Validation of a Modified Eddy Dissipation Concept Model for Stationary and Nonstationary Turbulent Diffusion Flames

A transient flame simulation tool based on unsteady Reynolds average Navier Stokes (RANS) is characterized for stationary and nonstationary flame applications with a motivation of performing computationally affordable flame stability studies. Specifically, the KIVA-3V code is utilized with incorporation of a recently proposed modified eddy dissipation concept for simulating turbulence-chemistry interaction along with a model for radiation loss. Detailed comparison of velocities, turbulent kinetic energies, temperature, and species are made with the experimental data of the turbulent, non-premixed DLR_A CH4/H-2/N-2 jet flame. The comparison shows that the model is able to predict flame structure very well. The effect of some of the modeling assumptions is assessed, and strategies to model a stationary diffusion flame are recommended. Unsteady flame simulation capabilities of the numerical model are assessed by simulating an acoustically excited, experimental, oscillatory H-2-air diffusion flame. Comparisons are made with oscillatory velocity field and OH plots, and the numerical code is observed to predict transient flame structure well.

Growth mechanism of the Nb(X)Si-2 and [Nb(X)](5)Si-3 phases by reactive diffusion in Nb (X = Ti, Mo, or Zr)-Si systems

The effects of Mo, Ti, and Zr on the diffusion and growth of the Nb(X)Si-2 and Nb(X)(5)Si-3 phases in an Nb(X)-Si system are analyzed. The integrated diffusion coefficients are determined from diffusion couple experiments and compared with the data previously calculated in a binary Nb-Si system. The growth rates of both phases are affected by the addition of Mo and Zr, whereas the addition of Ti has no effect. The atomic mechanism of diffusion is also discussed based on the crystal structure and the possible changes in the defect concentrations due to alloying. Finally, the growth mechanism of the phases is discussed on the basis of a physico-chemical approach. (C) 2011 Elsevier Ltd. All rights reserved.

First passage distributions for long memory processes

We study the distribution of first passage time for Levy type anomalous diffusion. A fractional Fokker-Planck equation framework is introduced.For the zero drift case, using fractional calculus an explicit analytic solution for the first passage time density function in terms of Fox or H-functions is given. The asymptotic behaviour of the density function is discussed. For the nonzero drift case, we obtain an expression for the Laplace transform of the first passage time density function, from which the mean first passage time and variance are derived.

Decoupling of diffusion from viscosity: Difference scenario for translational and rotational motions

Recent experiments have indicated a dramatically different viscosity dependence of the translational and the rotational diffusion coefficients in a supercooled liquid as the glass transition temperature is approached from above. While the translational motion seems to be decoupled from the rising viscosity (eta), the rotational motion seems to remain firmly coupled to eta. In order to understand the microscopic origin of this behavior, we have carried nut detailed theoretical calculations of both the quantities by using a self-consistent mode-coupling theory (MCT). it is found that when the size of the solute is same as that of the solvent molecules, the conventional MCT fails to predict the observed decoupling. The solvent inhomogeneity is found to play a decisive role in determining the decoupling. The difference in the viscosity dependence between rotation and translational diffusion coefficient is discussed.

An inverse problem for Helmholtz equation

This article is concerned with subsurface material identification for the 2-D Helmholtz equation. The algorithm is iterative in nature. It assumes an initial guess for the unknown function and obtains corrections to the guessed value. It linearizes the otherwise nonlinear problem around the background field. The background field is the field variable generated using the guessed value of the unknown function at each iteration. Numerical results indicate that the algorithm can recover a close estimate of the unknown function based on the measurements collected at the boundary.

On the Presumed Kinetic Consequences of Pre-equilibrium. Implications for the Michaelis-Menten Equation

The overall rate equation for a reaction sequence consisting of a pre-equilibrium and rate-determining steps should not be derived on the basis of the concentration of the intermediate product (X). This is apparently indicated by transition state theory (as the path followed to reach the highest energy transition state is irrelevant), but also proved by a straight-forward mathematical approach. The thesis is further supported by the equations of concurrent reactions as applied to the partitioning of X between the two competing routes (reversal of the pre-equilibrium and formation of product). The rate equation may only be derived rigorously on the basis of the law of mass action. It is proposed that the reactants acquire the overall activation energy prior to the pre-equilibrium, thus forming X in a high-energy state en route to the rate-determining transition state. (It is argued that conventional energy profile diagrams are misleading and need to be reinterpreted.) Also, these arguments invalidate the Michaelis-Menten equation of enzyme kinetics, and necessitate a fundamental revision of our present understanding of enzyme catalysis. (The observed ``saturation kinetics'' possibly arises from weak binding of a second molecule of substrate at the active site; analogous conclusions apply to reactions at surfaces).

Diffusion ordered spectroscopy for resolution of double bonded cis, trans-isomers

NMR spectroscopic separation of double bonded cis- and trans-isomers, that have different molecular shapes but identical mass have been carried out using Diffusion Ordered Spectroscopy (DOSY). The mixtures of fumaric acid and maleic acid, that have similar hydrodynamic radii, have resolved been on the basis of their diffusion coefficients arising due to their different tendencies to associate with micelles or reverse micelles. Sodium dodecyl sulfate (SDS) and Dioctyl sulfosuccinate sodium salt (AOT) have been used as the media to mimic the chromatographic conditions, modify the average mobility and to achieve differential diffusion rates. The best separation of the components has been achieved by Dioctyl sulfosuccinate sodium salt (AOT) in D2O solution. (C) 2012 Elsevier B.V. All rights reserved.

Linearization and Reconstruction of Non-linear Diffuse Optical Tomographic Image

Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f(x) = x(T)Ax - b(T)x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and ill-conditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f(x; e) = (x + e)(T) A(x + e) - b(T)(x + e) + c. The revised cost functional is f(x; e) = f(x) + e(T)Ae. The self guided spatial weighted prior (e(T)Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.

Gibbs Energy of Formation of Ca3Ti8Al12O37 and Phase Relations and Chemical Potentials in the System Al2O3-TiO2-CaO

The quaternary oxide in the system Al2O3-CaO-TiO2 is found to have the composition Ca3Ti8Al12O37 rather than CaTi3Al8O19 as reported in the literature. The standard Gibbs energy of formation of Ca3Ti8Al12O37 from component binary oxides is measured in the temperature range from 900 to 1250 K using a solid-state electrochemical cell incorporating single crystal CaF2 as the solid electrolyte. The results can be represented by the equation: delta G(f(0x))(0) (+/- 70)/J mol(-1) = -248474 - 15.706(T/K). Combining this information with thermodynamic data on calcium aluminates and titanates available in the literature, subsolidus phase relations in the pseudo-ternary system Al2O3-CaO-TiO2 are computed and presented as isothermal sections. The evolution of phase relations with temperature is highlighted. Chemical potential diagrams are computed at 1200 K, showing the stability domains of the various phases in the chemical potential-composition space. In each chemical potential diagram, chemical potential of one component is plotted against the cationic fraction of the other two components. The diagrams are valid at relatively high oxygen potentials where Ti is present in its four-valent state in all the oxide phases.

Diffusion mechanism in XSi2 and X5Si3 (X= Nb, Mo, V) phases

In view of the importance of the suicides in the high temperature applications, the diffusion behaviour is compared in different systems for two types of silicides, XSi2 and X5Si3 (X=Nb, Mo, V). Atomic mechanism of diffusion and defects present in the structure are discussed. In both the phases, Si has faster diffusion rate than the metal species. This is expected from the nearest neighbour (NN) bonds present in the XSi2 phase but rather unusual in the X5Si3 phase. Relative mobilities of the species calculated indicate the presence of high concentration of Si antisites. Moreover, the concentration of the defects is different in different systems to find different diffusion rates.

Diffusion mechanism in the mu phase in Nb-X (X = Ni, Co, Fe) systems

Nb is one of the common refractory elements added in Ni, Co and Fe based superalloys. This lead to the formation of brittle topological close packed (tcp) mu phase, which is deleterious to the structure. It mainly grows by interdiffusion and in the present article, the interdiffusion process in different Nb-X (X=Ni, Co, Fe) systems is discussed. The activation energy for interdiffusion is lower in the Co-Nb system (173 kJ/mol) than Fe-Nb system (233 kJ/mol), which is again lower than the value found in the Ni-Nb system (319.7 kJ/mol). The mole fraction of Nb in this phase is less than Fe or Co at stoichiometric compositions in the Nb-Fe (that is Fe7Nb6) and Nb-Co (that is Co7Nb6) systems. On the other hand, the mole fraction of Nb is higher than Ni in the same phase (Ni6Nb2) in Ni-Nb system. However, in all the phases, Nb has lower diffusion rate. Possible diffusion mechanism in this phase is discussed with respect to the crystal structure.

A versatile resolving agent for diffusion edited separation of enantiomers, complex mixtures and constitutional isomers

The study is the first report of the utilization of a crown ether as a new and versatile resolving agent for the diffusion edited separation of enantiomers, complex mixtures and constitutional isomers. As a consequence of different binding affinities of enantiomers of a chiral molecule and individual components of the complex mixtures with the crown ether, the molecules diffuse at different rates. The enhanced separation achieved due to matrix assisted diffusion permitted their separation in the diffusion dimension. The generality and wide utility of the new resolving agent and the methodology are demonstrated on diverse examples, such as an organic chiral molecule, constitutional isomers and complex mixture of molecules possessing different functional groups that possess nearly identical molecular weights.

Use of Fick's law and Maxwell–Stefan equations in computation of multicomponent diffusion

This article does not have an abstract.

Diffusion mechanism in the gold-copper system

Interdiffusion study is conducted in the Au-Cu system, which has complete solid solution in the higher temperature range and ordered phases in the lower temperature range. First experiments are conducted at higher temperatures, where atoms can diffuse randomly. Higher values of interdiffusion coefficients are found in the range of 40-50 at.% Cu. This trend is explained with the help of thermodynamic factor and possible concentration of vacancies. Following an experiment is conducted at 623 K (350 degrees C), where the ordered phases are grown. The interdiffusion coefficients at this temperature are compared after extrapolating the data calculated at higher temperatures.