FSHD1 patients were followed. The participation was 87% in MD2 and 80% in FSHD1. 1.5 T CMR was performed to assess functional parameters as well as myocardial tissue characterization applying T1 and T2 mapping, fat/water-separated imaging and late gadolinium enhancement. Focal fibrosis was detected in 23% of MD2) and 33% of FSHD1 subjects and fat infiltration in 32% of MD2 and 28% of FSHD1 subjects, respectively. The incidence of all focal findings was higher at follow-up. T2 decreased, whereas native T1 remained stable. Global extracellular volume fraction (ECV) decreased similarly to the fibrosis volume while the total cell volume remained unchanged. All patients with focal fibrosis showed a significant increase in left ventricular (LV) and right ventricular (RV) volumes. An increase of arrhythmic events was observed. All patients with ventricular arrhythmias had focal myocardial changes and an increased volume of both ventricles (LV end-diastolic volume (EDV) p = 0.003, RVEDV p = 0.031). Patients with supraventricular tachycardias had a significantly higher left atrial volume (p = 0.047).ConclusionWe observed a remarkably fast and progressive decline of cardiac morphology and function as well as a progression of rhythm disturbances, even in asymptomatic patients with a potential association between an increase in arrhythmias and progression of myocardial tissue damage, such as focal fibrosis and fat infiltration, exists. These results suggest that MD2 and FSHD1 patients should be carefully followed-up to identify early development of remodeling and potential risks for the development of further cardiac events even in the absence of symptoms.Trial registration ISRCTN, ID ISRCTN16491505. Registered 29 November 2017 – Retrospectively registered, http://www.isrctn.com/ISRCTN16491505

Global and Regional Changes in Perivascular Space in Idiopathic and Familial Parkinson's Disease.

The glymphatic system, including the perivascular space (PVS), plays a critical role in brain homeostasis. Although mounting evidence from Alzheimer's disease has supported the potential role of PVS in neurodegenerative disorders, its contribution in Parkinson's disease (PD) has not been fully elucidated. Although idiopathic (IPD) and familial PD (FPD) share similar pathophysiology in terms of protein aggregation, the differential impact of PVS on PD subtypes remains unknown. Our objective was to examine the differences in PVS volume fraction in IPD and FPD compared to healthy controls (HCs) and nonmanifest carriers (NMCs). A total of 470 individuals were analyzed from the Parkinson's Progression Markers Initiative database, including (1) IPD (n = 179), (2) FPD (LRRK2 [leucine-rich repeat kinase 2], glucocerebrosidase, or α-synuclein) (n = 67), (3) NMC (n = 101), and (4) HCs (n = 84). Total PVS volume fraction (%) was compared using parcellation and quantitation within greater white matter volume at global and regional levels in all cortical and subcortical white matter. There was a significant increase in global and regional PVS volume fraction in PD versus non-PD, particularly in FPD versus NMC and LRRK2 FPD versus NMC. Regionally, FPD and NMC differed in the medial orbitofrontal region, as did LRRK2 FPD versus NMC. Non-PD and PD differed in the medial orbitofrontal region and the banks of the superior temporal regions. IPD and FPD differed in the cuneus and lateral occipital regions. Our findings support the role of PVS in PD and highlight a potentially significant contribution of PVS to the pathophysiology of FPD, particularly LRRK2. © 2021 International Parkinson and Movement Disorder Society.

Proton radiography of explosively dispersed metal particles with varying volume fraction and varying carrier phase

A series of experiments were performed to provide validation data for explosively driven multiphase flows at moderate-to-high volume fractions. A $$13 \times 6$$ mm cylindrical packet of 115- $$\upmu $$ m steel particles was dispersed explosively. In contrast to shock tube studies, the particles were subjected to a high-Mach-number shock, in the presence of an ambient fluid, and a contact interface between the ambient and the explosive products. The first five experiments lowered the global volume fraction by replacing portions of the particle bed with hollow glass microspheres, dispersing the particles into vacuum. Three global fractions were investigated: 60%, 40%, and 20%. The next five experiments did not lower the volume fraction but instead varied the ambient fluid. Three ambient fluids were investigated: air, xenon, and SF $$_6$$ . To penetrate the optically opaque explosive products present and track the dispersed particle cloud, proton radiography was performed. The high-volume-fraction cases exhibit a piston-like motion for all ambient conditions, with an increasingly stochastic motion present for the lower volume fractions. Particle fronts extracted from the transmission radiographs exhibit almost constant velocity. Furthermore, centerline particle fronts for the high-volume-fraction cases, with both vacuum and varying ambient gas conditions, were almost the same, suggesting the primary impulse to particle bed motion arises from the contact interface between the ambient and the detonation products. Lower volume fractions were accelerated to higher velocities, behaving as though they were a single object of decreased density being acted on by a force of constant magnitude.

Effect of geometrical structure variations on the viscoelastic and anisotropic behaviour of cortical bone using multi-scale finite element modelling

Multi-scale finite element analysis is performed to ascertain the effect of geometrical changes at multiple structural scales on the mechanical properties of cortical bone. Finite element models are developed, with reference to experimental data from existing literature, to account for bone's viscoelastic behaviour and anisotropic structure from the most fundamental level of bone consisting of mineralised collagen fibrils, up to the macroscopic level consisting of osteons and the Haversian canals. A statistical approach is incorporated to perform sensitivity analyses on the effects of different geometrical parameters on the effective material properties of cortical bone at each length scale. Numerical results indicate that there is an exponential correlation between the mineral volume fraction and the effective stiffness constants at each length scale. This contributes to the exponential behaviour of the instantaneous moduli describing cortical bone's two-phase stress relaxation process: a fast and slow response relaxation behaviour. Results indicate that the fast response relaxation time is independent of bone's structural anisotropy, whilst being dependent on variations in the global mineral volume fraction between length scales. However, the slow response relaxation time is independent of the changes in mineral volume fraction. It is also observed that the slow response relaxation time varies with bone's anisotropic structure, and therefore, contributes to the anisotropic properties of bone.

Parametric study of the clustering transition in vibration driven granular gas system**Project supported by the National Natural Science Foundation of China (Grant Nos. U1738120, 11474326, and 11705256), Young Scholar of CAS “Light of West China” Program for Guanghui Yang (Grant No. 2018-98), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA21010202), and the International Cooperation Project

A parametric study of the clustering transition of a vibration-driven granular gas system is performed by simulation. The parameters studied include the global volume fraction of the system, the size of the system, the friction coefficient, and the restitution coefficient among particles and among particle–walls. The periodic boundary and fixed boundary of sidewalls are also checked in the simulation. The simulation results provide us the necessary “heating” time for the system to reach steady state, and the friction term needed to be included in the “cooling” time. A gas-cluster phase diagram obtained through Kolmogorov–Smirnov (K–S) test analysis using similar experimental parameters is given. The influence of the parameters to the transition is then investigated in simulations. This simulation investigation helps us gain understanding which otherwise cannot be obtained by experiment alone, and makes suggestions on the determination of parameters to be chosen in experiments.

Unveiling the impact of the effective particles distribution on strengthening mechanisms: A multiscale characterization of Mg+Y2O3 nanocomposites

Most models used to account for the hardening of nanocomposites only consider a global volume fraction of particles which is a simplified indicator that overlooks the particles size and spatial distribution. The current study aims at quantifying the effect of the real experimental particles spatial and size distribution on the strengthening of a magnesium based nanocomposites reinforced with Y2O3 particles processed by Friction Stir Processing (FSP). X-ray tomographic 3-D images allowed to identify the best FSP parameters for the optimum nanocomposite. A detailed analysis indicates that the observed hardening is mainly due to Orowan strengthening and the generation of geometrically necessary dislocations (GND) due to thermal expansion coefficients (CTE) mismatch between magnesium and Y2O3 particles. A multiscale characterization coupling 3D X-ray laboratory, synchrotron nanoholotomography and transmission electron microscopy (TEM) has been used to investigate particles size and spatial distribution over four orders of magnitude in length scales. Two dedicated micromechanical models for the two strengthening mechanisms are applied on the experimental particle fields taking into account the real particles size and spatial distribution, and compared to classical models based on average data. This required to develop a micromechanical model for CTE mismatch hardening contribution. This analysis reveals that the contribution from CTE mismatch is decreased by a factor two when taking into account the real distribution of particles instead of an average volume fraction.

Experimental study of negatively buoyant finite-size particles in a turbulent boundary layer up to dense regimes

We experimentally investigate the two-phase interplay in an open-channel turbulent boundary layer laden with finite-size particles at global volume fractions between 4 and 25 %. The working fluid (water) and the dispersed phase (hydrogel spheres) have closely matched refractive indices, allowing us to measure the properties of both phases using particle image velocimetry and particle tracking velocimetry, respectively. The particles have a diameter of approximately 9 % of the channel depth and are slightly denser than the fluid. The negative buoyancy causes a strong vertical concentration gradient, characterized by discrete and closely spaced particle layers parallel to the wall. Even at the lowest considered volume fractions, the near-wall fluid velocity and velocity gradients are strongly reduced, with large mean shear throughout most of the channel height. This indicates that the local effective viscosity of the suspension is greatly increased due to the friction between particle layers sliding over one another. The particles consistently lag the fluid and leave their footprint on its mean and fluctuating velocity profiles. The turbulent activity is damped near the wall, where the nearly packed particles disrupt and suppress large-scale turbulent fluctuations and redistribute some of the kinetic energy to smaller scales. On the other hand, in the outer region of the flow where the local particle concentration is low, the mean shear produces strong Reynolds stresses, with enhanced sweeps and ejections and frequent swirling events.

Finite element computation of the effective thermal conductivity of two-dimensional multi-scale heterogeneous media

PurposeThe simulation of heat conduction inside a heterogeneous material with multiple spatial scales would require extremely fine and ill-conditioned meshes and, therefore, the success of such a numerical implementation would be very unlikely. This is the main reason why this paper aims to calculate an effective thermal conductivity for a multi-scale heterogeneous medium.Design/methodology/approachThe methodology integrates the theory of reiterated homogenization with the finite element method, leading to a renewed calculation algorithm.FindingsThe effective thermal conductivity gain of the considered three-scale array relative to the two-scale array has been evaluated for several different values of the global volume fraction. For gains strictly above unity, the results indicate that there is an optimal local volume fraction for a maximum heat conduction gain.Research limitations/implicationsThe present approach is formally applicable within the asymptotic limits required by the theory of reiterated homogenization.Practical implicationsIt is expected that the present analytical-numerical methodology will be a useful tool to aid interpretation of the gain in effective thermal conductivity experimentally observed with some classes of heterogeneous multi-scale media.Originality/valueThe novel aspect of this paper is the application of the integrated algorithm to calculate numerical bulk effective thermal conductivity values for multi-scale heterogeneous media.

The devil's in the disequilibrium: multi-component analysis of dissolved carbon and oxygen changes under a broad range of forcings in a general circulation model

Abstract. The complexity of dissolved gas cycling in the ocean presents a challenge for mechanistic understanding and can hinder model intercomparison. One helpful approach is the conceptualization of dissolved gases as the sum of multiple, strictly defined components. Here we decompose dissolved inorganic carbon (DIC) into four components: saturation (DICsat), disequilibrium (DICdis), carbonate (DICcarb), and soft tissue (DICsoft). The cycling of dissolved oxygen is simpler, but can still be aided by considering O2, O2sat, and O2dis. We explore changes in these components within a large suite of simulations with a complex coupled climate–biogeochemical model, driven by changes in astronomical parameters, ice sheets, and radiative forcing, in order to explore the potential importance of the different components to ocean carbon storage on long timescales. We find that both DICsoft and DICdis vary over a range of 40 µmol kg−1 in response to the climate forcing, equivalent to changes in atmospheric pCO2 on the order of 50 ppm for each. The most extreme values occur at the coldest and intermediate climate states. We also find significant changes in O2 disequilibrium, with large increases under cold climate states. We find that, despite the broad range of climate states represented, changes in global DICsoft can be quantitatively approximated by the product of deep ocean ideal age and the global export production flux. In contrast, global DICdis is dominantly controlled by the fraction of the ocean filled by Antarctic Bottom Water (AABW). Because the AABW fraction and ideal age are inversely correlated among the simulations, DICdis and DICsoft are also inversely correlated, dampening the overall changes in DIC. This inverse correlation could be decoupled if changes in deep ocean mixing were to alter ideal age independently of AABW fraction, or if independent ecosystem changes were to alter export and remineralization, thereby modifying DICsoft. As an example of the latter, we show that iron fertilization causes both DICsoft and DICdis to increase and that the relationship between these two components depends on the climate state. We propose a simple framework to consider the global contribution of DICsoft+DICdis to ocean carbon storage as a function of the surface preformed nitrate and DICdis of dense water formation regions, the global volume fractions ventilated by these regions, and the global nitrate inventory.

Tuning Local Nanoparticle Arrangements in TiO2–Polymer Nanocomposites by Grafting of Phosphonic Acids

The influence of surface modification of TiO2 nanoparticles with phosphonic acid molecules on the structure of polymer nanocomposites has been studied by small-angle scattering and transmission electron microscopy. The grafting of phosphonic acids was done by phase transfer into chloroform, and polymer nanocomposites have been formulated by solvent casting with two polymers of slightly different hydrophobicity, PMMA and PEMA. By analyzing the shape of the scattering curves around the interparticle correlation peak, and in particular the depth of the correlation hole, information on nearest-neighbor correlations between nanoparticles is obtained. While local nanoparticle arrangements are found to be independent of the global particle volume fraction, they are controlled by the degree of hydrophobicity of the alkylphosphonic acid grafts with respect to hydrophobicity of the matrix. Quantitative analysis of the correlation hole thus evidences the fine-tuning of local nanocomposite structure with phosphonic acids.

Dissipation and inter-scale transfer in fully coupled particle and fluid motions in homogeneous isotropic forced turbulence

This work examines in detail the coupling mechanism between a stationary, homogeneous and isotropic turbulent (HIT) flow and particles, including the effect of particle-particle collisions. In order to illustrate how the physics can be elucidated of four-way interactions, a series of coupled Direct Numerical Simulations (DNS) of forced HIT are performed on a 1283 periodic box at two Taylor Reynolds numbers, 35.4 and 58.0, with interacting particles of different global Stokes numbers and volume fractions. The results show that fluid dissipation decreases up to 32% with increasing global Stokes numbers and particle volume fractions. Moreover, the corresponding dissipation when ignoring particle-particle collisions is over-estimated by up to 7% compared to the fully coupled simulations. A spectral analysis of the coupling mechanism reveals that the particles transfer energy from the large to the small scales, thereby explaining the difference in dissipation. Finally, a model spectrum for the coupling between the turbulent fluid and the particles is proposed.