Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media

Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media under periodic fluid flow by an asymptotic multi-scale expansion with drift. The microscopic setting is a two-component periodic composite consisting of a dilute electrolyte continuum (described by standard PNP equations) and a continuous dielectric matrix, which is impermeable to the ions and carries a given surface charge. Four new features arise in the upscaled equations: (i) the effective ionic diffusivities and mobilities become tensors, related to the microstructure; (ii) the effective permittivity is also a tensor, depending on the electrolyte/matrix permittivity ratio and the ratio of the Debye screening length to the macroscopic length of the porous medium; (iii) the microscopic fluidic convection is replaced by a diffusion-dispersion correction in the effective diffusion tensor; and (iv) the surface charge per volume appears as a continuous "background charge density", as in classical membrane models. The coefficient tensors in the upscaled PNP equations can be calculated from periodic reference cell problems. For an insulating solid matrix, all gradients are corrected by the same tensor, and the Einstein relation holds at the macroscopic scale, which is not generally the case for a polarizable matrix, unless the permittivity and electric field are suitably defined. In the limit of thin double layers, Poisson's equation is replaced by macroscopic electroneutrality (balancing ionic and surface charges). The general form of the macroscopic PNP equations may also hold for concentrated solution theories, based on the local-density and mean-field approximations. These results have broad applicability to ion transport in porous electrodes, separators, membranes, ion-exchange resins, soils, porous rocks, and biological tissues

Rate of Convergence of Phase Field Equations in Strongly Heterogeneous Media towards their Homogenized Limit

We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such free energies in homogeneous environments found a broad interest over the last decades and hence is now widely accepted and applied in both science and engineering. Here, we focus on strongly heterogeneous materials with perforations such as porous media. To the best of our knowledge, we present a general formal derivation of upscaled phase field equations for arbitrary free energy densities and give a rigorous justification by error estimates for a broad class of polynomial free energies. The error between the effective macroscopic solution of the new upscaled formulation and the solution of the microscopic phase field problem is of order $\epsilon^1/2$ for a material given characteristic heterogeneity $\epsilon$. Our new, effective, and reliable macroscopic porous media formulation of general phase field equations opens new modelling directions and computational perspectives for interfacial transport in strongly heterogeneous environments

Homogenization of a catalyst layer model for periodically distributed pore geometries in PEM fuel cells

We formally derive an effective catalyst layer model comprising the reduction of oxygen for periodically distributed pore geometries. By assumption, the pores are completely filled with water and the surrounding walls consist of catalyst particles which are attached to an electron conducting microstructure. The macroscopic transport equations are established by a multi-scale approach, based on microscopic phenomena at the pore level, and serve as a first step toward future optimization of catalyst layer designs

Basic and extendable framework for effective charge transport in electrochemical systems

We consider basic and easily extendible transport formulations for lithium batteries consisting of an anode (Li-foil), a separator (polymer electrolyte), and a composite cathode (composed of electrolyte and intercalation particles). Our mathematical investigations show the following novel features: (i) \emph{complete and very basic description of mixed transport processes} relying on a neutral, binary symmetric electrolyte resulting in a non-standard Poisson equation for the electric potential together with interstitial diffusion approximated by classical diffusion; (ii) \emph{ upscaled and basic composite cathode equations allowing to take geometric and material features of electrodes into account}; (iii) \emph{the derived effective macroscopic model can be numerically solved with well-known numerical strategies for homogeneous domains} and hence does not require to solve a high-dimensional numerical problem or to depend on a computationally involved multiscale discretisation strategies where highly heterogeneous and realistic, nonlinear, and reactive boundary conditions are still unexplored. We believe that the here proposed basic and easily extendible formulations will serve as a basic and simple setup towards a systematic theoretical and experimental understanding of complex electrochemical systems and their optimization, e.g. Li-batteries

Grain size tailoring of tungsten copper nanocomposites to affect local fracture characteristics

Tungsten offers outstanding material properties, and is therefore frequently considered as good candidate for high performance applications in harsh environments, e.g. fusion reactor shielding. However, tungsten lacks damage and fracture tolerance due to a high ductile to brittle transition temperature, thus remains hardly applicable to safety-relevant applications. By creating a composite and adding copper as ductile phase, damage as well as fracture tolerance are increased at the expense of material strength. Hence, additional strengthening of the ductile phase is desirable, i.e. by alloying copper with zinc. Elemental powders were used as a precursor to create alloys in the α -brass region, from 0 to 30 wt.% zinc, as in this compositional region brass exhibits high twinning tendency. To obtain brass powder, copper and zinc were alloyed via ball-milling in a preprocessing step, which was verified by XRD measurements. The bulk samples were subsequently fabricated with a constant tungsten content of 80 wt.% by consolidating the tungsten-brass powder mixture using high pressure torsion (HPT). Additionally, HPT was used to refine the grains to the nanocrystalline saturation regime to further increase strength while keeping the ductility as high as possible. To verify microstructural saturation, Vickers hardness measurements and microstructural investigations by means of SEM were performed, while TEM and TKD investigations provided insights regarding the grain size distribution. In-situ experiments on FIB milled micro-cantilevers were conducted in an SEM to analyze crack growth and determine the material\u27s fracture characteristics. We show that the saturation grain size depends on the ductile phase strength and HPT deformation temperature. Furthermore, fracture analysis reveals that the fracture process is dominated by intercrystalline fracture and that primarily inhomogeneities determine the achievable fracture toughness

SMAC Mimetic BV6 Induces Cell Death in Monocytes and Maturation of Monocyte-Derived Dendritic Cells

Background: Compounds mimicking the inhibitory effect of SMAC / DIABLO on X-linked inhibitor of apoptosis (XIAP) have been developed with the aim to achieve sensitization for apoptosis of tumor cells resistant due to deregulated XIAP expression. It turned out that SMAC mimetics also have complex effects on the NFkB system and TNF signaling. In view of the overwhelming importance of the NFkB transcription factors in the immune system, we analyzed here the effects of the SMAC mimetic BV6 on immune cells. Principal Findings: BV6 induced apoptotic and necrotic cell death in monocytes while T-cells, dendritic cells and macrophages were largely protected against BV6-induced cell death. In immature dendritic cells BV6 treatment resulted in moderate activation of the classical NFkB pathway, but it also diminished the stronger NFkB-inducing effect of TNF and CD40L. Despite its inhibitory effect on TNF- and CD40L signaling, BV6 was able to trigger maturation of immature DCs as indicated by upregulation of CD83, CD86 and IL12. Significance: The demonstrated effects of SMAC mimetics on immune cells may complicate the development of tumor therapeutic concepts based on these compounds but also arise the possibility to exploit them for the development of immune stimulatory therapies