Caratterizzazione di membrane metalliche e ionomeriche per applicazioni energetiche

The work of this thesis has been focused on the characterization of metallic membranes for the hydrogen purification from steam reforming process and also of perfluorosulphonic acid ionomeric (PFSI) membranes suitable as electrolytes in fuel cell applications. The experimental study of metallic membranes was divided in three sections: synthesis of palladium and silver palladium coatings on porous ceramic support via electroless deposition (ELD), solubility and diffusivity analysis of hydrogen in palladium based alloys (temperature range between 200 and 400 °C up to 12 bar of pressure) and permeation experiments of pure hydrogen and mixtures containing, besides hydrogen, also nitrogen and methane at high temperatures (up to 600 °C) and pressures (up to 10 bar). Sequential deposition of palladium and silver on to porous alumina tubes by ELD technique was carried out using two different procedures: a stirred batch and a continuous flux method. Pure palladium as well as Pd-Ag membranes were produced: the Pd-Ag membranes’ composition is calculated to be close to 77% Pd and 23% Ag by weight which was the target value that correspond to the best performance of the palladium-based alloys. One of the membranes produced showed an infinite selectivity through hydrogen and relatively high permeability value and is suitable for the potential use as a hydrogen separator. The hydrogen sorption in silver palladium alloys was carried out in a gravimetric system on films produced by ELD technique. In the temperature range inspected, up to 400°C, there is still a lack in literature. The experimental data were analyzed with rigorous equations allowing to calculate the enthalpy and entropy values of the Sieverts’ constant; the results were in very good agreement with the extrapolation made with literature data obtained a lower temperature (up to 150 °C). The information obtained in this study would be directly usable in the modeling of hydrogen permeation in Pd-based systems. Pure and mixed gas permeation tests were performed on Pd-based hydrogen selective membranes at operative conditions close to steam-reforming ones. Two membranes (one produced in this work and another produced by NGK Insulators Japan) showed a virtually infinite selectivity and good permeability. Mixture data revealed the existence of non negligible resistances to hydrogen transport in the gas phase. Even if the decrease of the driving force due to polarization concentration phenomena occurs, in principle, in all membrane-based separation systems endowed with high perm-selectivity, an extensive experimental analysis lack, at the moment, in the palladium-based membrane process in literature. Moreover a new procedure has been introduced for the proper comparison of the mass transport resistance in the gas phase and in the membrane. Another object of study was the water vapor sorption and permeation in PFSI membranes with short and long side chains was also studied; moreover the permeation of gases (i.e. He, N2 and O2) in dry and humid conditions was considered. The water vapor sorption showed strong interactions between the hydrophilic groups and the water as revealed from the hysteresis in the sorption-desorption isotherms and thermo gravimetric analysis. The data obtained were used in the modeling of water vapor permeation, that was described as diffusion-reaction of water molecules, and in the humid gases permeation experiments. In the dry gas experiments the permeability and diffusivity was found to increase with temperature and with the equivalent weight (EW) of the membrane. A linear correlation was drawn between the dry gas permeability and the opposite of the equivalent weight of PFSI membranes, based on which the permeability of pure PTFE is retrieved in the limit of high EW. In the other hand O2 ,N2 and He permeability values was found to increase significantly, and in a similar fashion, with water activity. A model that considers the PFSI membrane as a composite matrix with a hydrophilic and a hydrophobic phase was considered allowing to estimate the variation of gas permeability with relative humidity on the basis of the permeability in the dry PFSI membrane and in pure liquid water.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.