Wagner Theory Research Articles

Effect of the surface conductance on electrokinetic potential calculated from electrophoretic mobilities of the diamond particles in ethanol electrolyte solutions

Effect of the surface conductance on the ζ -potential of synthetic diamond particles (with sizes of 0.5–1 μm) determined from their electrophoretic mobility in ethanol solutions of 1:1 electrolytes over the range C =10 −5 –10 −2 M was studied. The conductivity of dilute diamond suspensions at the variable particle volume fraction was measured and the dependencies of surface conductivity ( K s ) on the electrolyte concentration were calculated by expression of the Wagner theory. It was found that K s has excessively high values, continually increasing with the growth of C and having high non-zero values at the points of a reversal of ζ -potential sign to positive, found at C =5×10 −4 M CsBr and C =10 −2 M NaClO 4 . Such character of the dependency K s (log C ) is explained by the preferable specific adsorption of cations and the main contribution of Stern layer to the surface conductance. It was found that the plots ζ (log C ), derived using Smoluchowski's equation, show a weak dependencies on C in the whole concentration range and disconcerting maxima. Incorporation of the experimental K s values in the Henry's equation brings to a linear character of the corresponding plots ζ (log C ) with the slope 20–25 mV per decade.

Growth kinetics of γ′ precipitates in superalloy IN-738LC during long term aging

Abstract In this research, results obtained on the growth kinetics of γ′ precipitates in superalloy IN-738LC are presented. It was found that when the coarsening of primary and secondary γ′ are considered together, the overall kinetic of coarsening followed a linear trend, as predicted by Lifshitz, Slyozov and Wagner (LSW) theory. However, when only the population of secondary γ′ was taken into account, growth rate for the secondary γ′ departed from the linear trend predicted by the theory. It is therefore suggested that the observed deviation of coarsening kinetics from linear behavior may be related to the short inter-particle distances in this system which caused elastic interaction energy to become dominant in the late stage and coarsening kinetics slow down.

A physically based model of the onset of crowning

The objective of this study is to investigate the capability of a physical two-phase model to predict the ignition of crown fuels by a surface fire and then to determine the degree of crowning. The model considers the hydrodynamic aspects of the flow and accounts for the basic physicochemical processes resulting from the thermal degradation of organic matter. Turbulence, soot formation, and its impact on radiation are considered in order to improve the physical insight. Calculations have been performed to investigate the effects of crown base height and aerial fuel moisture content on the onset of crowning. Numerical results are found to be consistent with experimental observations and the widely used Canadian Fire Behavior Prediction System classification by crown fraction burned. This model may be used to extend the domain of application of semiphysical theories, e.g., Van Wagner's theory, where fuel and environmental factors are generally determined from empirical observations of previous fires. It provides a means of adjusting these factors in other fire situations without requiring additional experiments.

Disproportionation of clustered protein-stabilized bubbles at planar air–water interfaces

The rate of shrinkage of air bubbles, of initial radius from 50 to 200 μm, injected beneath a planar air–water interface has been measured. Bubbles were stabilized in solutions of 0.05 wt% gelatin or pure β-lactoglobulin. It has been observed that small size differences between two closely spaced or touching bubbles result in markedly divergent rates of shrinkage for the two. By studying a number of different initial bubble configurations, it is demonstrated that the overall change in bubble size distribution is strongly dependent on local, interbubble gas diffusion. In this respect, the strong tendency for the gelatin-stabilized bubbles to aggregate and shrink, while remaining in contact, produced patterns of disproportionation significantly different from those observed with β-lactoglobulin. In β-lactoglobulin solutions, it was usually found that bubbles initially in contact shrank away from each other with time, becoming increasingly isolated as a result. A theoretical approach that can exactly incorporate the perturbation of local diffusion fluxes due to the proximity of two bubbles is presented. This enables one to map a “stability diagram” that delineates regions where the larger bubble of a pair will either shrink or grow, according to the relative size of the bubbles and their separation. Theoretical calculations show that it is possible for a bubble to exhibit more complex shrinkage behavior than is predicted by a mean field approach or the Lifshitz, Slyozov, and Wagner (LSW) theory of Ostwald ripening for dilute systems. The inclusion of dilatational elasticity in the theoretical model introduces additional complications, which are also briefly discussed.

The Wagner Theory of 2-Dimensional Constant Sprays and its Applications in Evolutionary Biology

The present work draws on classical projective geometry of general path spaces to further study biologically motivated models in the theory of Volterra-Hamilton systems with constant coefficients. In particular, it is shown here that 2-species systems of competitive, parasitic or mutualistic type are all projectively flat (time-sequencing equivalent) and unstable. Yet, they possess first integrals of the motion. Proofs are from Wagner theory, which is in essence, just the 2-dimensional Finsler geometry of semi-symmetric connections.

Numerical Approximation of the Lifshitz--Slyozov--Wagner Equation

The Lifshitz--Slyozov--Wagner theory of coarsening (Ostwald ripening) describes the late stages of the growth by diffusional mass transfer of the grains of a new phase from a supersaturated solution. It results in a nonlinear transport equation with a nonlocal nonlinearity for the volume distribution function of the grains. A time explicit finite volume numerical scheme is proposed to solve this equation in self-similar variables and is shown to converge under a CFL condition. Numerical simulations are also presented.

EMF behavior of oxygen concentration cells involving a ternary or higher oxide with mobile cations

Oxygen concentration cells have often been employed to determine the ionic transference number of a ternary or higher oxide, e.g., LiNbO 3 and Ca 1− x Li 2 x WO 4, on the basis of Wagner's classic theory [Z. Phys. Chem. B21 (1933) 25]. In this paper, we report on a unusual behavior of EMF of the oxygen concentration cell Pt, a O 2 ′|LiNbO 3| a O 2 ″ (=0.21),Pt to demonstrate that because of the unspecified, surplus degree(s) of freedom of the oxide, the EMF of the cell has no unique meaning in general. The unusual behavior is attributed to cationic unmixing induced by the oxygen potential gradient applied. Special cases are discussed in which one can determine the ionic transference number of ternary or higher oxides from the EMF of an oxygen concentration cell.

Theoretical V– I characteristics of the solid-oxide thermocell using the oxide ion and electronic mixed conductors

The theoretical relationships between the terminal voltage ( V) and external current ( I) of a solid-oxide thermocell using oxide ion–electron mixed conductors were derived based on Wagner's theory. The electrical transport parameters of Y 2Ti 2O 7 were used to calculate the theoretical V– I characteristics. A mixed discharge region, where the partial currents of the oxide ions and electronic carriers flow in the same direction, appeared under an air atmosphere.

Ostwald ripening under dislocation diffusion

The Lifshitz–Slyozov–Wagner theory is used to investigate the kinetics of decomposition of a supersaturated solid solution in the case that the interface between the nuclei of a new phase and the matrix is quasi-coherent. The size distribution is shown to be within a very narrow range of relative sizes ( r g /r c =6/5 ), and the critical and the average sizes of a nucleus varies as t 1/6 .

Molecular Diffusion of Oil/Water Emulsions in Surfactant-Free Conditions

Growth processes of hydrocarbon droplets (C6−C16: n-hexane, cyclohexane, n-octane, n-decane, n-dodecane, n-tetradecane, and n-hexadecane) in oil/water emulsions under surfactant-free conditions were examined by dynamic light scattering (DLS) and freeze-fracture electron microscopy (FFEM). DLS results showed that the growth rate of droplet size decreased with increase in hydrocarbon chain length. For example, n-hexane droplets grew within 1 h from submicrometer to micrometer droplets, while n-hexadecane droplets with sizes of several tens of nanometers kept their dispersibility for 24 h. We determined the growth processes as coalescence and molecular diffusion (Ostwald ripening) in terms of the Lifshitz−Slyozov−Wagner theory and the Smoluchowski equation. Furthermore, FFEM was used to examine the growth mechanism in detail. Direct imaging of n-hexane and cyclohexane droplets by FFEM allowed us to observe very fine oil droplets (∼10 nm in diameter) though DLS could not detect these droplets, suggesting tha...

Water surface impact loads acts on bulbous bow of ships

As a part of the project study concerning on ship structural design for oil spill prevention by collision, optimal design of flexible bulbous bow structure is studied to absorb kinetic energy of the colliding ship. Such a flexible bulbous bow is named as buffer bow. To formulate design criteria of the buffer bow, the hydrodynamic impact forces acts on the bulbous bow was studied theoretically and experimentally. For theoretical study, shape of the bulbous bow was approximated by an ellipsoid and von Karman's momentum theory was applied to estimate the slamming impact loads with given impact velocity of the emerged bow to free surface. Wagner's impact theory was also applied to study the effect of free surface swell up. Based on the momentum theoy, an estimation method of the impact loads was proposed. To validate the estimation method, a experiment was conducted at the 80m square tank of NMRI. A self-propelling container ship model was used for the experiment. The vertical and lateral shearing forces and bending moments at the root of the bulbous bow were measured. In this paper, the results of the study are presented.

The Lifshitz--Slyozov--Wagner Equation with Conserved Total Volume

The Lifshitz--Slyozov--Wagner theory of coarsening (Ostwald ripening) in alloys describes the time evolution of the sizes of the grains of a new phase growing by diffusional mass transfer from a supersaturated solid solution. The volume distribution function of the grains obeys a nonlinear transport equation with a nonlocal nonlinearity. Global existence of solutions is obtained for a large class of data including the ones derived by Lifshitz and Slyozov [J. Phys. Chem. Solids, 19 (1961), pp. 35--50] and Wagner [Z. Elektrochem., 65 (1961), pp. 581--591], and uniqueness of these solutions is proved in some cases.

Evolution of an Ensemble of Nanoparticles in a Colloidal Solution: Theoretical Study

The evolution of a nanosized particle in colloidal solution has been studied theoretically. The model developed is based on the size dependence of the activation energies of the growth and dissolution processes and takes into account the mass transport dynamics. Using this model, Monte Carlo simulations of the evolution of an ensemble of growing nanoparticles during Ostwald ripening have been performed, and conditions leading to either “focusing” or “defocusing” of the particle size distribution were found. The stationary particle size distribution inherent to the Ostwald ripening process in ensembles of nanoparticles less than 5 nm in radius is narrower and more symmetric than that predicted by the Lifshitz−Slyozov−Wagner theory valid for ensembles of larger (>20 nm in radius) colloidal particles. The growth of nanoparticles in the diffusion-controlled regime results in better final size distributions as compared with those grown in the reaction-controlled regime. The dependence of the particle size dist...

A random walk approach to Ostwald ripening

We investigate a numerical model of Ostwald ripening in which matter is discretised. The model is based on transport by random walk and certain rules at the phase interfaces which mimic the continuous solution of the diffusion and moving boundary problem. In the limit of low volume fractions the results from our simulations agree quantitatively with the results predicted by the Lifshitz–Slyosov–Wagner theory. In contrast to the LSW model, the volume fraction of particles enters our model as part of the diffusion problem and it may therefore be confidently used to investigate what happens when the volume fraction of particles increases.

Mathematical model of influence of rapid induction heating on nucleation and growth of precipitates

A mathematical model of the influence of rapid induction heating on the nucleation and growth of secondary phases in diffusion controlled processes has been developed. The total stress produced by the electromagnetic field and acting on the volume V of a specimen was derived and added to other external stresses applied to the system. Then, the total effective stress was introduced into mathematical equations of diffusion controlled nucleation and growth processes. In addition, the effect of rapid induction heating on the age hardening treatment of a selected cast nickel base superalloy, IN738LC, was investigated experimentally. For this purpose, two types of rapid aging with equal heating rates were applied: one treatment was induction aging and the other was salt bath aging. Microstructural characteristics of γ′ precipitates and hardening behaviour were studied by means of scanning electron microscopy (SEM), electron image analysis, transmission electron microscopy (TEM), and hardness testing. According to the results obtained, although the rates of heating in induction and salt bath aging were equal, the rates of nucleation and growth of γ′ precipitates in induction aging were much faster than those obtained in salt bath aging, especially in the first minutes of the aging process. Furthermore, the characteristics of γ′ precipitates with induction aging were more favorable than those with salt bath and normal aging. It was observed that the growth rate of γ′ in induction aging deviated considerably from the t1/3 growth law of the standard modified Lifshitz, Slyozov, and Wagner (MLSW) theory. The remarkable improvement of microstructural characteristics obtained with induction aging can be attributed to the existence of the external electromagnetic force produced by rapid induction heating.

Oxidation of metals with highly reactive vapors: Extension of wagner theory

In this article, a theoretical analysis of the behavior of metallic materials at high temperature in the presence of gaseous oxygen is presented. A generalized Wagner approach is presented in the limiting scenario of highly reactive vapors, Wagner’s theory being the lower limit for null reactivity. Oxygen transfer from the gas phase to the condensed phase is expressed in terms of oxygen effective pressure, accounting for the contribution of volatile oxides. The theoretical approach allows the prediction of the oxygen partial pressures in the feed gas corresponding to oxidation/deoxidation conditions. Such conditions can be different from those given by thermodynamic equilibrium by several orders of magnitude. Moreover, the actual oxygen partial pressure at the condensed phase interface can be expressed as a function of the feed-gas oxygen content, which is measurable. The theory is applicable for metals and nonmetallic materials, such as semiconductors, both in solid and liquid phase. An application to the molten silicon-oxygen system is presented.

Three-dimensional theory of water impact. Part 1. Inverse Wagner problem

The three-dimensional problem of blunt-body impact onto the free surface of an ideal incompressible liquid is considered within the Wagner theory. The theory is formally valid during an initial stage of the impact. The problem has been extensively studied in both two-dimensional and axisymmetric cases. However, there are no exact truly three-dimensional solutions of the problem even within the Wagner theory. At present, three-dimensional effects in impact problems are mainly handled approximately by using a sequence of two-dimensional solutions and/or aspect-ratio correction factor. In this paper we present exact analytical rather than approximate solutions to the three-dimensional Wagner problem. The solutions are obtained by the inverse method. In this method the body velocity and the projection on the horizontal plane of the contact line between the liquid free surface and the surface of the entering body are assumed to be given at any time instant. The shape of the impacting body is determined from the Wagner condition. It is proved that an elliptic paraboloid entering calm water at a constant velocity has an elliptic contact line with the free surface. Most of the results are presented for elliptic contact lines, for which analytical solutions of the inverse Wagner problem are available. The results obtained can be helpful in testing other numerical approaches and studying the influence of three-dimensional effects on the liquid flow and the hydrodynamic loads.

Ostwald Ripening of Alkane Emulsions Stabilized by Polyethylene Glycol Monolaurate

The Ostwald ripening of alkane in water emulsions stabilized by the surfactant poly(ethylene glycol) monolaurate (PEM) was investigated. Surprisingly the measured ripening rates were significantly below the rate which can be predicted by the Lifshitz−Slyozov−Wagner (LSW) theory and decreased in the presence of surfactant micelles. A possible explanation of the effect of these micelles is that they withdraw oil from the continuous phase and hence slow the transport of oil from smaller to larger droplets.

Nanoscale structural evolution of Al 3Sc precipitates in Al(Sc) alloys

Precipitation of the Al 3Sc (L1 2) phase in aluminum alloys, containing 0.1, 0.2 or 0.3 wt% Sc, is studied with conventional transmission and high-resolution (HREM) electron microscopies. The exact morphologies of the Al 3Sc precipitates were determined for the first time by HREM, in Al–0.1 wt% Sc and Al–0.3 wt% Sc alloys. The experimentally determined equilibrium shape of the Al 3Sc precipitates, at 300°C and 0.3 wt% Sc, has 26 facets, which are the 6 {100} (cube), 12 {110} (rhombic dodecahedron), and 8 {111} (octahedron) planes, a Great Rhombicuboctahedron. This equilibrium morphology had been predicted by first principles calculations of the pertinent interfacial energies. The coarsening kinetics obey the (time) 1/3 kinetic law of Lifshitz–Slyozov–Wagner theory and they yield an activation energy for diffusion, 164±9 kJ/mol, that is in agreement with the values obtained from tracer diffusion measurements of Sc in Al and first principles calculations, which implies diffusion-controlled coarsening.

Determination of Diffusion Coefficient of Nd<SUP>3+</SUP> in NdCrO<SUB>3</SUB> Based on Solid State Reaction

The solid state reaction, (1 /2 )Nd 2 O 3 + (1/2)Cr 2 O 3 → NdCrO 3 , was studied between 1473 K and 1773 K in air to determine the parabolic rate constant. The electrical conductivity of the NdCrO 3 phases separately equilibrated with Nd 2 O 3 and Cr 2 O 3 were measured between 1673 K and 1773 K in an argon-oxygen mixture. The standard Gibbs energy change for the solid state reaction was estimated from the activity dependence of the electrical conductivity of NdCrO 3 According to Wagner's theory, the diffusion coefficient of Nd 3+ in NdCrO 3 can be evaluated from the parabolic rate constant for the solid state reaction, the standard Gibbs energy change of the solid state reaction, and the defect equilibrium reaction in NdCrO 3 . From these data, the diffusion coefficient of Nd 3 in NdCrO 3 was given by D Ma3+ /m 2 s -1 = 1.3 × 10 -6 .exp(-343 kJ mol -1 /RT) (P O2 /Pa) 3/16 a 1/8 Cr2O3 where a Cr2O3 is the activity of Cr 2 O 3 and P O2 is the oxygen pressure. The obtained diffusion coefficient of Nd 3+ in NdCrO 3 was compared with that of Y 3+ in YCrO 3 and that of La 3+ in LaCrO 3 .