Showing papers on "Thermal diffusivity published in 1997"

Quantitative model of volume hologram formation in photopolymers

Abstract: A quantitative model is presented to describe the formation of volume holograms in a polymeric medium containing photopolymerizable acrylate monomers that undergo spatially modulated gelation as a result of exposure to a visible “write” beam. The model refines the simple diffusion model of Zhao and Mouroulis [J. Mod. Opt. 41, 1929 (1994)], by including cure dependence of both the photoreaction kinetics and the monomer diffusivity. These dependences are determined by experimental measurements, using near infrared spectroscopy to quantify the degree of cure and the time dependence of the hologram formation to infer the cure-dependent diffusivity. The cure-dependent diffusion coefficient can be fit by an expression from a free-volume theory, and the cure-dependent reaction rate coefficient is found to be proportional to the diffusivity, showing the reaction rate to be diffusion limited. With the model parameters determined experimentally, predictions are then made of the first, second, and third harmonics of the grating profile, and these are found to be in good agreement with the measured values. The results show the validity of the model and its usefulness in predicting the optimal exposure conditions and performance of a given holographic material.

Stability analysis of numerical interface conditions in fluid-structure thermal analysis

Abstract: SUMMARY This paper analyses the numerical stability of coupling procedures in modelling the thermal diffusion in a solid and a fluid with continuity of temperature and heat flux at the interface. A simple one-dimensional model is employed with uniform material properties and grid density in each domain. A number of different explicit and implicit algorithms are considered for both the interior equations and the boundary conditions. The analysis shows that in general these are stable provided that Dirichlet boundary conditions are imposed on the fluid and Neumann boundary conditions are imposed on the solid; in each case the imposed values are obtained from the other domains. # 1997 by John Wiley & Sons, Ltd.

Properties of Laminar Premixed CO/H/Air Flames at Various Pressures

Abstract: Effects of positive  ame stretch on the laminar burning velocities of CO/H2/air mixtures were studied both experimentally and computationally for outwardly propagating spherical laminar premixed  ames having concentrations of hydrogen in the fuel mixture of 3 – 50% by volume, fuel-equivalence ratios of 0.6 – 5.0, and pressures of 0.5 – 4.0 atm. Both measured and predicted ratios of unstretched to stretched laminar burning velocities varied linearly with Karlovitz numbers, yielding constant Markstein numbers for each reactant mixture and pressure. Effects of stretch on laminar burning velocities were modest at low hydrogen concentrations, but approached earlier results for hydrogen/air  ames as hydrogen concentrations increased. Predicted and measured  ame properties were in reasonably good agreement using several contemporary chemical reaction mechanisms.

Modeling Diffusion and Reaction in Soils: VII. Predicting Gas and Ion Diffusivity in Undisturbed and Sieved Soils

Abstract: The classical Penman (1940) and Millington-Quirk (1960, 1961) diffusivity models were transformed into general form by introducing a tortuosity parameter, m. Compared with measured diffusivities close to phase saturation (soil-water and soil-air saturation for ion and gas diffusivity, respectively), the Penman (1940) model was superior to the Millington-Quirk models independent of diffusion type. The combined use of the Penman model to predict the diffusivity at phase saturation together with a general Millington-Quirk model to predict relative decrease in diffusivity with decreasing phase content was labeled the Penman-Millington-Quirk (PMQ) model. The best fit of the new PMQ model to measured data was obtained with m = 3 (high tortuosity) and m = 6 (medium tortuosity) for gas diffusivity in undisturbed and sieved soils, respectively, and m = 1 (high tortuosity) for ion diffusivity. Measurements did not suggest a significant difference between ion diffusivity in undisturbed, sieved, or aggregated soils. The differences in m-values between diffusion types are likely caused by different diffusion pathways and geometries for ion and gas diffusivity as well as a large effect of soil heterogeneity and spatial variability on gas diffusivity. The PMQ model predicted gas diffusivity in sieved and undisturbed soil well, but a soil-type dependent model (Part IV ofthis series) was superior for predicting ion diffusivity. The new models seem promising for more accurately predicting gas and ion diffusion and, therefore, for improving simulations of diffusion-constrained chemical and biological reactions in soils.

Modelling of thermal desorption of hydrogen from metals

Abstract: The thermal desorption technique can be used in principle to determine the trapping characteristics of different microstructural trap sites in metals provided there are adequate models to fit to the experimental data. A brief review of models of thermal desorption is presented which indicates that there are limitations in the assumptions made or in the scope of existing models. A more rigorous mathematical model has now been developed which accounts for diffusion, detrapping, and retrapping at one or more type of trap site and which allows for varying trap occupancy. The effect of material and experimental variables on the thermal desorption spectrum has been evaluated and the validity of simple models of desorption assessed. The simpler analytical models, such as the detrapping model of Lee and Lee, in which diffusion is neglected relative to detrapping, do not inspire confidence and are applicable only under very limiting circumstances; for example, in low alloy steels at very low hydrogen contents. It is recommended that thermal desorption measurements be made at progressively decreasing values of initial hydrogen content until the simple analysis yields a consistent value for the trapping parameters. This experimental approach is applicable also to models of thermal desorption which account for diffusion using an effective diffusivity, since trap occupancy is neglected in these. The more rigorous model described herein can be used to determine the binding energy of the traps directly which, together with the density of trap sites, is the most important parameter with respect to hydrogen assisted cracking. The height of the energy barrier to trapping, at constant value of the binding energy, is shown to have only a modest effect on the thermal desorption spectrum compared with the impact of binding energy and of density of trap sites.

The influence of gas transport and porosity on methane oxidation in soils

Abstract: Two porosity-dependent parameters that affect gas transport in soils, gas diffusivity and air permeability, were assessed as possible indicators of methane oxidation rates. Soil gas diffusivity was measured in intact cores in the laboratory and in situ, and air permeability was measured in intact cores. An in situ method of measuring gas diffusivity was specifically modified for this purpose to use Freon in a portable probe. A laboratory (core) method of measuring gas diffusivity, using krypton 85, was also employed. Measurements were made at the soil surface and at a range of depths within the topsoil, in conjunction with in situ measurements of CH4 oxidation, in forest, arable, and set-aside soils at a lowland site and in a forest soil at an upland site, in southeast Scotland. The surface layer of soil caused marked variations in diffusivity measurements, particularly with the in situ method. At the upland site, where a 50-mm-thick surface organic layer was present, the in situ technique revealed a sharp decrease in diffusivity with depth. Only where gas transport was low, in the set-aside soil, was methane oxidation rate influenced by gas transport changes associated with increasing soil water content. Differences in CH4 oxidation rates related better to core gas diffusivities than to in situ diffusivities. The relationship was best at 50–150 mm depth where diffusivities were lower than at the surface. Air permeability, which is affected more by soil structure than diffusivity, appeared to be as relevant as the latter parameter to CH4 oxidation rate, particularly for land use changes associated with agriculture. Thus CH4 oxidation rate appears to be influenced by gas transport properties and soil structure, either at the surface in the litter layer or below the surface where the oxidizing microorganisms are likely to occur.

Translational Diffusion in Sucrose Solutions in the Vicinity of Their Glass Transition Temperature

Abstract: The prediction of the stability of low-moisture products is complex, particularly close to the glass transition temperature. This study demonstrates that the relations used to evaluate the influence of temperature on the viscosity of carbohydrate media cannot be applied to the diffusivity. The translational diffusion coefficient of a fluorescent molecule (fluorescein) is measured in sucrose−water mixtures as a function of temperature. The main result is that the mobility of the fluorescein is not simply coupled to the viscosity of the diffusion medium at temperatures close to the glass transition temperature. Indeed the WLF equation, which gives a good prediction of the viscosity, does not allow the determination of the diffusivity in a temperature range close to Tg because the translational diffusion follows a weaker temperature dependence. Different possible explanations for this apparent decoupling between translational diffusion and viscosity are suggested: a small change in the hydrodynamic radius o...

Transport coefficients of helium and argon-helium plasmas

Abstract: Calculated values of the viscosity, thermal conductivity, and electrical conductivity of helium, and mixtures of argon and helium, at high temperatures are presented. In addition, combined ordinary, pressure, and thermal diffusion coefficients are given for the mixtures. The calculations, which assume local thermodynamic equilibrium, are performed for atmospheric pressure plasmas in the temperature range from 300 to 30000 K. The results are compared with those of previously published studies. Significant discrepancies are found; these are attributed to the improved values of the collision integrals used here in calculating the transport coefficients.

Discontinuous cellular precipitation in a high-refractory nickel-base superalloy

Abstract: A discontinuous precipitation reaction has been investigated in a high-refractory content nickel-base alloy. The reaction transforms the two-phase γ-γ′ parent microstructure into a three-phase cellular structure with a γ′ matrix containing Re-rich P-phase and agglomerated γ lamellae. The reaction has been studied in polycrystalline material and in bicrystals with varying degrees of boundary misorientation at temperatures in the range of T/Tm=0.78 to 0.85. The early stages of the reaction are characterized by heterogeneous nucleation of P-phase precipitates and migration of the grain boundary. At low-angle, near-tilt boundaries misoriented by less than 10 deg, nucleation of P-phase particles was observed, but the cellular reaction did not occur, due to limited boundary mobility and diffusivity. The high degree of supersaturation of Re and W in the initial γ-γ′ alloy appears to be the primary driving force for the reaction. Small amounts of creep deformation did not significantly influence the extent of the transformation. The diffusivity of Re associated with the moving boundary was calculated to be 5×10−8 cm2 s−1 at 1093 °C, which is approximately four orders of magnitude greater than the bulk lattice diffusivity of tungsten.

Kinetics of hydrocarbon adsorption on activated carbon and silica gel

Abstract: Experimental breakthrough results of methane, ethane and propane in activated carbon and silica gel obtained over a wide range of gas compositions, bed pressures, interstitial velocities, and column temperatures were analyzed using a dynamic, nonisothermal, nontrace column breakthrough model. A linear driving force (LDF) approximation is used for particle uptake, and the Langmuir-Freundlich isotherm represents adsorption equilibrium. The LDF mass-transfer-rate coefficient (and, hence, effective particle diffusivity) and column-wall heat-transfer coefficient were determined. The results show that hydrocarbon transport in the activated carbon particles used is essentially by Knudsen and surface flow, while for the silica gel used the transport is primarily by Knudsen flow. For activated carbon, the experimentally derived LDF coefficients for all three sorbates are well correlated using an average effective diffusivity value. With regard to heat transfer, the column-wall Nusselt number is approximately constant for the range of Reynolds numbers considered. Simulations of multicomponent breakthrough in the activated-carbon bed based on independently measured single-component kinetic parameters and the extended Langmuir-Freundlich isotherm agree very well with experimental results. The computational efficiency gained by adopting the simpler extended Langmuir isotherm model is also investigated.

Heat, Water, and Solution Transfer in Unsaturated Porous Media: I -- Theory Development and Transport Coefficient Evaluation

Abstract: A detailed theory describing the simultaneous transfer of heat, water, and solute in unsaturated porous mediais developed The theory includes three fully-coupledpartial differential equations Heat, water, andsolute move in the presence of temperature, T; matricpressure head, Ψ m ; solution osmotic pressure head Ψ o ; and solute concentration C gradients Thetheory can be applied to describe the mass and energyin radioactive waste repositories, food processing,underground energy storage sites, buried electriccables positions, waste disposal sites, and inagricultural soil Several transport coefficients forheat, water, and solute are included in the theory The coefficients are evaluated for a silty clay loamsoil to clarify their dependence on water content (θ),T, and C The thermal vapor diffusivity D Tv first increased as θ increased to022 m3/m3 then decreased with furtherincreases in θ D Tv was 3 orders of magnitudegreater than either isothermal vapor D mv orosmotic vapor D ov , diffusivities at θ of020~m3/m3, T of 50°C, and C of 0001mol/kg All of the liquid and vapor water transport coefficients increased with increasing T D Tv decreased with increasing C to a greater extent thanD mv and D ov The effective thermalconductivity decreased slightly with increasing C Thesolute diffusion coefficient D d was 6 to 7orders of magnitude greater than the thermal soluteand salt sieving diffusion coefficients at θ of020~m3/m3, T of 50°C, and C of 0001 mol/kg

Fully coupled dynamic electro-thermal simulation

Abstract: Fully coupled dynamic electro-thermal simulation on chip and circuit level is presented. Temperature dependent thermal conductivity of silicon is taken into account, thus solving the nonlinear heat diffusion equation. The numerical solution is carried out by using the industry-standard simulator SABER, therefore for electro-thermal simulations we are able to use the common electrical compact models by adding a heat source and thermal pins to them. The application of this technique and need for electro-thermal simulation is illustrated with the simulation of a current control circuit built into a multiwatt package.

Physical Models of Boron Diffusion in Ultrathin Gate Oxides

Abstract: Based on a network defect model for the diffusion of B in SiO 2, we propose that B diffuses via a peroxy linkage defect whose concentration in the oxide changes under different processing conditions. We show that as the gate oxide is scaled below 80 A in thickness, additional chemical processes act to increase B diffusivity and decrease its activation energy, both as a function of the distance from the Si/SiO 2 interface. For a 15 A oxide, the B diffusivity at 900°C would increase by a factor of 24 relative to diffusion in a 100 A oxide. The role of nitridation of SiO 2 to create a barrier to B diffusion is modeled by assuming the N atoms compete with B for occupation of diffusion-defect sites. The model predicts that nitridation is ineffective in stopping B penetration when BF 2 implants are used to dope the polysilicon gate, and similarly for B implants when the gate oxide thickness decreases below approximately 30 to 40 A.

Silicate melts: Relaxation, rheology, and the glass transition

Abstract: Movement of magma within the Earth depends upon the density, compressibility, thermal expansion, viscosity, diffusivity, heat capacity, and thermal conductivity of silicate melts as a function of temperature, pressure, and composition. These physical properties are controlled by the atomic coordination and bond strengths of the melt. To contribute more to our understanding of geological processes than numerous measurements of physical properties of individual magmas of local interest, the relationship between melt structure and physical properties needs to be understood. In geological settings where the viscosity of the molten component is high (108-1014 Pa s), the melt structure requires a long time (seconds to weeks) to equilibrate in response to changes in pressure, temperature, and composition. The effects of this structural equilibration upon the viscosity, density, and compressibility of magmas and the time required for equilibration need to be included in discussions of magma ascent and emplacement and of crystal nucleation, growth, and segregation within magmas. The structural relaxation discussed here is the slowest relaxation process occurring in a silicate melt at a specific temperature and therefore represents the glass transition, which is a kinetic transition whose temperature is not a constant specific to a melt composition but depends upon the timescale on which measurements are performed. On the basis of the agreement between nuclear magnetic resonance measurements of Si-O bond exchange timescales and measured structural relaxation timescales, the structural equilibration observed in silicate melts appears to be due to the lifetime of the Si-O bonds in the melt. The following is a discussion of a range of different studies to determine the density, viscosity, thermal expansion, and compressibility of silicate melts, based on a central theme of the structural relaxation phenomenon and its use to calculate the physical properties of a melt, for example, using calorimetry data to calculate viscosity, volume, and thermal expansion in silicate melts at temperatures 50 K above the glass transition. This results in the determination of melt properties at conditions of direct geological interest, for example, the densities of granitic melts at 1050 K and viscosities of 109–1012 Pa s; observations of anomalously low, non-Newtonian viscosities and compressibilities in melts at conditions of high strain rate; the viscosities of volatile-bearing melts; and the viscosity of the melt phase in natural crystal- and bubble-bearing obsidians.