Numerical and analytical vibro-acoustic modelling of porous materials: the Cell Method for poroelasticity and the case of inclusions

Porous materials are widely used in many fields of industrial applications, to achieve the requirements of noise reduction, that nowadays derive from strict regulations. The modeling of porous materials is still a problematic issue. Numerical simulations are often problematic in case of real complex geometries, especially in terms of computational times and convergence. At the same time, analytical models, even if partly limited by restrictive simplificative hypotheses, represent a powerful instrument to capture quickly the physics of the problem and general trends. In this context, a recently developed numerical method, called the Cell Method, is described, is presented in the case of the Biot's theory and applied for representative cases. The peculiarity of the Cell Method is that it allows for a direct algebraic and geometrical discretization of the field equations, without any reduction to a weak integral form. Then, the second part of the thesis presents the case of interaction between two poroelastic materials under the context of double porosity. The idea of using periodically repeated inclusions of a second porous material into a layer composed by an original material is described. In particular, the problem is addressed considering the efficiency of the analytical method. A analytical procedure for the simulation of heterogeneous layers based is described and validated considering both conditions of absorption and transmission; a comparison with the available numerical methods is performed. ---------------- I materiali porosi sono ampiamente utilizzati per diverse applicazioni industriali, al fine di raggiungere gli obiettivi di riduzione del rumore, che sono resi impegnativi da norme al giorno d'oggi sempre più stringenti. La modellazione dei materiali porori per applicazioni vibro-acustiche rapprensenta un aspetto di una certa complessità. Le simulazioni numeriche sono spesso problematiche quando siano coinvolte geometrie di pezzi reali, in particolare riguardo i tempi computazionali e la convergenza. Allo stesso tempo, i modelli analitici, anche se parzialmente limitati a causa di ipotesi semplificative che ne restringono l'ambito di utilizzo, rappresentano uno strumento molto utile per comprendere rapidamente la fisica del problema e individuare tendenze generali. In questo contesto, un metodo numerico recentemente sviluppato, il Metodo delle Celle, viene descritto, implementato nel caso della teoria di Biot per la poroelasticità e applicato a casi rappresentativi. La peculiarità del Metodo delle Celle consiste nella discretizzazione diretta algebrica e geometrica delle equazioni di campo, senza alcuna riduzione a forme integrali deboli. Successivamente, nella seconda parte della tesi viene presentato il caso delle interazioni tra due materiali poroelastici a contatto, nel contesto dei materiali a doppia porosità. Viene descritta l'idea di utilizzare inclusioni periodicamente ripetute di un secondo materiale poroso all'interno di un layer a sua volta poroso. In particolare, il problema è studiando il metodo analitico e la sua efficienza. Una procedura analitica per il calcolo di strati eterogenei di materiale viene descritta e validata considerando sia condizioni di assorbimento, sia di trasmissione; viene effettuata una comparazione con i metodi numerici a disposizione.

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.

Stability, viscous dissipation and local thermal non-equilibrium in fluid saturated porous media

In this thesis, the field of study related to the stability analysis of fluid saturated porous media is investigated. In particular the contribution of the viscous heating to the onset of convective instability in the flow through ducts is analysed. In order to evaluate the contribution of the viscous dissipation, different geometries, different models describing the balance equations and different boundary conditions are used. Moreover, the local thermal non-equilibrium model is used to study the evolution of the temperature differences between the fluid and the solid matrix in a thermal boundary layer problem. On studying the onset of instability, different techniques for eigenvalue problems has been used. Analytical solutions, asymptotic analyses and numerical solutions by means of original and commercial codes are carried out.

Porous Polymeric Bioresorbable Scaffolds for Tissue Engineering

Tissue engineering is a discipline that aims at regenerating damaged biological tissues by using a cell-construct engineered in vitro made of cells grown into a porous 3D scaffold. The role of the scaffold is to guide cell growth and differentiation by acting as a bioresorbable temporary substrate that will be eventually replaced by new tissue produced by cells. As a matter or fact, the obtainment of a successful engineered tissue requires a multidisciplinary approach that must integrate the basic principles of biology, engineering and material science. The present Ph.D. thesis aimed at developing and characterizing innovative polymeric bioresorbable scaffolds made of hydrolysable polyesters. The potentialities of both commercial polyesters (i.e. poly-e-caprolactone, polylactide and some lactide copolymers) and of non-commercial polyesters (i.e. poly-w-pentadecalactone and some of its copolymers) were explored and discussed. Two techniques were employed to fabricate scaffolds: supercritical carbon dioxide (scCO2) foaming and electrospinning (ES). The former is a powerful technology that enables to produce 3D microporous foams by avoiding the use of solvents that can be toxic to mammalian cells. The scCO2 process, which is commonly applied to amorphous polymers, was successfully modified to foam a highly crystalline poly(w-pentadecalactone-co-e-caprolactone) copolymer and the effect of process parameters on scaffold morphology and thermo-mechanical properties was investigated. In the course of the present research activity, sub-micrometric fibrous non-woven meshes were produced using ES technology. Electrospun materials are considered highly promising scaffolds because they resemble the 3D organization of native extra cellular matrix. A careful control of process parameters allowed to fabricate defect-free fibres with diameters ranging from hundreds of nanometers to several microns, having either smooth or porous surface. Moreover, versatility of ES technology enabled to produce electrospun scaffolds from different polyesters as well as “composite” non-woven meshes by concomitantly electrospinning different fibres in terms of both fibre morphology and polymer material. The 3D-architecture of the electrospun scaffolds fabricated in this research was controlled in terms of mutual fibre orientation by properly modifying the instrumental apparatus. This aspect is particularly interesting since the micro/nano-architecture of the scaffold is known to affect cell behaviour. Since last generation scaffolds are expected to induce specific cell response, the present research activity also explored the possibility to produce electrospun scaffolds bioactive towards cells. Bio-functionalized substrates were obtained by loading polymer fibres with growth factors (i.e. biomolecules that elicit specific cell behaviour) and it was demonstrated that, despite the high voltages applied during electrospinning, the growth factor retains its biological activity once released from the fibres upon contact with cell culture medium. A second fuctionalization approach aiming, at a final stage, at controlling cell adhesion on electrospun scaffolds, consisted in covering fibre surface with highly hydrophilic polymer brushes of glycerol monomethacrylate synthesized by Atom Transfer Radical Polymerization. Future investigations are going to exploit the hydroxyl groups of the polymer brushes for functionalizing the fibre surface with desired biomolecules. Electrospun scaffolds were employed in cell culture experiments performed in collaboration with biochemical laboratories aimed at evaluating the biocompatibility of new electrospun polymers and at investigating the effect of fibre orientation on cell behaviour. Moreover, at a preliminary stage, electrospun scaffolds were also cultured with tumour mammalian cells for developing in vitro tumour models aimed at better understanding the role of natural ECM on tumour malignity in vivo.

Geological and hydrogeological features affecting migration, multi-phase partitioning and degradation of chlorinated hydrocarbons through unconsolidated porous media.

Chlorinated solvents are the most ubiquitous organic contaminants found in groundwater since the last five decades. They generally reach groundwater as Dense Non-Aqueous Phase Liquid (DNAPL). This phase can migrate through aquifers, and also through aquitards, in ways that aqueous contaminants cannot. The complex phase partitioning to which chlorinated solvent DNAPLs can undergo (i.e. to the dissolved, vapor or sorbed phase), as well as their transformations (e.g. degradation), depend on the physico-chemical properties of the contaminants themselves and on features of the hydrogeological system. The main goal of the thesis is to provide new knowledge for the future investigations of sites contaminated by DNAPLs in alluvial settings, proposing innovative investigative approaches and emphasizing some of the key issues and main criticalities of this kind of contaminants in such a setting. To achieve this goal, the hydrogeologic setting below the city of Ferrara (Po plain, northern Italy), which is affected by scattered contamination by chlorinated solvents, has been investigated at different scales (regional and site specific), both from an intrinsic (i.e. groundwater flow systems) and specific (i.e. chlorinated solvent DNAPL behavior) point of view. Detailed investigations were carried out in particular in one selected test-site, known as “Caretti site”, where high-resolution vertical profiling of different kind of data were collected by means of multilevel monitoring systems and other innovative sampling and analytical techniques. This allowed to achieve a deep geological and hydrogeological knowledge of the system and to reconstruct in detail the architecture of contaminants in relationship to the features of the hosting porous medium. The results achieved in this thesis are useful not only at local scale, e.g. employable to interpret the origin of contamination in other sites of the Ferrara area, but also at global scale, in order to address future remediation and protection actions of similar hydrogeologic settings.

Development of novel multi-substituted apatite nanophases with advanced functionalities for bone regeneration

In the field of bone substitutes is highly researched an innovative material able to fill gaps with high mechanical performances and able to stimulate cell response, permitting the complete restoration of the bone portion. In this respect, the synthesis of new bioactive materials able to mimic the compositional, morphological and mechanical features of bone is considered as the elective approach for effective tissue regeneration. Hydroxyapatite (HA) is the main component of the inorganic part of bone. Additionally ionic substitution can be performed in the apatite lattice producing different effects, depending from the selected ions. Magnesium, in substitution of calcium, and carbonate, in substitution of phosphate, extensively present in the biological bones, are able to improve properties naturally present in the apatitic phase, (i.e. biomimicry, solubility e osteoinductive properties). Other ions can be used to give new useful properties, like antiresorptive or antimicrobial properties, to the apatitic phase. This thesis focused on the development of hydroxyapatite nanophases with multiple ionic substitutions including gallium, or zinc ions, in association with magnesium and carbonate, with the purpose to provide double synergistic functionality as osteogenic and antibacterial biomaterial. Were developed bioactive materials based on Sr-substituted hydroxyapatite in the form of sintered targets. The obtained targets were treated with Pulsed Plasma Deposition (PED) resulting in the deposition of thin film coatings able to improve the roughness and wettability of PEEK, enhancing its osteointegrability. Were investigated heterogeneous gas-solid reactions, addressed to the biomorphic transformations of natural 3D porous structures into bone scaffolds with biomimetic composition and hierarchical organization, for application in load-bearing sites. The kinetics of the different reactions of the process were optimized to achieve complete and controlled phase transformation, maintaining the original 3-D morphology. Massive porous scaffolds made of ion-substituted hydroxyapatite and bone-mimicking structure were developed and tested in 3-D cell culture models.

Linear and nonlinear thermal instability of Newtonian and non-Newtonian fluid saturated porous media

The present work aims to investigate the influence of different aspects, such as non-standard steady solutions, complex fluid rheologies and non-standard porous-channel geometries, on the stability of a Darcy-Bénard system. In order to do so, both linear and nonlinear stability theories are considered. A linear analysis focuses on studying the dynamics of the single disturbance wave present in the system, while its nonlinear counterpart takes into consideration the interactions among the single modes. The scope of the stability analysis is to obtain information regarding the transition from an equilibrium solution to another one, and also information regarding the transition nature and the emergent solution after the transition. The disturbance governing equations are solved analytically, whenever possible, and numerical by considering different approaches. Among other important results, it is found that a cylinder cross-section does not affect the thermal instability threshold, but just the linear pattern selection for dilatant and pseudoplastic fluid saturated porous media. A new rheological model is proposed as a solution for singular issues involving the power-law model. Also, a generalised class of one parameter basic solutions is proposed as an alternative description of the isoflux Darcy--Bénard problem. Its stability is investigated.