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Статті в журналах з теми "Approche à interface diffuse"

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Автор: Grafiati

Опубліковано: 7 липня 2024

Оновлено: 7 липня 2024

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1

ELLIOTT, CHARLES M., and BJÖRN STINNER. "ANALYSIS OF A DIFFUSE INTERFACE APPROACH TO AN ADVECTION DIFFUSION EQUATION ON A MOVING SURFACE." Mathematical Models and Methods in Applied Sciences 19, no. 05 (May 2009): 787–802. http://dx.doi.org/10.1142/s0218202509003620.

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A diffuse interface model for an advection diffusion equation on a moving surface is formulated involving a small parameter ε related to the thickness of the interfacial layer. The coefficient functions degenerate on the boundary of the diffuse interface. In appropriately weighted Sobolev spaces, existence and uniqueness of weak solutions is shown. Using energy methods the convergence of solutions to the diffuse interface model to the solution to the equation on the moving surface as ε → 0 is proved. The approach is intended to be applied to phase field models describing the surface motion. Among other problems we have surfactants on liquid-liquid interfaces and species diffusion on moving grain boundaries in mind.

2

Gránásy, L. "Diffuse Interface Approach to Crystal Nucleation." Materials Science Forum 215-216 (June 1996): 451–58. http://dx.doi.org/10.4028/www.scientific.net/msf.215-216.451.

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3

Gránásy, L. "Diffuse Interface Approach to Vapour Condensation." Europhysics Letters (EPL) 24, no. 2 (October 10, 1993): 121–26. http://dx.doi.org/10.1209/0295-5075/24/2/008.

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4

Rätz, Andreas, and Axel Voigt. "PDE's on surfaces---a diffuse interface approach." Communications in Mathematical Sciences 4, no. 3 (2006): 575–90. http://dx.doi.org/10.4310/cms.2006.v4.n3.a5.

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5

Daher, Ali, Amine Ammar, and Abbas Hijazi. "Nanoparticles migration near liquid-liquid interfaces using diffuse interface model." Engineering Computations 36, no. 3 (April 8, 2019): 1036–54. http://dx.doi.org/10.1108/ec-03-2018-0153.

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Purpose The purpose of this paper is to develop a numerical model for the simulation of the dynamics of nanoparticles (NPs) at liquid–liquid interfaces. Two cases have been studied, NPs smaller than the interfacial thickness, and NPs greater than the interfacial thickness. Design/methodology/approach The model is based on the molecular dynamics (MD) simulation in addition to phase field (PF) method, through which the discrete model of particles motion is superimposed on the continuum model of fluids which is a new ide a in numerical modeling. The liquid–liquid interface is modeled using the diffuse interface model. Findings For NPs smaller than the interfacial thickness, the results obtained show that the concentration gradient of one fluid in the other gives rise to a hydrodynamic drag force that drives the NPs to agglomerate at the interface. Whereas, for spherical NPs greater than the interfacial thickness, the results show that such NPs oscillate at the interface which agrees with some experimental studies. Practical implications The results are important in the field of numerical modeling, especially that the model is general and can be used to study different systems. This will be of great interest in the field of studying the behavior of NPs inside fluids and near interfaces, which enters in many industrial applications. Originality/value The idea of superimposing the molecular dynamic method on the PF method is a new idea in numerical modeling.

6

Glasner, Karl. "A diffuse interface approach to Hele Shaw flow." Nonlinearity 16, no. 1 (October 28, 2002): 49–66. http://dx.doi.org/10.1088/0951-7715/16/1/304.

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7

Gránásy, László, and Dieter M. Herlach. "Diffuse interface approach to crystal nucleation in glasses." Journal of Non-Crystalline Solids 192-193 (December 1995): 470–73. http://dx.doi.org/10.1016/0022-3093(95)00430-0.

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8

Millett, Paul C., and Yu U. Wang. "Diffuse-interface field approach to modeling arbitrarily-shaped particles at fluid–fluid interfaces." Journal of Colloid and Interface Science 353, no. 1 (January 2011): 46–51. http://dx.doi.org/10.1016/j.jcis.2010.09.021.

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9

Rätz, Andreas, and Matthias Röger. "A new diffuse-interface approximation of the Willmore flow." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 14. http://dx.doi.org/10.1051/cocv/2021013.

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Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond to the intended sharp interface evolution. Here we introduce a new two-variable diffuse approximation that includes a rather simple but efficient penalization of the deviation from a quasi-one dimensional structure of the phase fields. We justify the approximation property by a Gamma convergence result for the energies and a matched asymptotic expansion for the flow. Ground states of the energy are shown to be one-dimensional, in contrast to the presence of saddle solutions for the usual diffuse approximation. Finally we present numerical simulations that illustrate the approximation property and apply our new approach to problems where the usual approach leads to an undesired behavior.

10

Boettinger, W. J., J. E. Guyer, C. E. Campbell, and G. B. McFadden. "Computation of the Kirkendall velocity and displacement fields in a one-dimensional binary diffusion couple with a moving interface." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2088 (October 9, 2007): 3347–73. http://dx.doi.org/10.1098/rspa.2007.1904.

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The moving interface problem in a one-dimensional binary α/β diffusion couple is studied using sharp and diffuse interface (Cahn–Hilliard) approaches. With both methods, we calculate the solute field and the Kirkendall marker velocity and displacement fields. In the sharp interface treatment, the velocity field is generally discontinuous at the interphase boundary, but can be integrated to obtain a displacement field that is continuous everywhere. The diffuse interface approach avoids this discontinuity, simplifies the integration and yet gives the same qualitative behaviour. Special features observed experimentally and reported in the literature are also studied with the two methods: (i) multiple Kirkendall planes, where markers placed on the initial compositional discontinuity of the diffusion couple bifurcate into two locations, and (ii) a Kirkendall plane that coincides with the interphase interface. These situations occur with special values of the interdiffusion coefficients and starting couple compositions. The details of the deformation in these special situations are given using both methods and are discussed in terms of the stress-free strain rate associated with the Kirkendall effect.

11

Barry Carter, C. "Recent applications of TEM to the study of interfaces." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 4 (August 1990): 308–9. http://dx.doi.org/10.1017/s0424820100174679.

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This paper will review the current state of understanding of interface structure and highlight some of the future needs and problems which must be overcome. The study of this subject can be separated into three different topics: 1) the fundamental electron microscopy aspects, 2) material-specific features of the study and 3) the characteristics of the particular interfaces. The two topics which are relevant to most studies are the choice of imaging techniques and sample preparation. The techniques used to study interfaces in the TEM include high-resolution imaging, conventional diffraction-contrast imaging, and phase-contrast imaging (Fresnel fringe images, diffuse scattering). The material studied affects not only the characteristics of the interfaces (through changes in bonding, etc.) but also the method used for sample preparation which may in turn have a significant affect on the resulting image. Finally, the actual nature and geometry of the interface must be considered. For example, it has become increasingly clear that the plane of the interface is particularly important whenever at least one of the adjoining grains is crystalline.A particularly productive approach to the study of interfaces is to combine different imaging techniques as illustrated in the study of grain boundaries in alumina. In this case, the conventional imaging approach showed that most grain boundaries in ion-thinned samples are grooved at the grain boundary although the extent of this grooving clearly depends on the crystallography of the surface. The use of diffuse scattering (from amorphous regions) gives invaluable information here since it can be used to confirm directly that surface grooving does occur and that the grooves can fill with amorphous material during sample preparation (see Fig. 1). Extensive use of image simulation has shown that, although information concerning the interface can be obtained from Fresnel-fringe images, the introduction of artifacts through sample preparation cannot be lightly ignored. The Fresnel-fringe simulation has been carried out using a commercial multislice program (TEMPAS) which was intended for simulation of high-resolution images.

12

Jančič, Mitja, Miha Založnik, and Gregor Kosec. "A sharp-interface mesoscopic model for dendritic growth." IOP Conference Series: Materials Science and Engineering 1274, no. 1 (January 1, 2023): 012046. http://dx.doi.org/10.1088/1757-899x/1274/1/012046.

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Abstract The grain envelope model (GEM) describes the growth of envelopes of dendritic crystal grains during solidification. Numerically the growing envelopes are usually tracked using an interface capturing method employing a phase field equation on a fixed grid. Such an approach describes the envelope as a diffuse interface, which can lead to numerical artefacts that are possibly detrimental. In this work, we present a sharp-interface formulation of the GEM that eliminates such artefacts and can thus track the envelope with high accuracy. The new formulation uses an adaptive meshless discretization method to solve the diffusion in the liquid around the grains. We use the ability of the meshless method to operate on scattered nodes to accurately describe the interface, i.e., the envelope. The proposed algorithm combines parametric surface reconstruction, meshless discretization of parametric surfaces, global solution construction procedure and partial differential operator approximation using monomials as basis functions. The approach is demonstrated on a two-dimensional h-adaptive solution of diffusive growth of dendrites and assessed by comparison to a conventional diffuse-interface fixed-grid GEM.

13

YUE, PENGTAO, CHUNFENG ZHOU, and JAMES J. FENG. "Sharp-interface limit of the Cahn–Hilliard model for moving contact lines." Journal of Fluid Mechanics 645 (February 22, 2010): 279–94. http://dx.doi.org/10.1017/s0022112009992679.

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Diffuse-interface models may be used to compute moving contact lines because the Cahn–Hilliard diffusion regularizes the singularity at the contact line. This paper investigates the basic questions underlying this approach. Through scaling arguments and numerical computations, we demonstrate that the Cahn–Hilliard model approaches a sharp-interface limit when the interfacial thickness is reduced below a threshold while other parameters are fixed. In this limit, the contact line has a diffusion length that is related to the slip length in sharp-interface models. Based on the numerical results, we propose a criterion for attaining the sharp-interface limit in computing moving contact lines.

14

Galina, Reshetova, and Romenski Evgeniy. "Diffuse interface approach to modeling wavefields in a saturated porous medium." Applied Mathematics and Computation 398 (June 2021): 125978. http://dx.doi.org/10.1016/j.amc.2021.125978.

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15

Brannick, J., C. Liu, T. Qian, and H. Sun. "Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach." Numerical Mathematics: Theory, Methods and Applications 8, no. 2 (May 2015): 220–36. http://dx.doi.org/10.4208/nmtma.2015.w12si.

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AbstractIn this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy of the system includes the kinetic energy and the mixing (interfacial) energies. The least action principle (or the principle of virtual work) is applied to derive the conservative part of the dynamics, with a focus on the reversible part of the stress tensor arising from the mixing energies. The dissipative part of the dynamics is then introduced through a dissipation function in the energy law, in line with Onsager's principle of maximum dissipation. The final system, formed by a set of coupled time-dependent partial differential equations, reflects a balance among various conservative and dissipative forces and governs the evolution of velocity and phase fields. To demonstrate the applicability of the proposed model, a few two-dimensional simulations have been carried out, including (1) the force balance at the three-phase contact line in equilibrium, (2) a rising bubble penetrating a fluid-fluid interface, and (3) a solid particle falling in a binary fluid. The effects of slip at solid surface have been examined in connection with contact line motion and a pinch-off phenomenon.

16

Kajzer, Adam, and Jacek Pozorski. "Diffuse interface models for two-phase flows in artificial compressibility approach." Journal of Physics: Conference Series 1101 (October 2018): 012013. http://dx.doi.org/10.1088/1742-6596/1101/1/012013.

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17

Smith, Alexander, Plinio Maroni, Michal Borkovec, and Gregor Trefalt. "Measuring Inner Layer Capacitance with the Colloidal Probe Technique." Colloids and Interfaces 2, no. 4 (November 27, 2018): 65. http://dx.doi.org/10.3390/colloids2040065.

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The colloidal probe technique was used to measure the inner layer capacitance of an electrical double layer. In particular, the forces were measured between silica surfaces and sulfate latex surfaces in solutions of monovalent salts of different alkali metals. The force profiles were interpreted with Poisson-Boltzmann theory with charge regulation, whereby the diffuse layer potential and the regulation properties of the interface were obtained. While the diffuse layer potential was measured in this fashion in the past, we are able to extract the regulation properties of the inner layer, in particular, its capacitance. We find systematic trends with the type of alkali metal ion and the salt concentration. The observed trends could be caused by difference in ion hydration, variation of the binding capacitance, and changes of the effective dielectric constant within the Stern layer. Our results are in agreement with recent experiments involving the water-silica interface based on a completely independent method using X-ray photoelectron spectroscopy in a liquid microjet. This agreement confirms the validity of our approach, which further provides a means to probe other types of interfaces than silica.

18

Malamud, F., E. Polatidis, M. Busi, J. Capek, L. Deillon, M. Bambach, P. Zehnder, A. Losko, and M. Strobl. "Bragg edge imaging characterization of multi-material laser powder-bed fusion specimens." Journal of Physics: Conference Series 2605, no. 1 (September 1, 2023): 012030. http://dx.doi.org/10.1088/1742-6596/2605/1/012030.

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Abstract Multi-material laser powder-bed fusion (M2LPBF) is a novel additive manufacturing approach that makes it possible to print different materials along the built direction and within a single layer of a component. At the interface between the different materials, the deposited powders melt, mix and solidify very rapidly, than can produce a range of desired and undesired phases, residual stresses and defects. Here we applied Bragg edge imaging to characterize M2LPBF specimens of stainless steel and CuCrZr with vertical and horizontal interfaces. A diffuse interface is observed in the samples with both vertical and horizontal interfaces. The analysis of the (111) and (200) Bragg edges height across the samples demonstrated a clear difference between the crystallographic texture of both alloys, with a strong alignment of the (002) planes along one of the transversal directions in the steel and a random texture within the copper alloy.

19

Hoglund, Eric R., De-Liang Bao, Andrew O’Hara, Sara Makarem, Zachary T. Piontkowski, Joseph R. Matson, Ajay K. Yadav, et al. "Emergent interface vibrational structure of oxide superlattices." Nature 601, no. 7894 (January 26, 2022): 556–61. http://dx.doi.org/10.1038/s41586-021-04238-z.

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AbstractAs the length scales of materials decrease, the heterogeneities associated with interfaces become almost as important as the surrounding materials. This has led to extensive studies of emergent electronic and magnetic interface properties in superlattices1–9. However, the interfacial vibrations that affect the phonon-mediated properties, such as thermal conductivity10,11, are measured using macroscopic techniques that lack spatial resolution. Although it is accepted that intrinsic phonons change near boundaries12,13, the physical mechanisms and length scales through which interfacial effects influence materials remain unclear. Here we demonstrate the localized vibrational response of interfaces in strontium titanate–calcium titanate superlattices by combining advanced scanning transmission electron microscopy imaging and spectroscopy, density functional theory calculations and ultrafast optical spectroscopy. Structurally diffuse interfaces that bridge the bounding materials are observed and this local structure creates phonon modes that determine the global response of the superlattice once the spacing of the interfaces approaches the phonon spatial extent. Our results provide direct visualization of the progression of the local atomic structure and interface vibrations as they come to determine the vibrational response of an entire superlattice. Direct observation of such local atomic and vibrational phenomena demonstrates that their spatial extent needs to be quantified to understand macroscopic behaviour. Tailoring interfaces, and knowing their local vibrational response, provides a means of pursuing designer solids with emergent infrared and thermal responses.

20

Franz, Sebastian, Hans-Görg Roos, Roland Gärtner, and Axel Voigt. "A Note on the Convergence Analysis of a Diffuse-domain Approach." Computational Methods in Applied Mathematics 12, no. 2 (2012): 153–67. http://dx.doi.org/10.2478/cmam-2012-0017.

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Abstract We analyse the error behaviour of a diffuse-domain approximation of an elliptic differential equation. In one dimension and for a half-plane problem in two dimensions an approximation quality of order one in the interface parameter is shown. Some supporting numerical experiments are also presented.

21

ODEN, J. TINSLEY, ANDREA HAWKINS, and SERGE PRUDHOMME. "GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING." Mathematical Models and Methods in Applied Sciences 20, no. 03 (March 2010): 477–517. http://dx.doi.org/10.1142/s0218202510004313.

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While a large and growing literature exists on mathematical and computational models of tumor growth, to date tumor growth models are largely qualitative in nature, and fall far short of being able to provide predictive results important in life-and-death decisions. This is largely due to the enormous complexity of evolving biological and chemical processes in living tissue and the complex interactions of many cellular and vascular constituents in living organisms. Several new technologies have emerged, however, which could lead to significant progress in this important area: (i) the development of so-called phase-field, or diffuse-interface models, which can be developed using continuum mixture theory, and which provide a general framework for modeling the action of multiple interacting constituents. These are based on generalizations of the Cahn–Hilliard models for spinodal decomposition, and have been used recently in certain tumor growth theories; (ii) the emergence of predictive computational methods based on the use of statistical methods for calibration, model validation, and uncertainty quantification; (iii) advances in imaging, experimental cell biology, and other medical observational methodologies; and (iv) the advent of petascale computing that makes possible the resolution of features at scales and at speeds that were unattainable only a short time in the past. Here we develop a general phenomenological thermomechanical theory of mixtures that employs phase-field or diffuse interface models of surface energies and reactions and which provides a framework for generalizing existing theories of the types that are in use in tumor growth modeling. In principle, the framework provides for the effects of M solid constituents, which may undergo large deformations, and for the effect of N - M fluid constituents, which could include highly nonlinear, non-Newtonian fluids. We then describe several special cases which have the potential of providing acceptable models of tumor growth. We then describe the beginning steps of the development of Bayesian methods for statistical calibration, model validation, and uncertainty quantification, which, with further work, could produce a truly predictive tool for studying tumor growth. In particular, we outline the processes of statistical calibration and validation that can be employed to determine if tumor growth models, drawn from the broad class of models developed here, are valid for prediction of key quantities of interest critical to making decisions on various medical protocols. We also describe how uncertainties in such key quantities of interest can be quantified in ways that can be used to establish confidence in predicted outcomes.

22

Hinze, Michael, and Christian Kahle. "Model Predictive Control of two-phase flow using a diffuse interface approach." PAMM 14, no. 1 (December 2014): 731–32. http://dx.doi.org/10.1002/pamm.201410348.

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23

Šatura, Lukáš, Mária Minichová, Michal Pavelka, Juraj Kosek, and Alexandr Zubov. "A Robust Physics-Based Calculation of Evolving Gas–Liquid Interfaces." Journal of Non-Equilibrium Thermodynamics 47, no. 2 (February 4, 2022): 143–54. http://dx.doi.org/10.1515/jnet-2021-0080.

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Abstract Density gradient theory describes the evolution of diffuse interfaces in both mixtures and pure substances by minimization of the total free energy, which consists of a non-convex bulk part and an interfacial part. Minimization of the bulk free energy causes phase separation while building up the interfacial free energy (proportional to the square of gradients of the species’ densities) and it results in the equilibrium shape of the interface. However, direct minimization of the free energy is numerically unstable and the coefficients in the interfacial part of the free energy are often estimated from experimental data (not determined from the underlying physics). In this paper we develop a robust physics-based numerical approach that leads to the interface density profiles for both pure substances and mixtures. The model is free of fitting parameters and validated by available experimental data.

24

Li, Xiangrong, John Lowengrub, Knut Erik Teigen, Axel Voigt, and Fan Wang. "A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface." Communications in Mathematical Sciences 7, no. 4 (2009): 1009–37. http://dx.doi.org/10.4310/cms.2009.v7.n4.a10.

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25

Chen, You, Chang Shu, Yu Sun, Li Ming Yang, and Yan Wang. "A diffuse interface IBM for compressible flows with Neumann boundary condition." International Journal of Modern Physics B 34, no. 14n16 (April 10, 2020): 2040070. http://dx.doi.org/10.1142/s0217979220400706.

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The recently proposed boundary condition-enforced immersed boundary-gas kinetic flux solver (IB-GKFS) is a new approach for simulation of compressible flows with curved and moving boundaries. In the previous application of IB-GKFS, only the Dirichlet boundary condition is considered, which cannot be applied directly to the Neumann boundary condition. In this paper, an auxiliary layer of Lagrangian points is introduced to tackle Neumann boundary condition. Two test cases, including flow around a circular cylinder and flow around a NACA0012 airfoil, are carried out for validation. The results obtained by the present scheme are compared with the reference data available in the literature. Good agreements are achieved, which indicate that the developed method can effectively simulate the compressible flow with Neumann boundary condition.

26

Divya, Velpula, and M. V. Sangaranarayanan. "Electrodeposition of Polymer Nanostructures using Three Diffuse Double Layers: Polymerization beyond the Liquid/Liquid Interfaces." Electrochemical Energy Technology 4, no. 1 (April 28, 2018): 6–20. http://dx.doi.org/10.1515/eetech-2018-0002.

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Abstract Nanostructured conducting polymers have received immense attention during the past few decades on account of their phenomenal usefulness in diverse contexts, while the interface between two immiscible liquids is of great interest in chemical and biological applications. Here we propose a novel Electrode(solid)/Electrolyte(aqueous)/Electrolyte(organic) Interfacial assembly for the synthesis of polymeric nanostructures using a novel concept of three diffuse double layers. There exist remarkable differences between the morphologies of the polymers synthesized using the conventional electrode/electrolyte method and that of the new approach. In contrast to the commonly employed electrodeposition at liquid/liquid interfaces, these polymer modified electrodes can be directly employed in diverse applications such as sensors, supercapacitors etc.

27

Vodička, Roman. "A computational model of interaction between material and interface cracks." MATEC Web of Conferences 310 (2020): 00003. http://dx.doi.org/10.1051/matecconf/202031000003.

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A quasi-static model for numerical solution of initiation and propagation of cracks along interfaces or inside materials is developed. The two types of cracks are modelled by the material damage theory with two independent damage parameters introduced. For cracks at the interface, in fact represented by contact of construction components, cohesive or adhesive contact is considered, for which several computational relationships based on energetic formulation exist. Accordingly, the appropriate modelling of bulk damage also includes energy consideration. In terms of cracks, it leads to so called diffuse cracks. The computational approach is referred to as phase field models. These will cause damage in a very narrow band representing the actual crack. The computational analysis provides stress-strain quantities and the damage variables to simulate both interface and material cracks. The proposed mathematical approach has a variational form based on an energetic formulation looking for a kind of weak solution. The solution is approximated by a time stepping procedure, a finite element code, and it utilizes quadratic programming algorithms.

28

Fan, Hang, Kun Zhang, Guansong He, Zhijian Yang, and Fude Nie. "Ab initio determination of interfacial thermal conductance for polymer-bonded explosive interfaces." AIP Advances 12, no. 6 (June 1, 2022): 065005. http://dx.doi.org/10.1063/5.0094018.

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Understanding the thermal transport in polymer-bonded explosives (PBXs) is critical for enhancing the safety and reliability during PBX design, especially in the absence of effective experimental measurements. In this work, we rigorously investigated the phonon properties of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) and polyvinylidene fluoride (PVDF) and calculated the interfacial thermal conductance using an ab initio approach. The diffuse mismatch model and anharmonic inelastic model were adopted to examine the interfacial thermal conductance as a function of temperature for the TATB–PVDF interface. Our calculation results indicate that low-frequency phonon modes and the two-phonon process play dominant roles in the thermal transport at interfaces. In contrast, high-order phonon processes involving three to eight phonons accounted for around 8% of the interfacial thermal conductance at the TATB–PVDF interface. Phonon properties, such as the velocity and degree of phonon density overlap, are discussed for the TATB–PVDF and 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX)–PVDF interfaces to estimate the interfacial thermal conductance of PBXs. This study provides a theoretical explanation for the establishment of a research method for PBX thermal transport.

29

Jang, Taejin, Lubhani Mishra, Akshay Subramaniam, Maitri Uppaluri, and Venkat R. Subramanian. "Immersed Interface and Diffuse-Domain Approach for Current-Potential Distributions and Electrodeposition Problems." ECS Meeting Abstracts MA2022-02, no. 23 (October 9, 2022): 947. http://dx.doi.org/10.1149/ma2022-0223947mtgabs.

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Several numerical approaches are being developed to solve the moving boundary models which predict the morphological evolution of the electrode surface during electrodeposition. Despite these significant research efforts over a broad range of materials, scales, and purposes, the prediction of the shape evolution of the electrodes over time is still a challenging problem. One needs to solve these moving boundary problems, as the potential and current distributions within the cell get affected by the geometry.1-2 In this work, we will demonstrate a recently developed numerical framework based on the diffused domain approach using phase-field models for two classical example, Hull cell and copper deposition in trenches.3 The original model equation was carefully reformulated as a diffuse-domain/immerse domain approach for steady state current-potential distribution problems.4-5 Then the shape change problem is cast as a transient phase-field problem to predict the shape changes of the electrode during electrodeposition. A comparative analysis has also been performed for the efficiency, accuracy, speed, and convergence of the present solutions for the Hull cell with other available numerical and even analytical methods. It can be stated that the present phase-field model is robust and efficient for predicting the shape changes of the electrode over time without oscillations. Acknowledgments This research was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the US Department of Energy (DoE) through the Advanced Battery Materials Research Program (Battery500 Consortium) References V. R. Subramanian, and R. E. White, J. Electrochem. Soc, 149(10) C498 (2002). R. Alkire, T. Bergh, and R. L. Sani, J. Electrochem. Soc., 125, 1981 (1978). T. Jang, L. Mishra, S. A. Roberts, A. Subramaniam, M. Uppaluri, M. P. Gururajan, J. Zhang, and V. R. Subramanian, “BattPhase – A convergent, non-oscillatory, efficient algorithm and code for predicting shape changes in lithium metal batteries using phase-field models – 1. Secondary Current Distribution,” ECSarXiv (2022), doi:10.1149/osf.io/k2vu6 C. S. Peskin, Acta Numer., 11, 479 (2003). X. Li, J. Lowengrub, A. Ratz and A. Voigt, Commun. Math. Sci., 7, 81 (2009).

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Cheng, Tian-Le, You-Hai Wen, and Jeffrey A. Hawk. "Diffuse interface approach to modeling crystal plasticity with accommodation of grain boundary sliding." International Journal of Plasticity 114 (March 2019): 106–25. http://dx.doi.org/10.1016/j.ijplas.2018.10.012.

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De Maio, Umberto, Nicholas Fantuzzi, Fabrizio Greco, Lorenzo Leonetti, and Andrea Pranno. "Failure Analysis of Ultra High-Performance Fiber-Reinforced Concrete Structures Enhanced with Nanomaterials by Using a Diffuse Cohesive Interface Approach." Nanomaterials 10, no. 9 (September 9, 2020): 1792. http://dx.doi.org/10.3390/nano10091792.

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Recent progresses in nanotechnology have clearly shown that the incorporation of nanomaterials within concrete elements leads to a sensible increase in strength and toughness, especially if used in combination with randomly distributed short fiber reinforcements, as for ultra high-performance fiber-reinforced concrete (UHPFRC). Current damage models often are not able to accurately predict the development of diffuse micro/macro-crack patterns which are typical for such concrete structures. In this work, a diffuse cohesive interface approach is proposed to predict the structural response of UHPFRC structures enhanced with embedded nanomaterials. According to this approach, all the internal mesh boundaries are regarded as potential crack segments, modeled as cohesive interfaces equipped with a mixed-mode traction-separation law suitably calibrated to account for the toughening effect of nano-reinforcements. The proposed fracture model has been firstly validated by comparing the failure simulation results of UHPFRC specimens containing different fractions of graphite nanoplatelets with the available experimental data. Subsequently, such a model, combined with an embedded truss model to simulate the concrete/steel rebars interaction, has been used for predicting the load-carrying capacity of steel bar-reinforced UHPFRC elements enhanced with nanoplatelets. The numerical outcomes have shown the reliability of the proposed model, also highlighting the role of the nano-reinforcement in the crack width control.

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Kaka, Fiyanshu, Ravi K. Singh, P. C. Ramamurthy, and Abhik Choudhury. "Modeling process–structure–property relationship in organic photovoltaics using a robust diffuse interface approach." AIP Advances 10, no. 6 (June 1, 2020): 065304. http://dx.doi.org/10.1063/5.0009355.

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Feireisl, Eduard, Madalina Petcu, and Dalibor Pražák. "Relative energy approach to a diffuse interface model of a compressible two‐phase flow." Mathematical Methods in the Applied Sciences 42, no. 5 (January 22, 2019): 1465–79. http://dx.doi.org/10.1002/mma.5436.

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Farokhirad, Samaneh, Taehun Lee, and Jeffrey F. Morris. "Effects of Inertia and Viscosity on Single Droplet Deformation in Confined Shear Flow." Communications in Computational Physics 13, no. 3 (March 2013): 706–24. http://dx.doi.org/10.4208/cicp.431011.260112s.

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AbstractLattice Boltzmann simulations based on the Cahn-Hilliard diffuse interface approach are performed for droplet dynamics in viscous fluid under shear flow, where the degree of confinement between two parallel walls can play an important role. The effects of viscosity ratio, capillary number, Reynolds number, and confinement ratio on droplet deformation and break-up in moderately and highly confined shear flows are investigated.

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Perekatova, Valeriya, Alexey Kostyuk, Mikhail Kirillin, Ekaterina Sergeeva, Daria Kurakina, Olga Shemagina, Anna Orlova, Aleksandr Khilov, and Ilya Turchin. "VIS-NIR Diffuse Reflectance Spectroscopy System with Self-Calibrating Fiber-Optic Probe: Study of Perturbation Resistance." Diagnostics 13, no. 3 (January 26, 2023): 457. http://dx.doi.org/10.3390/diagnostics13030457.

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We report on the comparative analysis of self-calibrating and single-slope diffuse reflectance spectroscopy in resistance to different measurement perturbations. We developed an experimental setup for diffuse reflectance spectroscopy (DRS) in a wide VIS-NIR range with a fiber-optic probe equipped with two source and two detection fibers capable of providing measurements employing both single- and dual-slope (self-calibrating) approaches. In order to fit the dynamic range of a spectrometer in the wavelength range of 460–1030 nm, different exposure times have been applied for short (2 mm) and long (4 mm) source-detector distances. The stability of the self-calibrating and traditional single-slope approaches to instrumental perturbations were compared in phantom and in vivo studies on human palm, including attenuations in individual channels, fiber curving, and introducing optical inhomogeneities in the probe–tissue interface. The self-calibrating approach demonstrated high resistance to instrumental perturbations introduced in the source and detection channels, while the single-slope approach showed resistance only to perturbations introduced into the source channels.

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Wang, Xiaoqiang, and Qiang Du. "Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches." Journal of Mathematical Biology 56, no. 3 (August 15, 2007): 347–71. http://dx.doi.org/10.1007/s00285-007-0118-2.

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Chen, Ching-Yao, and Pei-Yu Yan. "A diffuse interface approach to injection-driven flow of different miscibility in heterogeneous porous media." Physics of Fluids 27, no. 8 (August 2015): 083101. http://dx.doi.org/10.1063/1.4928906.

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Delali Bensah, Yaw, and J. A. Sekhar. "Solidification Morphology and Bifurcation Predictions with the Maximum Entropy Production Rate Model." Entropy 22, no. 1 (December 26, 2019): 40. http://dx.doi.org/10.3390/e22010040.

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The use of the principle of maximum entropy generation per unit volume is a new approach in materials science that has implications for understanding the morphological evolution during solid–liquid interface growth, including bifurcations with or without diffuseness. A review based on a pre-publication arXiv preprint is first presented. A detailed comparison with experimental observations indicates that the Maximum Entropy Production Rate-density model (MEPR) can correctly predict bifurcations for dilute alloys during solidification. The model predicts a critical diffuseness of the interface at which a plane-front or any other form of diffuse interface will become unstable. A further confidence test for the model is offered in this article by comparing the predicted liquid diffusion coefficients to those obtained experimentally. A comparison of the experimentally determined solute diffusion constant in dilute binary Pb–Sn alloys with those predicted by the various solidification instability models (1953–2011) is additionally discussed. A good predictability is noted for the MEPR model when the interface diffuseness is small. In comparison, the more traditional interface break-down models have low predictiveness.

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Cordesse, Pierre, Ruben Di Battista, Quentin Chevalier, Lionel Matuszewski, Thibaut Ménard, Samuel Kokh, and Marc Massot. "A diffuse interface approach for disperse two-phase flows involving dual-scale kinematics of droplet deformation based on geometrical variables." ESAIM: Proceedings and Surveys 69 (2020): 24–46. http://dx.doi.org/10.1051/proc/202069024.

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The purpose of this contribution is to derive a reduced-order two-phase flow model in- cluding interface subscale modeling through geometrical variables based on Stationary Action Principle (SAP) and Second Principle of Thermodynamics in the spirit of [6, 14]. The derivation is conducted in the disperse phase regime for the sake of clarity but the resulting paradigm can be used in a more general framework. One key issue is the definition of the proper potential and kinetic energies in the Lagrangian of the system based on geometrical variables (Interface area density, mean and Gauss curvatures...), which will drive the subscale kinematics and dissipation, and their coupling with large scales of the flow. While [14] relied on bubble pulsation, that is normal deformation of the interface with shape preservation related to pressure changes, we aim here at tackling inclusion deformation at constant volume, thus describing self-sustained oscillations. In order to identify the proper energies, we use Direct Numerical Simulations (DNS) of oscillating droplets using ARCHER code and recently devel- oped library, Mercur(v)e, for mean geometrical variable evaluation and analysis preserving topological invariants. This study is combined with historical analytical studies conducted in the small perturba- tion regime and shows that the proper potential energy is related to the surface difference compared to the spherical minimal surface. A geometrical quasi-invariant is also identified and a natural definition of subscale momentum is proposed. The set of Partial Differential Equations (PDEs) including the conservation equations as well as dissipation source terms are eventually derived leading to an original two-scale diffuse interface model involving geometrical variables.

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Ghosh, Manoj, Muhannad Hendy, Jonathan Raush, and Kasra Momeni. "A Phase-Field Model for In-Space Manufacturing of Binary Alloys." Materials 16, no. 1 (December 31, 2022): 383. http://dx.doi.org/10.3390/ma16010383.

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The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.

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Zhu, Yimei, L. Wu, and V. V. Volkov. "Multiprobe Studies Of Interfaces In Complex Crystals Using Advanced Electron Microscopy." Microscopy and Microanalysis 5, S2 (August 1999): 96–97. http://dx.doi.org/10.1017/s1431927600013805.

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The small probe size and high spatial resolution of TEM offer unique capabilities for studying interfaces of materials. Compared with neutron and x-ray diffraction, TEM is often considered nonquantitative. In HREM, especially, atomic images can alter significantly with imaging parameters that are often difficult to determine experimentally. The weakness of the HREM can be circumvented by a multiprobe approach, i.e., the combined use of a wide range of TEM techniques, such as B-F/D-F imaging, nano-probe EDS and EELS, electron diffraction, and strain-field characterization. Quantitative analysis, based on the calculations and experimental TEM data, is often necessary to correctly derive the crystal-, chemical-, and electronic-structure of an interface.We review our multiprobe approach in studying interfaces in complex systems of superconductors, starting with the simplest interface, twin boundary, in YBa2Cu3O7-δ. Although HREM suggested that there are two types of twin boundaries, with and without a ˜d110 lattice translation at the boundaries, the structural characteristics of the interfaces were determined by analyses of the interfacial δ-α fringe and the associated diffuse scattering, while EELS revealed their association with the local oxygen/hole concentration.

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Grün, Günther, Francisco Guillén-González, and Stefan Metzger. "On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass Densities." Communications in Computational Physics 19, no. 5 (May 2016): 1473–502. http://dx.doi.org/10.4208/cicp.scpde14.39s.

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AbstractIn the first part, we study the convergence of discrete solutions to splitting schemes for two-phase flow with different mass densities suggested in [Guillen-Gonzalez, Tierra, J.Comput.Math. (6)2014]. They have been formulated for the diffuse interface model in [Abels, Garcke, Grün, M3AS, 2012, DOI:10.1142/S0218202511500138] which is consistent with thermodynamics. Our technique covers various discretization methods for phase-field energies, ranging from convex-concave splitting to difference quotient approaches for the double-well potential. In the second part of the paper, numerical experiments are presented in two space dimensions to identify discretizations of Cahn-Hilliard energies which are ϕ-stable and which do not reduce the acceleration of falling droplets. Finally, 3d simulations in axial symmetric geometries are shown to underline even more the full practicality of the approach.

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Shen, Biao, Jiewei Liu, Junichiro Shiomi, Gustav Amberg, Minh Do-Quang, Masamichi Kohno, Koji Takahashi, and Yasuyuki Takata. "Effect of dissolved gas on bubble growth on a biphilic surface: A diffuse-interface simulation approach." International Journal of Heat and Mass Transfer 126 (November 2018): 816–29. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2018.06.043.

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Kou, Jisheng, Shuyu Sun, and Xiuhua Wang. "A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State." SIAM Journal on Scientific Computing 42, no. 1 (January 2020): B30—B56. http://dx.doi.org/10.1137/19m1251230.

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Liu, Xinmin, Rui Tian, Rui Li, Wuquan Ding, Hang Li, and Ruo Yuan. "Principles for the determination of the surface potential of charged particles in mixed electrolyte solutions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2180 (August 2015): 20150064. http://dx.doi.org/10.1098/rspa.2015.0064.

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The Gouy–Chapman surface potential is a key parameter for many interfacial phenomena in physical, chemical and biological systems. Existing theoretical approaches allow the determination of the surface potential at a solid–liquid interface only in single electrolyte solutions; however, mixed electrolytes are often encountered in practical applications. The development of a theoretical approach for the determination of the surface potential in mixed electrolyte solutions is therefore a desirable goal. In this study, this important issue was resolved for the first time. Based on the analytical solutions of the nonlinear Poisson–Boltzmann equation in different mixed electrolyte solutions, corresponding mathematical relationships were developed between the surface potential and the mean ionic concentration in the diffuse layer. As the mean ionic concentration in the diffuse layer can be easily determined, the surface potential could be calculated using the newly derived equations. The effects of electrolyte composition on the surface potential were theoretically quantified in the new equations, while only counterionic type was taken into account for mixed electrolyte solutions in the current studies.

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Delouei, A. Amiri, M. Nazari, M. H. Kayhani, and S. Succi. "Immersed Boundary – Thermal Lattice Boltzmann Methods for Non-Newtonian Flows Over a Heated Cylinder: A Comparative Study." Communications in Computational Physics 18, no. 2 (July 30, 2015): 489–515. http://dx.doi.org/10.4208/cicp.060414.220115a.

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AbstractIn this study, we compare different diffuse and sharp interface schemes of direct-forcing immersed boundary — thermal lattice Boltzmann method (IB-TLBM) for non-Newtonian flow over a heated circular cylinder. Both effects of the discrete lattice and the body force on the momentum and energy equations are considered, by applying the split-forcing Lattice Boltzmann equations. A new technique based on predetermined parameters of direct forcing IB-TLBM is presented for computing the Nusselt number. The study covers both steady and unsteady regimes (20<Re<80) in the power-law index range of 0.6<n<1.4, encompassing both shear-thinning and shear-thickening non-Newtonian fluids. The numerical scheme, hydrodynamic approach and thermal parameters of different interface schemes are compared in both steady and unsteady cases. It is found that the sharp interface scheme is a suitable and possibly competitive method for thermal-IBM in terms of accuracy and computational cost.

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Weger, Michael, Oswald Knoth, and Bernd Heinold. "An urban large-eddy-simulation-based dispersion model for marginal grid resolutions: CAIRDIO v1.0." Geoscientific Model Development 14, no. 3 (March 15, 2021): 1469–92. http://dx.doi.org/10.5194/gmd-14-1469-2021.

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Abstract. The ability to achieve high spatial resolutions is an important feature for numerical models to accurately represent the large spatial variability of urban air pollution. On the one hand, the well-established mesoscale chemistry transport models have their obvious shortcomings due to the extensive use of physical parameterizations. On the other hand, obstacle-resolving computational fluid dynamics (CFD) models, although accurate, are still often too computationally intensive to be applied regularly for entire cities. The major reason for the inflated computational costs is the required horizontal resolution to meaningfully apply obstacle discretization, which is mostly based on boundary-fitted grids, e.g., the marker-and-cell method. In this paper, we present the new City-scale AIR dispersion model with DIffuse Obstacles (CAIRDIO v1.0), in which the diffuse interface method, simplified for non-moving obstacles, is incorporated into the governing equations for incompressible large-eddy simulations. While the diffuse interface method is widely used in two-phase modeling, this method has not been used in urban boundary-layer modeling so far. It allows us to consistently represent buildings over a wide range of spatial resolutions, including grid spacings equal to or larger than typical building sizes. This way, the gray zone between obstacle-resolving microscale simulations and mesoscale simulations can be addressed. Orographic effects can be included by using terrain-following coordinates. The dynamic core is compared against a standard quality-assured wind-tunnel dataset for dispersion-model evaluation. It is shown that the model successfully reproduces dispersion patterns within a complex city morphology across a wide range of spatial resolutions tested. As a result of the diffuse obstacle approach, the accuracy test is also passed at a horizontal grid spacing of 40 m. Although individual flow features within individual street canyons are not resolved at the coarse-grid spacing, the building effect on the dispersion of the air pollution plume is preserved at a larger scale. Therefore, a very promising application of the CAIRDIO model lies in the realization of computationally feasible yet accurate air-quality simulations for entire cities.

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Pranno, Andrea, Fabrizio Greco, Lorenzo Leonetti, Paolo Lonetti, Paolo Nevone Blasi, and Umberto De Maio. "Cracking analysis in Ultra-High-Performance Fiber-Reinforced Concrete with embedded nanoparticles via a diffuse interface approach." Procedia Structural Integrity 39 (2022): 688–99. http://dx.doi.org/10.1016/j.prostr.2022.03.142.

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Greco, Fabrizio, Lorenzo Leonetti, Raimondo Luciano, Arturo Pascuzzo, and Camilla Ronchei. "A detailed micro-model for brick masonry structures based on a diffuse cohesive-frictional interface fracture approach." Procedia Structural Integrity 25 (2020): 334–47. http://dx.doi.org/10.1016/j.prostr.2020.04.038.

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Amirian, Benhour, Bilen Emek Abali, and James David Hogan. "The study of diffuse interface propagation of dynamic failure in advanced ceramics using the phase-field approach." Computer Methods in Applied Mechanics and Engineering 405 (February 2023): 115862. http://dx.doi.org/10.1016/j.cma.2022.115862.

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