Anisotropic Diffusivity Research Articles

Parameterization of Frontal Symmetric Instabilities. I: Theory for Resolved Fronts

A parameterization is proposed for the effects of symmetric instability (SI) on a resolved front. The parameterization is dependent on external forcing by surface buoyancy loss and/or down-front winds, which reduce potential vorticity (PV) and lead to conditions favorable for SI. The parameterization consists of three parts. The first part is a specification for the vertical eddy viscosity, which is derived from a specified ageostrophic circulation resulting from the balance of the Coriolis force and a Reynolds momentum flux (a turbulent Ekman balance), with a previously proposed vertical structure function for the geostrophic shear production. The vertical structure of the eddy viscosity is constructed to extract the mean kinetic energy of the front at a rate consistent with resolved SI. The second part of the parameterization represents a near-surface convective layer whose depth is determined by a previously proposed polynomial equation. The third part of the parameterization represents diffusive tracer mixing through small-scale shear instabilities and SI. The diabatic, vertical component of this diffusivity is set to be proportional to the eddy viscosity using a turbulent Prandtl number, and the along-isopycnal tracer mixing is represented by an anisotropic diffusivity tensor.Preliminary testing of the parameterization using a set of idealized models shows that the extraction of total energy of the front is consistent with that from SI-resolving LES, while yielding mixed layer stratification, momentum, and potential vorticity profiles that compare favorably to those from an extant boundary layer parameterization (Large et al., 1994). The new parameterization is also shown to improve the vertical mixing of a passive tracer in the LES.

Novel fiber orientation evaluation method for CFRP/CFRTP based on measurement of anisotropic in-plane thermal diffusivity distribution

This study proposes a new method for evaluating fiber orientation of sheet-like fiber reinforced materials based on thermal diffusivity measurements. The experimental apparatus comprises a laser, function generator, microscope, and thermographic camera. The surface of a sample is heated periodically by a laser spot, and the thermal response on the rear side of the sample is measured by a lock-in thermographic camera to obtain in-plane thermal diffusivity distribution. This thermal diffusivity angular distribution is directly related to the fiber orientation distribution (FOD). In this study, FOD density function can be obtained to fit the thermal diffusivity angular distribution. At first, the feasibility of this method was verified using a unidirectional (UD) carbon fiber reinforced plastic with a known FOD. The FOD of the UD sample can be estimated within 0.3° at the maximum. The method was then applied to a carbon fiber reinforced thermoplastic (CFRTP) sample having discontinuous fibers. The thermal diffusivity angular distributions were measured, and the FOD fitting method was applied to the results. The FOD can be evaluated from the fiber orientation angle and strength. Finally, mapping measurements were conducted using a CFRTP sheet molded by the long fiber thermoplastic-direct method. The mapping measurement is valid for the measurement of large scale samples.

Simultaneous measurements of anisotropic thermal diffusivity and thermal effusivity of liquid crystals using temperature wave analysis method

Simultaneous measurements of anisotropic thermal diffusivity and thermal effusivity in the phase transition of the liquid crystal 4′-(pentyloxy)-4-biphenyl carbonitrile (5OCB), Cry–53–N–68–Iso, are demonstrated using the temperature wave analysis method. A detailed calibration procedure for determining thermal diffusivity (α), thermal effusivity (e), thermal conductivity (λ), and heat capacity per unit volume (Cpρ) is proposed utilizing hexaethylene glycol monododecyl ether (C12E6) as a calibration material, the heat capacity of which is precisely determined using a calorimetric method.

On mesh restrictions to satisfy comparison principles, maximum principles, and the non-negative constraint: Recent developments and new results

ABSTRACTThis article concerns mesh restrictions that are needed to satisfy several important mathematical properties—maximum principles, comparison principles, and the nonnegative constraint—for a general linear second-order elliptic partial differential equation. We critically review some recent developments in the field of discrete maximum principles, derive new results, and discuss some possible future research directions in this area. In particular, we derive restrictions for a three-node triangular (T3) element and a four-node quadrilateral (Q4) element to satisfy comparison principles, maximum principles, and the nonnegative constraint under the standard single-field Galerkin formulation. Analysis is restricted to uniformly elliptic linear differential operators in divergence form with Dirichlet boundary conditions specified on the entire boundary of the domain. Various versions of maximum principles and comparison principles are discussed in both continuous and discrete settings. In the literature, it is well-known that an acute-angled triangle is sufficient to satisfy the discrete weak maximum principle for pure isotropic diffusion. Herein, we show that this condition can be either too restrictive or not sufficient to satisfy various discrete principles when one considers anisotropic diffusivity, advection velocity field, or linear reaction coefficient. Subsequently, we derive appropriate restrictions on the mesh for simplicial (e.g., T3 element) and nonsimplicial (e.g., Q4 element) elements. Based on these conditions, an iterative algorithm is developed to construct simplicial meshes that preserve discrete maximum principles using existing open source mesh generators. Various numerical examples based on different types of triangulations are presented to show the pros and cons of placing restrictions on a computational mesh. We also quantify local and global mass conservation errors using representative numerical examples and illustrate the performance of metric.

Uniform Convergent Tailored Finite Point Method for Advection–Diffusion Equation with Discontinuous, Anisotropic and Vanishing Diffusivity

We propose two tailored finite point methods for the advection---diffusion equation with anisotropic tensor diffusivity. The diffusion coefficient can be very small in one direction in some part of the domain and be discontinuous at the interfaces. When flows advect from the vanishing-diffusivity region towards the non-vanishing diffusivity region, standard numerical schemes tend to cause spurious oscillations or negative values. Our proposed schemes have uniform convergence in the vanishing diffusivity limit, even when the solution exhibits interface and boundary layers. When the diffusivity is along the coordinates, the positivity and maximum principle can be proved. We use the value as well as their derivatives at the grid points to construct the scheme for nonaligned case, which makes it can achieve good accuracy and convergence for the derivatives as well, even when there exhibit boundary or interface layers. Numerical experiments are presented to show the performance of the proposed scheme.

Electrospun Magnetic Nanofiber as Multifunctional Flexible EMI-Shielding Layer and its Optimization on the Effectiveness

We developed a flexible and micro-thick electromagnetic interference (EMI) shielding nanofabric layer that also functions as a water resisting and heat sinking material. Electrospinning followed by a simple heat treatment process was carried on to produce the EMI-shielding Ni/C hybrid nanofibers. The ambient oxygen partial pressure (<TEX>$pO_2$</TEX> = 0.1, 0.7, 1.3 Torr) applied during the heat treatment was varied in order to optimize the effectiveness of EMI-shielding by modifying the size and crystallinity of the magnetic Ni nanoparticles distributed throughout the C nanofibers. Permittivity and permeability of the nanofibers under the electromagnetic (EM) wave frequency range of 300 MHz~1 GHz were measured, which implied the EMI-shielding effectiveness (SE) optimization at <TEX>$pO_2$</TEX> = 0.7 Torr during the heat treatment. The materials' heat diffusivity for both in-plane direction and vertical direction was measured to confirm the anisotropic thermal diffusivity that can effectively deliver and sink the local heat produced during device operations. Also, the nanofibers were aged at room temperature in oxygen ambient for water resisting function.

Dynamically Consistent Parameterization of Mesoscale Eddies—Part II: Eddy Fluxes and Diffusivity from Transient Impulses

This work continues development of the framework for dynamically consistent parameterization of mesoscale eddy effects in non-eddy-resolving ocean circulation models. Here, we refine and extend the previous results obtained for the double gyres and aim to account for the eddy backscatter mechanism that maintains eastward jet extension of the western boundary currents. We start by overcoming the local homogeneity assumption and by taking into account full large-scale circulation. We achieve this by considering linearized-dynamic responses to finite-time transient impulses. Feedback from these impulses on the large-scale circulation are referred to as footprints. We find that the local homogeneity assumption yields only quantitative errors in most of the gyres but breaks down in the eastward jet region, which is characterized by the most significant eddy effects. The approach taken provides new insights into the eddy/mean interactions and framework for parameterization of unresolved eddy effects. Footprints provide us with maps of potential vorticity anomalies expected to be induced by transient eddy forcing. This information is used to calculate the equivalent eddy potential vorticity fluxes and their divergences that partition the double-gyre circulation into distinct geographical regions with specific eddy effects. In particular, this allows approximation of the real eddy effects that maintain the eastward jet extension of the western boundary currents and its adjacent recirculation zones. Next, from footprints and their equivalent eddy fluxes and from underlying large-scale flow gradients, we calculate spatially inhomogeneous and anisotropic eddy diffusivity tensor. Its properties suggest that imposing parameterized source terms, that is, equivalent eddy flux divergences, is a better parameterization strategy than implementation of the eddy diffusion.

Investigating the Eddy Diffusivity Concept in the Coastal Ocean

AbstractThis paper aims to test the validity, utility, and limitations of the lateral eddy diffusivity concept in a coastal environment through analyzing data from coupled drifter and dye releases within the footprint of a high-resolution (800 m) high-frequency radar south of Martha’s Vineyard, Massachusetts. Specifically, this study investigates how well a combination of radar-based velocities and drifter-derived diffusivities can reproduce observed dye spreading over an 8-h time interval. A drifter-based estimate of an anisotropic diffusivity tensor is used to parameterize small-scale motions that are unresolved and underresolved by the radar system. This leads to a significant improvement in the ability of the radar to reproduce the observed dye spreading.

Effect of thermo-hydrodynamic instability on structure and characteristics of filtration combustion wave of solid fuel

Numerical modelling of flame front stability for the inverse wave (with trailing combustion front) of filtration combustion of solid fuel is performed. The problem is treated in terms of dimensionless variables and parameters. It is found that propagation of a plane combustion front becomes unstable under certain conditions. In this case the front spontaneously inclines. The thermo-hydrodynamic mechanism is supposed to be responsible for instability developing. Anisotropic effective mass diffusivity (dispersion) is also taken into account. It turns out that anisotropic diffusivity affects structure and conversion distribution of the inclined combustion front. It is shown that the key parameters determining stability of combustion wave are dimensionless gas flow rate and width of reactor. The range of these parameters corresponding to the stable plane front is determined. It is shown that stability occurs either for small reactor widths (dimensionless values <1), or low gas flow rate (below 0.2). The optimised values of considered dimensionless parameters for maximal productivity are determined.

Formation Mechanisms and Thermodynamic Stability of Domain Structure in Partially (de)Lithiated Olivine Nanoparticles

The mechanism of Li intercalation in olivine LiFePO4 is a subject of intensive study in recent years. The formation of metastable solid solution is now recognized as an important factor in enabling the excellent high-rate performance of this material. On the other hand, phase separation occurs at low to moderate charge/discharge rates or during rest, leading to the domain structures of coexisting LiFePO4 and FePO4 phases. As defects such as cracks and dislocations are frequently nucleated at domain boundaries, understanding the domain formation phenomenon has significant implications for predicting the degradation of olivine cathode. Despite numerous studies, the formation mechanism, morphology and stability of domain structure in olivine remain to be further elucidated. Previously, a notable experimental observation by Chen et al. [1] reveal intriguing ordered LiFePO4/FePO4 domains separated by parallel (100) phase boundaries in chemically delithiated LiFePO4 particles. However, the absence of (010) phase boundaries in this structure is puzzling since the strongly anisotropic Li diffusivity should prefer a facile phase separation in the [010] direction. While 2D depth-averaged models have been employed to explain the observed domain structure [2], more detailed three-dimensional simulations are required to shed light on this issue. In this work, we carried out 3D phase-field simulations and domain energy calculations to examine the phase separation and domain formation mechanism in free-standing, partially (de)lithiated olivine particles. The employed phase-field model quantitatively captures the effects of Li diffusion anisotropy, interface charge transfer kinetics, coherency stress and stress relaxation at particle surface. Our calculations expose the intricate interplay between thermodynamic driving force and kinetic constraints in the domain formation process, and lead to the following findings: 1) Li exchange between [010] diffusion channels crucially influences domain morphology. When such exchange is negligible, a novel, metastable checkboard pattern containing both (100) and (010) phase boundaries emerges from spontaneous phase separation (or spinodal decomposition) along [010]. In comparison, the stripe pattern reported by Chen et al. is thermodynamically more favorable by eliminating the (010) boundaries, but its formation is kinetically viable only when Li transport between [010] channels is allowed by two possible mechanisms, i.e. i) [100] lattice hopping enabled by the presence of defects and ii) inter-channel exchange through electrolyte. Under the circumstance where inter-channel Li transport has a much larger characteristic time than Li diffusion in the [010] direction, we predict that the checkboard structure will exist as an intermediate structure that can be observed experimentally. 2) Periodic domain structure in free-standing olivine particles is a kinetically stabilized feature. When the volume expansion of olivine particles is not severely constrained by their surrounding, theoretical calculations show that both elastic and interface energy stored in a particle decreases monotonically with domain length, dictating that the thermodynamic equilibrium domain structure should have only one phase boundary in the particle. However, the domain structure can be effectively “frozen” at a finite length scale due to the increasingly sluggish domain coarsening kinetics. Simulations show that the kinetically stabilized domain size is proportional to [010] particle thickness, which is consistent with experiment. The metastability of the periodic domain pattern explains why it is not universally observed in olivine particles prepared under similar conditions [3]. This study shows the important role of kinetic constraints in domain structure evolution in LiFePO4, which provides new insights on potential avenues to improve control of domain morphology via engineering the kinetic properties of olivine materials.

Atomic Insight into the Lithium Storage and Diffusion Mechanism of SiO2/Al2O3 Electrodes of Lithium Ion Batteries: ReaxFF Reactive Force Field Modeling.

Atomically deposited layers of SiO2 and Al2O3 have been recognized as promising coating materials to buffer the volumetric expansion and capacity retention upon the chemo-mechanical cycling of the nanostructured silicon- (Si-) based electrodes. Furthermore, silica (SiO2) is known as a promising candidate for the anode of next-generation lithium ion batteries (LIBs) due to its superior specific charge capacity and low discharge potential similar to Si anodes. In order to describe Li-transport in mixed silica/alumina/silicon systems we developed a ReaxFF potential for Li-Si-O-Al interactions. Using this potential, a series of hybrid grand canonical Monte Carlo (GCMC) and molecular dynamic (MD) simulations were carried out to probe the lithiation behavior of silica structures. The Li transport through both crystalline and amorphous silica was evaluated using the newly optimized force field. The anisotropic diffusivity of Li in crystalline silica cases is demonstrated. The ReaxFF diffusion study also verifies the transferability of the new force field from crystalline to amorphous phases. Our simulation results indicates the capability of the developed force field to examine the energetics and kinetics of lithiation as well as Li transportation within the crystalline/amorphous silica and alumina phases and provide a fundamental understanding on the lithiation reactions involved in the Si electrodes covered by silica/alumina coating layers.

The behavior of a multilayered porous thermo-elastic medium with anisotropic thermal diffusivity and permeability

With the aid of integral transform techniques, this paper presents an extended precise integration solution for thermal consolidation problems of a multilayered porous thermo-elastic medium with anisotropic thermal diffusivity and permeability due to a heat source. From the fundamental governing equations, ordinary differential equations are derived by employing Laplace–Hankel transforms. By applying the extended precise integration method, equations in the transformed domain can be solved, and the actual solutions are further obtained by adopting a numerical inverse transformation. The accuracy and feasibility of the proposed theory is demonstrated by contrastive analysis with existing studies. Finally, several examples are carried out to investigate the influence of heat source’s type, axial distance, burial depth of heat source, ratio of thermo-permeability, permeability anisotropy, thermal diffusivity anisotropy and stratification on the thermal consolidation process.

Inhomogeneous Temperature Fields, Current Distribution, Stability and Heat Transfer in Superconductor 1G Multi-filaments

This paper is focused on simulations of how a superconductor reacts to extreme, suddenly changing operation conditions imposed by strong over-currents. An attempt is made to shed light on the physics of current transport behind, as far as this can be achieved with numerical simulations. For this purpose, temperature and current distribution in multi-filamentary high-temperature superconductors is investigated in a finite element analysis with high spatial and time resolution. An extra subsection is devoted to the involved heat transfer problem. As a result, resistive (Ohmic and flux flow) and zero loss states would co-exist in parallel if over-current cannot be compensated, for example, by switching it to a shunt. Anisotropic thermal diffusivity of high-temperature superconductors, in particular of BSCCO, would obstruct thermalisation of losses, and compensating of field and current in-homogeneities would become impossible within acceptable periods of time.

Morphological evolution and migration of void in bi-piezoelectric interface based on nonlocal phase field method

This paper reports the result of investigation into the morphological evolution and migration of void in bi-piezoelectric material interface by utilizing nonlocal phase field model and finite element method (FEM), where the small scale effect containing the long-range forces among atoms is considered. The nonlocal elastic strain energy and the nonlocal electric energy around the void are firstly calculated by the finite element method. Then based on the finite difference method (FDM), the thermodynamic equilibrium equation containing the surface energy and anisotropic diffusivity is solved to simulate the morphological evolution and migration of elliptical void in bi-piezoelectric films interface. Results show that the way of load condition plays a significant role in the evolution process, and the boundary of void's long axis gradually collapses toward the center of ellipse. In addition, the evolutionary speed of left boundary gradually decreases with scale effect coefficient growth. This work can provide references for the safety evaluation of piezoelectric materials in micro electro mechanical system.

Photo-controllable thermal diffusivity and thermal conductivity driven by the orientation change of nematic liquid crystal with azo-dendrimers

We measured the temperature dependences of anisotropic thermal properties, i.e., thermal diffusivity, thermal effusivity, thermal conductivity, and heat capacity per unit volume, of a nematogen 4′-n-pentyloxybiphenyl-4-carbonitrile (5OCB) containing a small amount (0.02 wt. %) of dendritic azobenzene derivatives (azo-dendrimer), using a temperature wave method. The azo-dendrimers spontaneously adsorb on cell surfaces and act as a command surface, i.e., photo-induced planar/homeotropic alignment by ultraviolet/visible light illumination. By using this effect, we demonstrated thermal property changes except for the heat capacity by almost two times within a few tens of seconds. The phenomenon can be applied to a sheet with photo-controllable thermal diffusivity or thermal conductivity.

Highly selective mixed-matrix membranes with layered fillers for molecular separation

Two-dimensional (2D) layered porous materials are of a considerable interest to researchers due to differences in the sizes of in-plane and out-of-plane confinement. These layered materials have been blended with polymers for the fabrication of mixed-matrix membranes (MMMs) for applications involving separation. The polymers in MMMs serve as a matrix and the 2D layered materials serve as filler used to enhance the separation performance (diffusivity and selectivity) of the polymeric matrix. Unfortunately, the existing models for estimating the effective diffusivity of MMMs with layered fillers are unable to provide reliable predictions. This study proposed a numerical approach to the estimation of effective diffusivity and the selectivity of MMMs using layered fillers based on the mass transfer simulations. In the proposed models, we took into account two critical parameters of the layered fillers: anisotropic diffusivity and orientation distributions. The predictive ability of the proposed approach was evaluated via comparison with experimental data. Finally, we outline the design of highly selective MMMs with layered porous materials based on the proposed methodology.

Micro–Macro Analysis of Thermal Diffusion Anisotropy and Particle Orientation in a Composite Material

To clarify the effect of orientation disorder on anisotropic thermal diffusivity in a uniaxially oriented composite sample, we derive microscopic thermal diffusivities inversely from the macroscopic ones by specifying local particle orientation directions in unit segments having a size of \(l \times l \times l\). To solve the inverse problem, two new models based on the assumption of linearity in thermal property patterns are introduced and compared with a series resistance model. Results show that the square of an average of local microscopic diffusivity pattern radii \(\sqrt{L^*_{\phi _i(\varTheta )}}\) reasonably describes the macroscopic thermal diffusivity \(L_{(\varTheta )}\): \(\left\{ 1/N\sum _i \sqrt{L^*_{\phi _i(\varTheta )}}\right\} ^2 =L_{(\varTheta )}\), where \(\phi _i(\varTheta )\) is the angle between the uniaxial direction (perpendicular to plate-shaped particles) in the i-th unit segment and a direction \(\varTheta \) measured with respect to the macroscopic particle orientation plane (parallel to particles). Microscopic thermal diffusivity \(L^*_{\phi }\) obtained for smaller \(l\ ({\sim } 10~\upmu \hbox {m}\)) is consistent with the analysis of a simple geometrical model system.

Multimodel analysis of anisotropic diffusive tracer‐gas transport in a deep arid unsaturated zone

AbstractGas transport in the unsaturated zone affects contaminant flux and remediation, interpretation of groundwater travel times from atmospheric tracers, and mass budgets of environmentally important gases. Although unsaturated zone transport of gases is commonly treated as dominated by diffusion, the characteristics of transport in deep layered sediments remain uncertain. In this study, we use a multimodel approach to analyze results of a gas‐tracer (SF6) test to clarify characteristics of gas transport in deep unsaturated alluvium. Thirty‐five separate models with distinct diffusivity structures were calibrated to the tracer‐test data and were compared on the basis of Akaike Information Criteria estimates of posterior model probability. Models included analytical and numerical solutions. Analytical models provided estimates of bulk‐scale apparent diffusivities at the scale of tens of meters. Numerical models provided information on local‐scale diffusivities and feasible lithological features producing the observed tracer breakthrough curves. The combined approaches indicate significant anisotropy of bulk‐scale diffusivity, likely associated with high‐diffusivity layers. Both approaches indicated that diffusivities in some intervals were greater than expected from standard models relating porosity to diffusivity. High apparent diffusivities and anisotropic diffusivity structures were consistent with previous observations at the study site of rapid lateral transport and limited vertical spreading of gas‐phase contaminants. Additional processes such as advective oscillations may be involved. These results indicate that gases in deep, layered unsaturated zone sediments can spread laterally more quickly, and produce higher peak concentrations, than predicted by homogeneous, isotropic diffusion models.

Does anisotropy promote spatial uniformity of stent-delivered drug distribution in arterial tissue?

In this article we investigate the role of anisotropic diffusion on the resulting arterial wall drug distribution following stent-based delivery. The arterial wall is known to exhibit anisotropic diffusive properties, yet many authors neglect this, and it is unclear what effect this simplification has on the resulting arterial wall drug concentrations. Firstly, we explore the justification for neglecting the curvature of the cylindrical arterial wall in favour of using a Cartesian coordinate system. We then proceed to consider three separate transport regimes (convection dominated, diffusion dominated, reaction dominated) based on the range of parameter values available in the literature. By comparing the results of a simple one-dimensional model with those of a fully three-dimensional numerical model, we demonstrate, perhaps surprisingly, that the anisotropic diffusion can promote the spatial uniformity of drug concentrations, and furthermore, that the simple analytical one-dimensional model is an excellent predictor of the three-dimensional numerical results. However, the level of uniformity and the time taken to reach a uniform concentration profile depends on the particular regime considered. Furthermore, the more uniform the profile, the better the agreement between the one-dimensional and three-dimensional models. We discuss the potential implications in clinical practice and in stent design.

An anisotropic Reynolds mass flux model for the simulation of chemical reaction in gas-particle CFB risers

A model is proposed for numerical simulation of the multiphase flow coupled with chemical reaction in gas-particle circulating fluidized bed (CFB) risers. The proposed model is based on the newly developed computational mass transfer (CMT) methodology (Yu and Yuan, 2014) featuring the use of Reynolds mass flux equation to close the turbulent mass transfer equation, so that the anisotropic turbulent mass diffusion in CFB riser can be realized in the simulation. The proposed model consists of the turbulent mass transfer equation for the species with its Reynolds mass flux closure and the relevant formulations of computational fluid dynamics (CFD). With the proposed model, the species concentration and solid volume fraction as well as the velocity distributions along the CFB riser can be predicted. To validate the proposed model, simulation is carried out for the catalytic ozone decomposition in a gas-particle CFB riser. The simulated results are compared with the experimental data and satisfactory agreement is found in both axial/radial distributions of ozone concentration and solid volume fraction. Furthermore, the anisotropic turbulent mass diffusivities are also predicted and validated by the experimental data reported in literature.