Boundary layer scaling in Rayleigh-Benard convection

Accepted versio

The thermal dehydration of natural zeolites

The zeolites constitute a group of minerals of much interest from geological, mineralogical and technological points of view. Structurally, they are tectosilicates with an 'open' framework containing channels and cavities which accommodate cations and water molecules. Generally, these cations are exchangeable and the water molecules can be removed or replaced reversibly without disrupting the framework.Because of the widespread occurrence of zeolites in various environments, they offer a fruitful field of investigation to geologists and this has led to the recognition of the so-called zeolite facies.Technologically, no mineral group is as versatile in its application possibilities as the zeolites. This is due to their high physical stability and specific sorptive properties. For this reason, zeolites are synthesized on a large scale and then appropriately named molecular sieves. In recent years large and relatively pure deposits of useful zeolites have been discovered. Since these can be made available at relatively low cost, the interest in natural zeolites is rapidly reviving.For many applications, zeolites have to be activated by heating. This involves dehydration of the minerals and consequently often causes drastic, but usually reversible, changes in the structure and unit-cell dimensions. Hence, the thermal properties of zeolites have been studied for many years. A brief review of this work is given in chapter 2. Because of the unsystematic approach in which inadequate techniques were often employed, the results have frequently been both inaccurate and controversial.In chapter 3, the dehydration process which is a composite reaction, is analysed. Zeolite dehydration appears to occur according to one or more of three basic types. Type 1 is a discrete reaction over a relatively short temperature range accompanied by a sharp peak in the DTA curve and a marked crystallographic transformation. Type 2 consists of a sequence of small dehydration steps resulting in a broad, often somewhat irregular DTA peak accompanied by small stepwise lattice adaptations. With type 3, dehydration occurs gradually without any apparent break, also resulting in a broad and smooth DTA peak. The lattice may either adapt gradually or remain virtually unaltered.Water vapour pressure strongly influences the reaction temperature and the dehydration process appears to occur so rapidly that equilibrium is instantly reached. The dehydration-rehydration hysteresis effect occurring in several zeolites, is not caused by possible non-equilibrium conditions of the dehydration reaction but by the lattice transformation.The so-called 'loosely held' water, denoted in chemical analyses as H 2 O-, appeared to be adsorbed internally in the structure instead of on the external surface.In chapter 4 a systematic thermal investigation of the zeolites belonging to the natrolite group, using dynamic methods of thermal analysis, is given. Upon heating and dehydration all members of this group react by a contraction of the lattice along the a and b axes and often an expansion along the c axis, in accordance with the general fibrous structure.Natrolite shows the highest thermal stability of the group and has a low (α) and a high (β) metaphase. Its isotypes mesolite and scolecite show a mutually resembling thermal behaviour which is very different from that of natrolite. The isotypes thomsonite and gonnardite also show a mutual resemblance with certain aspects of both natrolite and mesolite/scolecite. The relationship of edingtonite with the other members was not reflected by its thermal behaviour. X-ray data of all meta-phases were collected.With the aid of the DTA inhibited diffusion method pressure-temperature relations of zeolite dehydration reactions have been studied in chapter 5. The Clausius-Clapeyron equation appeared to be applicable and facilitated calculation of thermodynamic parameters of the reactions. For 18 zeolites more than 50 values for the heat of hydration have been calculated of which only a few had to be rejected because of non-equilibrium experimental conditions. From the reaction entropy change, values for the entropy of water in zeolites were calculated. These indicated that at least three types of water can be present in zeolites: 1. crystal water or low-entropy water with a standard entropy of 30-47 J/mole/deg (7 -11 cal/mole/deg); 2. zeolitic water or high-entropy water with a standard entropy in the range of 58-72 J/mole/deg (14 -17 cal/mole/deg); 3. so-called 'loosely bound' water with a high standard entropy of 58-63 J/mole/deg (14-15 cal/mole/deg).Low entropy appears to be associated with water molecules occupying 'fixed positions' in the structure whereas high entropy is associated with molecules possessing a higher degree of disorder because they are not coordinated in fixed positions

Wind and boundary layers in Rayleigh-Benard convection. Part 2: boundary layer character and scaling

The effect of the wind of Rayleigh-Benard convection on the boundary layers is studied by direct numerical simulation of an L/H=4 aspect-ratio domain with periodic side boundary conditions for Ra={10^5, 10^6, 10^7} and Pr=1. It is shown that the kinetic boundary layers on the top- and bottom plate have some features of both laminar and turbulent boundary layers. A continuous spectrum, as well as significant forcing due to Reynolds stresses indicates undoubtedly a turbulent character, whereas the classical integral boundary layer parameters -- the shape factor and friction factor (the latter is shown to be dominated by the pressure gradient) -- scale with Reynolds number more akin to laminar boundary layers. This apparent dual behavior is caused by the large influence of plumes impinging onto and detaching from the boundary layer. The plume-generated Reynolds stresses have a negligible effect on the friction factor at the Rayleigh numbers we consider, which indicates that they are passive with respect to momentum transfer in the wall-parallel direction. However, the effect of Reynolds stresses cannot be neglected for the thickness of the kinetic boundary layer. Using a conceptual wind model, we find that the friction factor C_f should scale proportional to the thermal boundary layer thickness as C_f ~ lambda_Theta, while the kinetic boundary layer thickness lambda_u scales inversely proportional to the thermal boundary layer thickness and wind Reynolds number lambda_u ~ lambda_Theta^{-1} Re^{-1}. The predicted trends for C_f and \lambda_u are in agreement with DNS results

Wind and boundary layers in Rayleigh-Benard convection. Part 2: boundary layer character and scaling

The effect of the wind of Rayleigh-Benard convection on the boundary layers is studied by direct numerical simulation of an L/H=4 aspect-ratio domain with periodic side boundary conditions for Ra={10^5, 10^6, 10^7} and Pr=1. It is shown that the kinetic boundary layers on the top- and bottom plate have some features of both laminar and turbulent boundary layers. A continuous spectrum, as well as significant forcing due to Reynolds stresses indicates undoubtedly a turbulent character, whereas the classical integral boundary layer parameters -- the shape factor and friction factor (the latter is shown to be dominated by the pressure gradient) -- scale with Reynolds number more akin to laminar boundary layers. This apparent dual behavior is caused by the large influence of plumes impinging onto and detaching from the boundary layer. The plume-generated Reynolds stresses have a negligible effect on the friction factor at the Rayleigh numbers we consider, which indicates that they are passive with respect to momentum transfer in the wall-parallel direction. However, the effect of Reynolds stresses cannot be neglected for the thickness of the kinetic boundary layer. Using a conceptual wind model, we find that the friction factor C_f should scale proportional to the thermal boundary layer thickness as C_f ~ lambda_Theta, while the kinetic boundary layer thickness lambda_u scales inversely proportional to the thermal boundary layer thickness and wind Reynolds number lambda_u ~ lambda_Theta^{-1} Re^{-1}. The predicted trends for C_f and \lambda_u are in agreement with DNS results

Deformations in Crystals Induced by External Electric Fields

This thesis presents the experimental study of electric-field-induced deformations in single crystals. It is well known that an external electric field applied to a piezoelectric crystals deforms the shape of the crystal on a macroscopic level. On the microscopic scale this deformation implies a change of the unit cell. Even though the relative change of the unit cell is small (Δd/d = 10−5 – 10−4), it can be measured by X-ray diffraction. The positions of the Bragg reflections are related to the unit cell parameters. Careful measurements of electric-field-induced changes in positions of Bragg reflections reveal the deformation of the unit cell. The intensities of the Bragg reflections are related to the electron density distribution in the unit cell, which reaches local maxima at the atomic positions. Displacements of atoms, rotations of molecules and polarization of the electron density change the diffracted intensities. Hence, careful measurements of electric field induced changes in diffracted intensities can reveal these deformations