Qianlong Liu

Physalis method for heterogeneous mixtures of dielectrics and conductors: Accurately simulating one million particles using a PC

Prosperettis seminal Physalis method, an Immersed Boundary/spectral method, had been used extensively to investigate fluid flows with suspended solid particles. Its underlying idea of creating a cage and using a spectral general analytical solution around a discontinuity in a surrounding field as a computational mechanism to enable the accommodation of physical and geometric discontinuities is a general concept, and can be applied to other problems of importance to physics, mechanics, and chemistry. In this paper we provide a foundation for the application of this approach to the determination of the distribution of electric charge in heterogeneous mixtures of dielectrics and conductors. The proposed Physalis method is remarkably accurate and efficient. In the method, a spectral analytical solution is used to tackle the discontinuity and thus the discontinuous boundary conditions at the interface of two media are satisfied exactly. Owing to the hybrid finite difference and spectral schemes, the method is spectrally accurate if the modes are not sufficiently resolved, while higher than second-order accurate if the modes are sufficiently resolved, for the solved potential field. Because of the features of the analytical solutions, the derivative quantities of importance, such as electric field, charge distribution, and force, have the same order of accuracy as the solved potential field during postprocessing. This is an important advantage of the Physalis method over other numerical methods involving interpolation, differentiation, and integration during postprocessing, which may significantly degrade the accuracy of the derivative quantities of importance. The analytical solutions enable the user to use relatively few mesh points to accurately represent the regions of discontinuity. In addition, the spectral convergence and a linear relationship between the cost of computer memory/computation and particle numbers results in a very efficient method. In the present paper, the accuracy of the method is numerically investigated by example computations using one dielectric particle, one isolated conductor particle, one conductor particle connected to an external source with imposed voltage, and two conductor/dielectric particles with strong interactions. The efficiency of the method is demonstrated with one million particles, which suggests that the method can be used for many important engineering applications of broad interest.

HeteroFoaMs: Electrode Modeling in Nanostructured Heterogeneous Materials for Energy Systems

Hetero geneous F unctio na l M aterials, e.g., “HeteroFoaMs” are at the heart of countless energy systems, including (from left to right below) heat storage materials (a), batteries (b), solid oxide fuel cells (c), and polymer electrolyte fuel cells (d). HeteroFoaMs are generally nano-structured and porous to accommodate transport of gasses or fluids, and must be multi-functional (i.e., active operators on mass, momentum, energy or charge, in combinations). This paper will discuss several aspects of modeling the relationships between the constituents and microstructure of these material systems and their device functionalities. Technical advances based on these relationships will also be identified and discussed. Three major elements of the general problem of how to model HeteroFoaM electrodes will be addressed. Modeling approaches for ionic charge transfer with electrochemistry in the nano-structured porosity of the electrode will be discussed. Second, the effect of morphology and space charge on conduction through porous doped ceria particle assemblies, and their role in electrode processes will be modeled and described. And third, the effect of local heterogeneity and morphology on charge distributions and polarization in porous dielectric electrode materials will be analyzed using multi-physics field equations set on the details of local morphology. Several new analysis methods and results, as well as experimental data relating to these approaches will be presented. The value, capabilities, and limitations of the approaches will be evaluated.Copyright

Heterogeneous mixtures of elliptical particles: Directly resolving local and global properties and responses

In our earlier papers, Prosperettis seminal Physalis method for fluid flows was extended to directly resolve electric fields in finite-sized particles and to investigate accurately the mutual fluid-particle, particle-particle, and particle-boundary interactions for circular/spherical particles. For the first time, the method makes the accurate prediction of the local charge distribution, force and torque on finite-sized particles possible. In the present work, the method is extended to heterogeneous mixtures of elliptical particles to further investigate the effects of the orientation and anisotropy. The direct resolution of the effect of fields in heterogeneous mixtures of elliptical particles to determine local and global properties and responses has many applications in engineering, mechanics, physics, chemistry, and biology. The method can be applied to heterogeneous materials, heterogeneous functional materials, microfluidics, and devices such as electric double layer capacitors. In the present paper, the accuracy of the method is extensively investigated even for very challenging problems, for example, for elongated rod-like particles with very high aspect ratios. The accuracy and efficiency of the method suggests that it can be used for many important applications of broad interest.

Meso-design of heterogeneous dielectric material systems: Structure property relationships

Heterogeneous materials are inherently dielectric, and charge distribution and transport in such materials involves complex local fields and polarizations that are remarkably sensitive to morphology and the interaction of conduction and permittivity. Trial and error design of such material systems is time consuming and expensive, and often ineffectual. However, heterogeneous materials are essential for energy conversion and storage, and they have become the foundation for major advances in the performance of devices such as batteries, fuel cells, separation membranes, and solar cells. The present paper presents some relationships in support of rational design based on an extensive experimental validation of the concepts and analysis that form a foundation for that design. Salient results include the prediction and confirmation of volume fraction effects (including nondilute mixtures), and the prediction and direct measurement of surface charge effects at internal interfaces as a function of constituent morphology and orientation.

Rational durability design of heterogeneous functional materials: Some first principles

The present paper proposes a rational approach to the design of constituents, their morphology, and their multiscale arrangement in heterogeneous functional material systems to control the evolution of their properties, morphology, and performance as they interact over specified histories of applied mechanical, electrical, chemical, and thermal fields. The principal thrust of the paper is the postulate of a “first law” for such an approach, which states that “only 100 percent efficient systems are 100 percent durable; the durability is controlled by non-conservative changes in the material state, which are uniquely reflected in changes in the material compliance to applied fields.” The application of the “first law of rational durability design” is discussed for mechanical and electrical applied fields acting upon primarily two-phase heterogeneous material systems. A rational design analysis is demonstrated, and the results are compared with experimental data for fiber-reinforced control materials. The application of the concepts to heterogeneous functional materials (HeteroFoaM) used in fuel cells, batteries, membranes, and electrolyzers is also discussed.

HeteroFoaMs: Electrode Modeling in Nano-Structured Heterogeneous Materials for Energy Systems

Hetero geneous F unctio na l M aterials, e.g., “HeteroFoaMs” are at the heart of countless energy systems, including (from left to right below) heat storage materials (a), batteries (b), solid oxide fuel cells (c), and polymer electrolyte fuel cells (d). HeteroFoaMs are generally nano-structured and porous to accommodate transport of gasses or fluids, and must be multi-functional (i.e., active operators on mass, momentum, energy or charge, in combinations). This paper will discuss several aspects of modeling the relationships between the constituents and microstructure of these material systems and their device functionalities. Technical advances based on these relationships will also be identified and discussed. Three major elements of the general problem of how to model HeteroFoaM electrodes will be addressed. Modeling approaches for ionic charge transfer with electrochemistry in the nano-structured porosity of the electrode will be discussed. Second, the effect of morphology and space charge on conduction through porous doped ceria particle assemblies, and their role in electrode processes will be modeled and described. And third, the effect of local heterogeneity and morphology on charge distributions and polarization in porous dielectric electrode materials will be analyzed using multi-physics field equations set on the details of local morphology. Several new analysis methods and results, as well as experimental data relating to these approaches will be presented. The value, capabilities, and limitations of the approaches will be evaluated.Copyright

Processing-Property Relationships in Advanced Multi-Functional Composite Materials: Management of Dielectric Behavior

Many of the advanced composite materials used in aerospace, energy storage and conversion, and electrical devices are multifunctional, i.e., they operate on (or in the presence of) some combination of mechanical, thermal, electrical, chemical, and magnetic fields. Designing composite materials for airplanes, for example, must include not only structural, but also thermal and electrical considerations. Most energy storage and conversion devices are made from advanced composite materials, and they must be designed to interact and sustain their functions in multiple fields, often mechanical, electrical, electrochemical, and thermal. The functional characteristics of such materials are not only controlled by the constituent properties, but are highly dependent on the size, shape, geometry, arrangement, and interfaces between the constituent materials, the extrinsic factors controlled by processing. That is the subject of the present paper. In particular, we will focus on the design of microstructure in heterogeneous materials to manage the dielectric properties and character of such materials.