Effective Diffusion Coefficient

2018 ◽  
Vol 384 ◽  
pp. 130-135
Author(s):  
Jorge A. Gordillo
Keyword(s):  
Interdiffusion Coefficient ◽  
Nanocrystalline Materials ◽  
Effective Diffusion ◽  
Average Frequency ◽  
Solute Diffusion ◽  
Segregation Coefficient ◽  
Two Phase ◽  
Random Walk Theory ◽  
And Diffusion ◽  
Impurities And Diffusion

The diffusion of a B element into an A matrix was studied by the random walk theory. Considering that concentration of B element in the A matrix is very low, the jumps of diffusing atoms are independent of each other. The A matrix is a two-region material with different properties, such as a two-phase material, a single crystal with dislocations, or regions influenced by other solute and a polycrystalline material.It is assumed that material B has a penetration that allows it to cross each region of material A several times. This implies that jumps across the surface between those regions have an average frequency and, as a consequence, there is an interdiffusion coefficient between them. The interdiffusion coefficient between those regions is different than the coefficient of the diffusion in each region.Expressions were obtained that allow to delimit the ranges of validation with greater precision than the corrected Hart-Mortlock equation for solute diffusion. In addition, an original relationship was obtained between the segregation coefficient and parameters specific to the diffusion. New powerful tools were also found that can help to understand diffusion in nanocrystalline materials, diffusion in metals influenced by impurities and diffusion produced by different mechanisms.

Diffusion of Zinc in Two-Phase Mg-Al Alloy

2007 ◽  
Vol 263 ◽  
pp. 189-194
Author(s):  
Ivo Stloukal ◽  
Jiří Čermák
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Effective Diffusion ◽  
Residual Activity ◽  
Diffusion Path ◽  
Al Alloy ◽  
Serial Sectioning ◽  
Two Phase ◽  
Interphase Boundaries ◽  
The Mean

Coefficient of 65Zn heterodiffusion in Mg17Al12 intermetallic and in eutectic alloy Mg - 33.4 wt. % Al was measured in the temperature region 598 – 698 K using serial sectioning and residual activity methods. Diffusion coefficient of 65Zn in the intermetallic can be written as DI = 1.7 × 10-2 m2 s-1 exp (-155.0 kJ mol-1 / RT). At temperatures T ≥ 648 K, where the mean diffusion path was greater than the mean interlamellar distance in the eutectic, the effective diffusion coefficient Def = 2.7 × 10-2 m2 s-1 exp (-155.1 kJ mol-1 / RT) was evaluated. At two lower temperatures, the diffusion coefficients 65Zn in interphase boundaries were estimated: Db (623 K) = 1.6 × 10-12 m2 s-1 and Db (598 K) = 4.4 × 10-13 m2 s-1.

A Ternary, Two-Phase, Mathematical Model of Oil Recovery With Surfactant Systems

1984 ◽  
Vol 24 (06) ◽  
pp. 606-616 ◽  
Author(s):  
Charles P. Thomas ◽  
Paul D. Fleming ◽  
William K. Winter
Keyword(s):  
Mathematical Model ◽  
Oil Recovery ◽  
Arbitrary Number ◽  
The Other ◽  
Phase System ◽  
Chemical Flooding ◽  
Two Phase ◽  
Oil Displacement ◽  
Surfactant Systems ◽  
And Diffusion

Abstract A mathematical model describing one-dimensional (1D), isothermal flow of a ternary, two-phase surfactant system in isotropic porous media is presented along with numerical solutions of special cases. These solutions exhibit oil recovery profiles similar to those observed in laboratory tests of oil displacement by surfactant systems in cores. The model includes the effects of surfactant transfer between aqueous and hydrocarbon phases and both reversible and irreversible surfactant adsorption by the porous medium. The effects of capillary pressure and diffusion are ignored, however. The model is based on relative permeability concepts and employs a family of relative permeability curves that incorporate the effects of surfactant concentration on interfacial tension (IFT), the viscosity of the phases, and the volumetric flow rate. A numerical procedure was developed that results in two finite difference equations that are accurate to second order in the timestep size and first order in the spacestep size and allows explicit calculation of phase saturations and surfactant concentrations as a function of space and time variables. Numerical dispersion (truncation error) present in the two equations tends to mimic the neglected present in the two equations tends to mimic the neglected effects of capillary pressure and diffusion. The effective diffusion constants associated with this effect are proportional to the spacestep size. proportional to the spacestep size. Introduction In a previous paper we presented a system of differential equations that can be used to model oil recovery by chemical flooding. The general system allows for an arbitrary number of components as well as an arbitrary number of phases in an isothermal system. For a binary, two-phase system, the equations reduced to those of the Buckley-Leverett theory under the usual assumptions of incompressibility and each phase containing only a single component, as well as in the more general case where both phases have significant concentrations of both components, but the phases are incompressible and the concentration in one phase is a very weak function of the pressure of the other phase at a given temperature. pressure of the other phase at a given temperature. For a ternary, two-phase system a set of three differential equations was obtained. These equations are applicable to chemical flooding with surfactant, polymer, etc. In this paper, we present a numerical solution to these equations paper, we present a numerical solution to these equations for I D flow in the absence of gravity. Our purpose is to develop a model that includes the physical phenomena influencing oil displacement by surfactant systems and bridges the gap between laboratory displacement tests and reservoir simulation. It also should be of value in defining experiments to elucidate the mechanisms involved in oil displacement by surfactant systems and ultimately reduce the number of experiments necessary to optimize a given surfactant system.

Experimental Determination of Statistical Properties of Two-Phase Turbulent Motion

1960 ◽  
Vol 82 (3) ◽  
pp. 609-621 ◽  
Author(s):  
S. L. Soo ◽  
H. K. Ihrig ◽  
A. F. El Kouh
Keyword(s):  
Gas Phase ◽  
Tracer Diffusion ◽  
Statistical Properties ◽  
Solid Particles ◽  
Turbulent Motion ◽  
Two Phase ◽  
Gaseous State ◽  
Diffusion Technique ◽  
And Diffusion

Experimental methods for the determination of certain statistical properties of turbulent conveyance and diffusion of solid particles in a gaseous state are presented. Methods include a tracer-diffusion technique for the determination of gas-phase turbulent motion and a photo-optical technique for the determination of motion of solid particles. Results are discussed and compared with previous analytical results.

The Application of Numerical Simulation to Liquid Pipeline Leakage at LNG Terminal in China

2020 ◽  
Author(s):  
Zhichao Guo ◽  
Zhaoci Li
Keyword(s):  
Numerical Simulation ◽  
Liquid Phase ◽  
Natural Gas ◽  
Diffusion Process ◽  
Gas Phase ◽  
Stokes Equations ◽  
Response Strategy ◽  
Movement Trajectory ◽  
Two Phase ◽  
And Diffusion

Abstract In 2018, China’s natural gas import reached 90.39 million tons, and the liquefied natural gas (LNG) import was 53.78 million tons, accounting for 59.5% of total natural gas imports. With the construction of LNG terminals, more studies on the leakage of LNG storage and transportation facilities have emerged to prevent catastrophic consequences such as explosions and frostbite. However, most of previous researches focused on gas pipeline leakage after LNG gasification, and few of those have been done on LNG liquid pipeline leakage. In this paper, Fluent software is used to numerically simulate the process of LNG liquid pipeline leakage. After the occurrence of LNG leakage, it will suffer the process of endothermic, evaporation, and diffusion, which is considered as a two-phase diffusion process. The Euler-Lagrangian method is introduced to simulate the diffusion process of gas phase and liquid phase separately. In the simulation, the liquid phase is regarded as discrete droplets for discrete processing. The movement trajectory, heat transfer process and evaporation process of each droplet are tracked respectively. Different from the liquid phase, the gas phase is regarded as a continuous phase and the Navier-Stokes equations are adopted for calculation. Thereafter, coupling calculations of two phase are performed to determine the concentration field and temperature field of the LNG liquid pipeline leakage. As a supplement to this research, the influence of wind speed on LNG leakage and diffusion process is analysed in detail. Finally, the numerical simulation method is applied to a coastal LNG terminal in northern China to determine the distribution of natural gas concentration and temperature, as well as delimit the combustion range. The results can provide scientific reference for the delimitation of risky zones and the formulation of emergency response strategy.

What is Behind the Inverse Hall-Petch Behavior in Nanocrystalline Materials?

2006 ◽  
Vol 976 ◽  
Author(s):  
Christopher Carlton ◽  
P. J. Ferreira
Keyword(s):  
Grain Size ◽  
Yield Strength ◽  
Strain Rate ◽  
Grain Boundaries ◽  
Nanocrystalline Materials ◽  
Critical Value ◽  
Petch Relationship ◽  
And Diffusion ◽  
Critical Grain Size

AbstractAn inverse Hall-Petch effect has been observed for nanocrystalline materials by a large number of researchers. This result implies that nanocrystalline materials get softer as grain size is reduced below a critical value. Postulated explanations for this behavior include dislocation based mechanisms and diffusion based mechanisms. In this paper, we report an explanation for the inverse Hall-Petch effect based on the statistical absorption of dislocations by grain boundaries, showing that the yield strength is both dependent on strain rate and temperature, and that it deviates from the Hall-Petch relationship at a critical grain size.

Diffusion in the Presence of Twin Boundaries

2007 ◽  
Vol 263 ◽  
pp. 201-206 ◽  
Author(s):  
Vĕra Rothová
Keyword(s):  
Anomalous Diffusion ◽  
Activation Enthalpy ◽  
Effective Diffusion ◽  
Type A ◽  
Transition Regime ◽  
Twin Boundaries ◽  
Self Diffusion ◽  
High Fraction ◽  
Type Ab ◽  
And Diffusion

In this paper, four examples from the literature are introduced in which the presence of high density of twin boundaries could explain an anomalous diffusion behavior. (i) In the case of the grain boundary (GB) self-diffusion in nickel, leakage from the random GBs to considerably high fraction of deformation and/or annealing twins in the samples studied can be a reason for the diverse literature values of activation enthalpy. The diffusion model including participation of two types of GBs is essential for data evaluation. (ii) Segregation of Ge atoms with negligible solubility to twin boundaries and diffusion in both type A and type AB transition regime can clarify the unusual 71Ge diffusion in the Mg alloys. (iii) Anomalous diffusion of gold in polycrystalline silicon presented in the literature was discussed here. Because profiles corresponding to type AB transition regime were detected, transition from type B to type A diffusion regime could be an alternative explanation of the anomaly. (iv) Effective diffusion of the 63Ni tracer in the presence of unidirectional defects in single-crystalline β-tin might be a simple reason for the uncommon features published earlier: low activation enthalpy, high diffusion anisotropy and values of the extrapolated solid-state Ni diffusion coefficients above those in the Sn liquid phase.

Two-Dimensional Pore Pressure Distribution Model to Evaluate Effects of Shale Semipermeable Membrane Characteristics

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Jia Wei ◽  
Yuanfang Cheng ◽  
Chuanliang Yan
Keyword(s):  
Diffusion Coefficient ◽  
Pressure Distribution ◽  
Pore Pressure ◽  
Effective Diffusion Coefficient ◽  
Early Stage ◽  
Drilling Fluid ◽  
Effective Diffusion ◽  
Solute Diffusion ◽  
Sensitivity Analyses ◽  
Distribution Model

During the drilling of shale formations, drilling fluids can intrude into the wellbore, raise the pore pressure, and lead to wellbore instability. Based on the thermodynamic theory, a new model was established to calculate pore pressure. The model considers the effects of solute diffusion and solution convection and conducts sensitivity analyses. The results show that the drilling fluid activity significantly affects the pore pressure distribution. The pore pressure under high drilling fluid activity will increase rapidly in the early stage. Low drilling fluid activity can effectively suppress the growth of pore pressure. And a low effective diffusion coefficient of solute and a high membrane efficiency also help to reduce pore pressure. Therefore, reducing drilling fluid activity should be conducted in priority in drilling fluid design. Lowering its solute effective diffusion coefficient and increasing its viscosity can also be considered as auxiliary methods.

Diffusionsgrenzstrom und verwandte Probleme bei Elektrolytschmelzen mit drei ionischen Bestandteilen / Limiting Diffusion Current and Related Problems of Ionic Melts with Three Ion Constituents

1974 ◽  
Vol 29 (12) ◽  
pp. 1935-1936 ◽  
Author(s):  
R. Haase
Keyword(s):  
Interdiffusion Coefficient ◽  
Diffusion Current ◽  
Simultaneous Occurrence ◽  
Ionic Melts ◽  
Electrode Interface ◽  
Electric Flux ◽  
And Diffusion ◽  
Internal Transport ◽  
Limiting Value ◽  
Limiting Diffusion Current

Starting from the general equation for the simultaneous occurrence of electromigration and diffusion in an ionic melt with three ion constituents, we derive the rigorous expression for the electric flux at an electrode interface. This expression contains the ratio of the interdiffusion coefficient of the melt to the internal transport number of the ion constituent that does not cross the interface. In the case of the limiting diffusion current (occurring in the problem of diffusion overvoltage), the electric flux contains the limiting value for infinite dilution of the interdiffusion coefficient.

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