Dans un contexte d’augmentation constante des volumes de boues d’épuration à traiter, l’optimisation du traitement des boues est un enjeu primordial. Les étapes de traitement, et de transport mettent en jeu des écoulements qu’il est nécessaire de comprendre et de prédire afin, par exemple, de pour pouvoir estimer les pertes de charges en conduite ou bien pour dimensionner les installations de pompage. D’un point de vue physique, les boues peuvent être considérées comme une suspension de particules dans un gel suspendant. Ainsi, le comportement rhéologique des boues d’épuration présente des similitudes importantes avec les suspensions colloïdales et les gels polymériques. Ces trois types de matériaux, i.e. les boues d’épuration, les gels colloïdaux et les suspensions polymériques, présentent un comportement rhéologique complexe dépendant du temps et de la sollicitation imposée. Ils présentent un comportement dual, solide aux contraintes faibles, et liquide pour des contraintes élevées. La transition solide-liquide est généralement modélisée par la définition d’un seuil de contrainte ou de déformation, supposé séparer les régimes solide et liquide. Cependant, cette notion de seuil suppose une transition abrupte, et s’oppose aux observations expérimentales qui mettent en évidence une transition continue et progressive. L’étude de la littérature a permis de mettre en évidence une nécessité d’améliorer la compréhension et la modélisation du phénomène de transition solide-liquide. De plus, il est nécessaire d’unifier la description des régimes solide et liquide sous un même modèle, afin de mettre en lien une continuité mathématique avec le caractère continu et progressif du phénomène physique modélisé. Une analyse des résultats disponibles dans la littérature nous a permis de construire un modèle mathématique unique pour décrire le comportement solide et le comportement liquide des matériaux étudiés. Les hypothèses posées à partir de la littérature pour construire ce modèle ont ensuite été validées expérimentalement. Le modèle proposé est basé sur la décomposition de la complaisance du matériau en la somme d’une contribution solide et d’une contribution liquide, dépendant du temps, de la sollicitation appliquée et de l’histoire du matériau. Ce modèle permet une description commune des comportements solides et liquides du matériau, en tenant compte de l’existence d’une élasticité résiduelle y compris pour des contraintes élevées, et d’une dissipation visqueuse faible pour les contraintes faibles, conformément aux résultats expérimentaux. Ces travaux de thèse ont permis de mettre en évidence le fait que le mécanisme de transition solide-liquide était piloté non pas par la contrainte ou par la déformation, mais par la complaisance du matériau. De plus, ils ont permis d’ouvrir la voie à une nouvelle manière d’appréhender la thixotropie et la transition solide-liquide des matériaux pâteux. En effet, le comportement d’un matériau pâteux est piloté par deux paramètres : un module élastique plateau correspondant à un état totalement structuré, et une viscosité infinie correspondant à un état totalement déstructuré. Ces paramètres intrinsèques au matériau sont alors pondérés par des évolutions de la microstructure, menant à une compétition entre les effets élastiques et les effets visqueux. Ainsi, la différence entre un comportement de type loi de puissance et un comportement de type loi de puissance à seuil peut être expliquée simplement par l’apparition d’effets élastiques non négligeables. / In a context of constant increasing volumes of wastewater treatment sludge, optimizing the treatment of sludge appears to be crucial. Each step of treatment and transportation involves flows. It appears necessary to understand and predict these flows in order, for example, to estimate pressure drops in pipes or to size properly pumping facilities. In a physical point of view, sludge can be considered as a suspension of particles in a gel. Thus, its rheological behaviour presents significant similarities to that of colloidal suspensions of polymeric gels. These three types of materials, i.e. wastewater treatment sludge, colloidal suspensions and polymeric gels, present a complex rheological behaviour which depend on both time and the applied solicitation. They exhibit a dual behaviour, solid at low shear stresses, and liquid when the applied shear stress is high. The solid-liquid behaviour is generally modelled by defining a critical shear stress or a critical strain, supposed to be the limit between the solid and liquid regimes. Nevertheless, this concept implies an abrupt transition, unlike experimental observations showing a continuous and progressive transition. The study of the literature permitted to highlight the need to improve the understanding and modelling of the solid-liquid transition. Moreover, it appears necessary to unify the description of the solid and liquid regime in a unique model, in order to link a mathematical continuity with thecontinuous and progressive nature of the physical phenomenon to model. The study of the results available in the literature permited us to build a unique mathematical model to describe both the solid behaviour and the liquid behaviour of the studied materials. The assumptions made from the literature results have thus been experimentally validated. The proposed model is based on the decomposition of the compliance of the material in the sum of a solid contribution and a liquid contribution, depending on time, the applied solicitation and the story of the material. This model permits a unique description of solide and liquid regimes of the material, taking into account the existence of a residual elasticity at high shear stresses, and a viscous dissipation for low shear stresses, in accordance with experimental results. This work permitted to highlight the fact that the solid-liquid transition mecanism is controlled by the compliance of the material, and not the shear stress or the strain. Moreover, it opened the way to a new way of understanding the thixotropy and the solid-liquid transition of pasty materials. Thus, the behaviour of a pasty material is controlled by two parameters : a plateau elastic modulus corresponding to a totally structured state, and an infinite viscosity corresponding to a totally destructured state. These parameters intrinsic to the material are pondered by the evolutions of the microstructure, leading to a competition between elastic and viscous effects. Thus, the difference between the power law behaviour and the Herschel-Bulkley behaviour can be simply explained by the apparition of elastic effects that can’t be neglected.

Diffusion plays an important role in a number of processes like heterogeneous catalysis, corrosion, separation and purification of chemicals of industrial importance, steel hardening, fuel cells, and solid electrolytes for batteries. It also plays a vital role in several biological processes like transport across biomembranes, nerve impulse, flow of blood and permeation of ingested drug. The elementary process of diffusion in solids is quite different from those in liquids. Similarly, the mode of diffusion in porous solid where different regimes such Knudsen regime exists bears little similarity to those in a dense close-packed crystalline solid. Chapter 1 provides a brief introduction to basics of diffusion in different phases of condensed matter. Among the various phases discussed are liquids, close-packed crystalline solids (e.g., body-centered cubic solids), amorphous solids (e.g. glasses) and microporous crystalline solids (e.g., zeolites). Diffusion in these widely differing phases often bears no resemblance to each other; the rate of diffusion in these phases varies over many orders of magnitude and the elementary step and mechanism in the diffusion process are very different. Brief introduction to theories for diffusion in these phases is provided. Various experimental techniques to measure diffusivities are discussed. Different microscopic models to explain the Quasi Elastic Neutron Scattering (QENS) spectra of these phases yield an insight into the elementary step of the diffusion process. Notwithstanding the fact that completely different models are invoked to explain diffusion in different phases, there are certain underlying generic behaviour across these widely differing phases as the recent work on size dependence of diffusion in these phases demonstrate. Diffusion of a molecule or species (in the context of diffusion within condensed phases) without loss of generality may be said to occur in a medium. A universal behaviour observed is that self diffusivity exhibits a maximum as a function of the size of the diffusant when the diffusant is confined to a medium, as a result of what is known as the Levitation Effect. Such a maximum in self diffusivity has been seen in widely differing medium: microporous solids, dense liquids, ions in polar solvents, etc. The aim of the thesis is to investigate and further explore such universal behaviour and demonstrate for the first time the existence of common trends across different condensed phases in spite of difference in the detail at the microscopic level. In Chapter 2, we report a molecular dynamics study of diffusion of diatomic species AB within zeolite Y. The bond length of A-B as well as the interaction of A and B with the host zeolite atoms are varied. The results demonstrate that for the symmetric case (when A=B or AA), there exists a preferred bond length (determined by the bottleneck or window diameter) when the diffusivity is maximum. This is in agreement with previous results on monatomic species which also exhibit a similar diffusivity maximum. More importantly, no such maximum is seen when the interaction asymmetric is introduced in AB. Slight asymmetry in the interaction gives rise to a weak maximum while large asymmetry in interaction obliterates the diffusivity maximum. These results suggest that the importance of interaction between the diffusant and the medium in Levitation Effect or size-dependent diffusivity maximum. Further, it also demonstrates for the first time the close association between an inversion centre (in a statistical sense and not in the crystallographic sense) and the Levitation Effect. In Chapter 3, a study of size dependence of solutes in a Lennard-Jones liquid is reported. Einstein and others derived the reciprocal dependence of the self-diffusivity D on the solute radius ru for large solutes based on kinetic theory. We examine here (a) the range of ru over which Stokes-Einstein (SE) dependence is valid and (b) the precise dependence for small solutes outside of the SE regime. We show through molecular dynamics simulations that there are two distinct regimes for smaller solutes: (i) the interaction or Levitation Effect (LE) regime for solutes of intermediate sizes and (ii) the D 1/ru2 for still smaller solutes. We show that as the solute-solvent size ratio decreases, the breakdown in the Stokes-Einstein relationship leading to the LE regime has its origin in dispersion interaction between the solute and the solvent. These results explain reports of enhanced solute diffusion in solvents existing in the literature seen for small solutes for which no explanation exists. Several properties have been computed to understand the nature of solute motion in different regimes. We investigate in Chapter 4, the dependence of self diffusivity on the size of the diffusant in a disordered medium with the objective of understanding the experimentally observed correlation between self diffusivity and activation energy seen in a wide variety of glasses. Typically, it is found in many ionic glasses that a higher conductivity is associated with lower activation energy and vice versa. Our understanding of transport in glasses as provided by existing theories does not offer an explanation of this correlation. We have carried out molecular dynamics simulation as a function of the size of the impurity atom or diffusant (both neutral and charged) in a model host amorphous matrix. We find that there is a maximum in self diffusivity as a function of the size of the impurity atom suggesting that there is an appropriate size for which the diffusivity is maximum. The activation energy is found to be the lowest for this size of the impurity. A similar maximum has previously been found in other condensed phases such as confined fluids and dense liquids and has its origin in the Levitation Effect. The implications of this result for understanding ionic conductivity in glasses are discussed. Our result suggests that there is a relation between microscopic structure of the amorphous solid, diffusivity or conductivity and activation energy. The nature of this relationship is discussed in terms of the Levitation parameter showing that diffusivity is maximum when the size of the neck or doorway radius is comparable with the size of the diffusant. Our computational results here are in excellent agreement with independent experimental results which show that structural features of the glass are important in determining the ionic conductivity. In Chapter 5, we report results of molecular dynamics investigations into neutral impurity diffusing within an amorphous solid as a function of the size of the diffusant and density of the host amorphous matrix. We find that self diffusivity exhibits an anomalous maximum as a function of the size of the impurity species. An analysis of properties of the impurity atom with maximum diffusivity shows that it is associated with lower mean square force, reduced backscattering of velocity autocorrelation function, near-exponential decay of the intermediate scattering function (as compared to stretched-exponential decay for other sizes of the impurity species) and lower activation energy. These results demonstrate the existence of well known size-dependent diffusivity maximum in disordered solids. Further, we show that the diffusivity maximum is observed at lower impurity diameters with increase in density. This is explained in terms of the levitation parameter and the void structure of the amorphous solid. We demonstrate that these results imply contrasting dependence of self diffusivity (D) on the density of the amorphous matrix, . D increases with  for small sizes of the impurity but shows an increase followed by a decrease for intermediate sizes of the impurity atom. For large sizes of the impurity atom, D decreases with increase in . These contrasting dependence arises naturally from the existence of Levitation Effect. In Chapter 6, we discuss size dependence of impurity diffusion in an ordered system. We report molecular dynamics simulation studies to understand the role of impurity size and impurity-host interaction on impurity diffusivity in a body centered cubic solid. The simulation studies have been performed for a set of impurity-host interaction parameter ih (i=impurity, h=host atom) for a range of impurity sizes in rigid and flexible bcc solids. A double maximum is seen corresponding to two different sizes of the impurity species. Anomalous maximum is seen for a larger size of the impurity species in the case of the rigid host as compared to flexible host. The second anomalous diffusivity disappears with decrease in ih in flexible bcc solid. For one of the ih where double diffusivity maxima are observed, various properties are analysed to understand the anomalous diffusion behaviour. The impurity with anomalous diffusion has lower activation energy as compared to other impurities. Among the two anomalous impurities, the impurity with higher diffusivity has lower activation energy. The anomalous regime impurities as associated with velocity autocorrelation function with little or no backscattering, minimum average mean square force due to host atoms, lower activation energy. The self intermediate scattering function shows faster decay and a single relaxation time for anomalous regime impurity and two relaxation times for other impurity sizes. The wavenumber dependence of diffusivity of impurities shows oscillatory behaviour except for the anomalous regime impurities which show monotonic dependence on wavenumber. Chapter 7 discusses the influence of temperature induced solid-liquid phase transition on the size-dependent diffusivity. We report results for two distinct cases: (a) when the phase change is associated with corresponding changes in density and (b) when the phase change occurs at constant density. The latter is carried out so as to obtain the influence of disorder on the size-dependent diffusion or Levitation Effect. Studies with variable density are useful to understand the effect of disorder as well as change in density on size-dependent diffusivity. Two diffusivity maxima in the solid face-centred cubic phase is seen when the impurity-medium interaction is sufficiently large. One of these diffusivity maximum disappears with decrease in h. The impurities near the diffusivity maximum show velocity autocorrelation function with little backscattering, minimum in the average mean square force, lower activation energy, faster decay of self intermediate scattering function with a single relaxation time and a monotonic decay in wavevector dependence of diffusivity. Chapter 8 reports molecular dynamics simulations of a model guest tetrahedral molecule AX4 with differing bond lengths lAX have been carried out in a sphere with different surface roughness. The rotational-diffusion coefficient Dr shows a maximum for a particular value of lAX. This corresponds to the distance at which the interaction of the guest with the atoms of the host is most favourable. Although, the intensity of the maximum decreases with increase in the roughness of the confining surface, it is seen that the maximum exists even for a reasonably high degree of roughness. The observed maximum arises from the minimum in the torque on the tetrahedral molecule from its interaction with the confining medium due to mutual cancellation of forces. Activation energy for rotation is seen to be also a minimum for the bond length for which Dr is a maximum. These results suggest that there is a maximum in the rotational-diffusion coefficient when the rotating molecule is confined to a sphere of comparable size similar to the maximum in translational diffusion coefficient seen in porous solids and known as the Levitation Effect. On increase in the roughness of the sphere surface, the value of lAX at which the maximum in Dr is seen decreases. This is similar to the shift seen in the size of the diffusant corresponding to maximum diffusivity in the case of translational diffusivity. In Chapter 9 possible extensions to the work reported in the previous chapters and the directions to take are discussed. Symmetry plays an important role in size dependent diffusivity maximum in microporous crystalline solids; it would be interesting to investigate if similar role of symmetry exists in case of liquids and other disordered solids. Previous work from this laboratory on ions in water has shown the importance of electrostatic interactions. In the light of this, it would be interesting to see the influence of long-range interactions in breakdown of Stokes-Einstein relationship in liquids. Effect of density of the medium on impurity diffusion can be studied over a wide range of densities in case of supercritical fluids such as ions in water (where electrostatic interactions are present) and these can provide greater insight into dependence of diffusion on density. The origin of two diffusivity maxima in case of body-centered and face-centred cubic solids needs a detailed investigation to understand its origin. Quantification of disorder and its effect on size dependence of diffusion would be of interest. A detailed comparison with experimental data of matrix isolated molecules to understand and verify the dependence of rotational diffusivity on the size of the molecule as well as the cavity radius would be instructive.

The thesis involves computer simulation and theoretical studies of dynamics of water under confinement and structural transformation in different complex systems. Based on the systems and phenomena of interest, the work has been classified in to three major parts: I. Dynamics of water under confinement II. Dynamics of water in presence of amphiphilic solutes III. Structural transformation in complex systems The three parts have further been divided into nine chapters. Brief chapter wise outline of the thesis is discussed below. Part I deals with the dynamics of water in confined systems. In Chapter I.1, we provide a brief introduction of water dynamics inc on fined systems. We also give a brief outline of relevant experimental and theoretical techniques used to study the water dynamics under confinement. Chapter I.2 describes a model based analytical study of dynamical correlation in confined systems. Here, we introduce a novel one dimensional Ising model to investigate the propagation and annihilation of dynamical correlations in confined systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles (RMs).In our model, the two spins located at the two end cells are oriented in the opposite directions to mimic the surface effects present in the real systems. These produce opposing polarizations which propagate from the surface to the center, thus producing bulk like condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm).We show that the model satisfactorily reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is non-exponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of the relaxation of spins undergoes a change with the emergence of homogeneous dynamics, where the decay is predominantly exponential. In Chapter I.3, layer-wise distance dependent orientation relaxation of water confined in reverse micelle s(RM)is studied using theoretical and computational tools. We use both a newly constructed spins on a ring (SOR) Ising-type model with modified Shore-Zwanzig rotational dynamics and atomistic simulations with explicit water. Our study explores the size effect of RMs and the role of intermolecular correlations, compromised by the presence of a highly polar surface, on the distance (from the surface) dependence of water relaxation. The SOR model can capture some aspects of distance dependent orientation relaxation, such as acceleration of orientation relaxation at intermediate layers. In atomistic simulations, layer-wise decomposition of hydrogen bond (H-bond) formation pattern clearly reveal that the H-bond arrangement of water at a certain distance away from the surface can remain frustrated due to interaction with the polar surface head groups. We show that this layer-wise analysis also reveals the presence of a non-monotonic, slow relaxation component which can be attributed to the frustration effect and is accentuated in small to intermediate size RMs. For larger RMs, the long-time component decreases monotonically from the interface to the interior of the RMs with slowest relaxation observed at the interface. In ChapterI.4, we present theoretical two dimensional infrared spectroscopic (2D-IR) studies of water confined within RMs of various sizes. Here we focus again mainly on the altered dynamics of confined water by performing a layer-wise decomposition of water. We aim to quantify the relative contributions to the calculated 2D-IR spectra by water molecules located in different layers. The spectra of 0-1 transition clearly show substantial elongation along the diagonal, due to in homogeneous broadening and incomplete spectral diffusion, in the surface water layer of different size of RMs studied in this work. Our study reveals that the motion of the surface water molecules is sub-diffusive, establishing the constrained nature of their dynamics. This is further supported by the two peak nature of the angular analogue of the van Hove correlation function. With increasing system size the motion of water molecules becomes more diffusive in nature and the structural diffusion is observed to be almost completed in the central layer of larger RMs. Comparisons between experiment and simulation help establishing the correspondence between the spectral decomposition available in experimental 2D-IR with the spatial decomposition of simulated 2D-IR. Simulations also allow a quantitative exploration of the relative role of water, sodium ions and sulfonate head groups in irrational dephasing. Interestingly, the negative cross correlation between forces on oxygen and hydrogen of O-H bond in bulk water significantly decreases in the surface layer of different RMs. This negative cross correlation gradually increases in the central layer with increasing size of the RMs and this is found to be partly responsible for the faster relaxation rate of water in the central layer. Part II consists of two chapters and focuses on the dynamics of water in presence of amphiphilic solutes. In Chapter II.1, we present a brief introduction of water – DMSO binary mixture and various anomalous properties of the same. In Chapter II.2, we present theoretical IR study of water dynamics in water–DMSO binary mixtures of different compositions. We show that with increasing DMSO concentration, the IR absorption peak maxima show the presence of structural transformation in similar concentration range, observed in earlier studies. Analysis of H-bonded network near hydrophilic and hydrophobic part of DMSO also suggests that average number of hydrogen bonds near the hydrophobic parts possess maxima at the same concentration range. We also show that with increasing DMSO concentration water dynamics becomes very slow. This has been supported by the diagonal elongation of the 2D-IR spectra and also the slow decay of frequency fluctuation correlation n function (FFCF) and the orientation time correlation function (OTCF). The decoupling of the OTCF establishes that water-DMSOH-bond is much stronger than that of water-water. The last part (Part III) consists of three chapters that deal with structural transformation in various complex systems. In Chapter III.1, we introduce polydisperse systems and present existing theoretical, computer simulation and experimental studies. It also contains the importance and diversity of polydisperse system in nature. In Chapter III.2, we present computer simulation study of melting of polydisperse Lennard-Jones (LJ) system with Gaussian polydispersity in size. The phase diagram reproduces the existence of an early temperature in variant terminal polydispersity (δt0.11), with no signature of re-entrant melting. The absence of re-entrant melting can be attributed to the influence of attractive part of the potential on melting. We find that at terminal polydispersity the fractional density change approaches zero that seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction system undergoes a sharp transition from crystalline solid to disordered state with increasing polydispersity. This has been quantified by second and third order rotational invariant bond orientational orders as well as by the average inherent structure energy. The translational order parameter also indicates similar structural change The free energy calculation further supports the nature of the transition. The third order bond orientational order shows that with increasing polydispersity, local cluster favors more icosahedral-like arrangements and thus the system loses its crystalline symmetry. In Chapter III.3, we present study of phase transition and effect of confinement on it in SOR model. This system is similar to our SOR model discussed in Chapter I.3. The spins execute continuous rotation under a modified XY Hamiltonian. In order to understand the nature of phase transition in such confined spin systems we have performed extensive Monte Carlo simulations. The system size dependence of Binders cumulant, specific heat, order parameter and finite size scaling of order parameter universally suggest the existence of a phase transition. The absence of hysteresis and Scaling of Binders energy cumulant minimum confirm the continuous nature of the transition. The finite size scaling analyses give rise to the mean field nature of the transition. Plausible applications of the proposed model in modeling dipolar liquids in confined systems are also discussed. In Appendix A, we discuss a preliminary study of front propagation in a non-equilibrium system. The model system analogous to the super cooled liquid shows non-Avrami domain growth during rejuvenation. The origin of the non-Avrami nature of the domain growth and the presence of cross over are also discussed. In Appendix B, we discuss umbrella a sampling technique and WHAM analysis which is used in ChapterIII.2 to get the free energy of polydisperse LJ system.