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Reaction, diffusion

Koenig U and Schultze J W 1992 Solid State Ion. DIffus. Reactions 53-56 255... [Pg.2737]

Deterministic air quaUty models describe in a fundamental manner the individual processes that affect the evolution of pollutant concentrations. These models are based on solving the atmospheric diffusion —reaction equation, which is in essence the conservation-of-mass principle for each pollutant species... [Pg.379]

Numerical and some analytical solutions of the diffusion/reaction equations are represented closely by an empirical curve/fit,... [Pg.2096]

Time dC dt Flow + u- 91 Diffusion Reaction = - ar Reactor Type General... [Pg.253]

Several methods have been employed to study chemical reactions theoretically. Mean-field modeling using ordinary differential equations (ODE) is a widely used method [8]. Further extensions of the ODE framework to include diffusional terms are very useful and, e.g., have allowed one to describe spatio-temporal patterns in diffusion-reaction systems [9]. However, these methods are essentially limited because they always consider average environments of reactants and adsorption sites, ignoring stochastic fluctuations and correlations that naturally emerge in actual systems e.g., very recently by means of in situ STM measurements it has been demon-... [Pg.390]

F. Otalora, J. M. Garcia-Ruiz. Computer model of the diffusion/reaction interplay in the gel acupuncture method. J Cryst Growth 169 2>6, 1996. [Pg.931]

A large class of reaction-diffusion reactions may be expressed by the (deceptively simple) equation... [Pg.419]

Both questions have been recently addressed via a surface diffusion-reaction model developed and solved to describe the effect of electrochemical promotion on porous conductive catalyst films supported on solid electrolyte supports.23 The model accounts for the migration (backspillover) of promoting anionic, O5, species from the solid electrolyte onto the catalyst surface. The... [Pg.500]

The oxidation or reduction of a substrate suffering from sluggish electron transfer kinetics at the electrode surface is mediated by a redox system that can exchange electrons rapidly with the electrode and the substrate. The situation is clear when the half-wave potential of the mediator is equal to or more positive than that of the substrate (for oxidations, and vice versa for reductions). The mediated reaction path is favored over direct electrochemistry of the substrate at the electrode because, by the diffusion/reaction layer of the redox mediator, the electron transfer step takes place in a three-dimensional reaction zone rather than at the surface Mediation can also occur when the half-wave potential of the mediator is on the thermodynamically less favorable side, in cases where the redox equilibrium between mediator and substrate is disturbed by an irreversible follow-up reaction of the latter. The requirement of sufficiently fast electron transfer reactions of the mediator is usually fulfilled by such revemible redox couples PjQ in which bond and solvate... [Pg.61]

A link between laminar and turbulent lifted flames has been demonstrated based on the observation of a continuous transition from laminar to turbulent lifted flames, as shown in Figure 4.3.13 [56]. The flame attached to the nozzle lifted off in the laminar regime, experienced the transition by the jet breakup characteristics, and became turbulent lifted flames as the nozzle flow became turbulent. Subsequently, the liftoff height increased linearly and finally blowout (BO) occurred. This continuous transition suggested that tribrachial flames observed in laminar lifted flames could play an important role in the stabilization of turbulent lifted flames. Recent measurements supported the existence of tribrachial structure at turbulent lifted edges [57], with the OH zone indicating that the diffusion reaction zone is surrounded by the rich and lean reaction zones. [Pg.63]

Fluid flow and reaction engineering problems represent a rich spectrum of examples of multiple and disparate scales. In chemical kinetics such problems involve high values of Thiele modulus (diffusion-reaction problems), Damkohler and Peclet numbers (diffusion-convection-reaction problems). For fluid flow problems a large value of the Mach number, which represents the ratio of flow velocity to the speed of sound, indicates the possibility of shock waves a large value of the Reynolds number causes boundary layers to be formed near solid walls and a large value of the Prandtl number gives rise to thermal boundary layers. Evidently, the inherently disparate scales for fluid flow, heat transfer and chemical reaction are responsible for the presence of thin regions or "fronts in the solution. [Pg.376]

In 1902, Wagner published an analysis, based on diffusion reactions, of the oxidation of the surface of a metal. His interpretation has remained a classic in solid state diffusion analysis. The surface of a metal consists of metal atoms bound to the inner structure by a series of hybrid-bonds. If oxygen gas is present (air), the metal can form an oxide coating ... [Pg.146]

Migrating Species Occurring in a Solid-Gas Diffusion Reaction... [Pg.153]

To understand this effect, consider the following. Suppose we have a situation where A reacts with B to form a solid solution. AB. Let us further suppose that the diffusion reaction is ... [Pg.153]

We have now presented all of the possible diffusion reactions in spinel synthesis. These are summarized as follows ... [Pg.159]

It is for this reason that we write the solid state diffusion reaction for the magnesium aluminate spinel as follows ... [Pg.161]

Using our model, we would illust ate the diffusion reactions with the... [Pg.161]

Note that we have two diffusion reactions which form the metasilicate, one proceeding from the cationic species and the other from anionic species. This has an amazing effect on the overall reaction, as shown in the following diagram, given as 4.9.11. on the next page. [Pg.165]

Sequence of Phases Formed as a Function of Time, As Caused by the Prevailing Diffusion Reactions... [Pg.166]

In the sequence of diffusion reactions, we note that Ca2Si04 is formed immediately, followed by Ca4Si207. Both begin to disappear when CaSiOs... [Pg.166]

For the spinel, Hercyanite, draw a diagram illustrating the probable ion diffusion processes, give the diffusion conditions and the diffusion reactions if the diffusion coefficents for the cation and anion are ... [Pg.177]

Reactor type Multi-plate-stack with two diffusers Reaction channel No. 1 400 pm 400 pm width depth length 50 mm... [Pg.267]

Fast reaction Ha Z Numerical solution of diffusion-reaction equations in the film needed... [Pg.285]

This example involves the same diffusion-reaction situation as in the previous example, ENZSPLIT, except that here a dynamic solution is obtained, using the method of finite differencing. The substrate concentration profile in the porous biocatalyst is shown in Fig. 5.252. [Pg.647]

This article presents a brief account of theory and practical aspects of rotating hemispherical electrodes. The fluid flow around the RHSE, mass transfer correlations, potential profile, and electrochemical application to the investigations of diffusivity, reaction rate constants, intermediate reaction products, passivity, and AC techniques are reviewed in the following sections. [Pg.172]

Contact diffusion Reaction with a change Noncontact Solvatochromism ... [Pg.193]

The time approach relies entirely on independent diffusion-reaction time without reference to distances. The reaction product inherits the time sequence of one of the parents chosen at random however, its residual time to react with another species is scaled inversely relative to its mutual diffusion confident. A heuristic correction is also made for the change of reaction radius (Clifford et al, 1986). [Pg.223]


See other pages where Reaction, diffusion is mentioned: [Pg.98]    [Pg.127]    [Pg.473]    [Pg.154]    [Pg.156]    [Pg.157]    [Pg.159]    [Pg.162]    [Pg.163]    [Pg.163]    [Pg.166]    [Pg.172]    [Pg.173]    [Pg.173]    [Pg.174]    [Pg.457]    [Pg.394]    [Pg.103]    [Pg.89]    [Pg.590]    [Pg.180]   
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See also in sourсe #XX -- [ Pg.329 ]

See also in sourсe #XX -- [ Pg.96 , Pg.97 , Pg.98 , Pg.99 , Pg.100 ]

See also in sourсe #XX -- [ Pg.429 ]




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A Multicomponent Diffusion in the Presence of Reaction

AUTOCATALYTIC REACTIONS IN PLUG-FLOW AND DIFFUSION REACTORS

Acid diffusion reaction mechanism

Advection-reaction-diffusion equation

Algorithms diffusion with reaction

Analysis of Diffusion Reactions in Spinel

Analysis of Diffusion Reactions in the Solid State

Analytical Solutions for Diffusion and Early Diagenetic Reactions

Anthracene, diffusion control reactions

Application of ILDM Methods in Reaction Diffusion Systems

Aqueous-Phase Diffusion and Reaction

Attachment reactions, diffusion controlled

Bimolecular reactions diffusion theory

Biofilm diffusion-reaction process

Calculation of Diffusive Fluxes and Diagenetic Reaction Rates

Catalytic reactions pore diffusion effects

Chemical Reaction and Diffusion inside a Catalyst Particle

Chemical reaction and diffusion

Chemical reaction and rotational diffusion rates

Chemical reaction influenced by intraparticle diffusion

Chemical reaction without diffusion

Chemical reactions diffusion-controlled

Chemical waves, reaction-diffusion process

Complex Reactions with Pore Diffusion

Conditional fluxes reaction/diffusion

Consecutive reactions diffusion limited

Contact diffusion controlled reactions

Convection-Diffusion Equation with Reactions

Convection-diffusion-reaction equation

Convective diffusion equation with chemical reactions

Coulombic interactions diffusion-controlled reactions

Criteria for diffusion control of a catalytic reaction

Criterion of First Phase Choice at Reaction-Diffusion Processes

Cure reactions diffusion control

Cylindrical catalyst pellets diffusion/reaction

Diffuse oxidation reactions

Diffuse reaction zone models

Diffuse reflectance infrared Fourier transform reaction

Diffusion Associated with Chemical Reaction

Diffusion Control of Reactions

Diffusion Controlled Interfacial Reaction

Diffusion Controlled Reactions Neutral Species

Diffusion and First-Order Heterogeneous Reactions

Diffusion and Heterogeneous Chemical Reactions in Isothermal Catalytic Pellets

Diffusion and Pseudo-Homogeneous Chemical Reactions in Isothermal Catalytic Pellets

Diffusion and Reaction in Spherical Catalyst Pellets

Diffusion and Reaction in a Porous Structure

Diffusion and Reaction in a Single Cylindrical Pore within the Catalyst Pellet

Diffusion and Reaction of the Products

Diffusion and Reactions in the Liquid Phase

Diffusion and bimolecular reactions

Diffusion and catalytic reaction

Diffusion and catalytic reaction, isothermal

Diffusion and reaction

Diffusion and reaction in a slab

Diffusion and reaction in pores

Diffusion and reaction in pores. Effectiveness

Diffusion and reaction in porous

Diffusion and reaction in porous catalysts

Diffusion and reaction kinetics

Diffusion and reaction on nonpermeable catalysts

Diffusion and reaction rate

Diffusion and reaction, split boundary solution

Diffusion calculations—reaction models

Diffusion chemical reaction

Diffusion coefficient, and reaction rate

Diffusion coefficients reactions

Diffusion control cathodic reaction under

Diffusion control of homogeneous reactions

Diffusion controlled homogeneous polymer reactions

Diffusion controlled limit, reaction

Diffusion controlled propagation reactions

Diffusion controlled reaction kinetics

Diffusion controlled reaction rates

Diffusion controlled reaction, transient effects

Diffusion controlled reactions collision frequencies

Diffusion controlled reactions encounters

Diffusion controlled reactions in polymer degradation

Diffusion controlled reactions with initially separated reactants

Diffusion controlled reactions, supercritical fluids

Diffusion coupled with interface reaction

Diffusion effects carbon burning reaction

Diffusion effects first order reactions

Diffusion effects involving reaction rates

Diffusion effects on biomoleeular reactions

Diffusion effects, electron-transfer bulk reaction

Diffusion equations droplet phase reactions

Diffusion interface reactions

Diffusion mass transfer-limited reactions

Diffusion mass-transfer-controlled reactions

Diffusion metamorphic reactions

Diffusion plus reaction

Diffusion reaction control

Diffusion reaction dynamics

Diffusion reaction resistances

Diffusion reaction, relaxation

Diffusion regime of reaction

Diffusion resistance with complex reactions

Diffusion theory of reactions

Diffusion with a first order reaction

Diffusion with a second order reaction

Diffusion with catalytic surface reaction

Diffusion with chemical reaction

Diffusion with homogeneous reaction

Diffusion with reaction

Diffusion, Vibrations and Chemical Reactions

Diffusion, coefficient controlled bimolecular reactions

Diffusion, mass reaction systems

Diffusion-Controlled Fast Reactions

Diffusion-Controlled Rapid Reactions

Diffusion-Controlled Solid State Reactions. Andriy M. Gusak

Diffusion-controlled bimolecular reaction

Diffusion-controlled homogeneous reactions

Diffusion-controlled limit on reaction rate

Diffusion-controlled macromolecular reactions

Diffusion-controlled oxygen-reduction reaction

Diffusion-controlled polymer reactions

Diffusion-controlled polymer termination reactions

Diffusion-controlled reaction program

Diffusion-controlled reaction rate constant

Diffusion-controlled reactions

Diffusion-controlled reactions in solution, spin statistics

Diffusion-controlled reactions theory

Diffusion-controlled reactions, activation

Diffusion-controlled reactions, activation definition

Diffusion-controlled reactions. Black sphere model

Diffusion-enhanced reaction

Diffusion-limited reactions

Diffusion-limited reactions, Smoluchowski equation

Diffusion-limited surface reaction

Diffusion-reaction model

Diffusion-reaction problems potential effects

Diffusion-reaction theory

Diffusion/reaction mass transfer equation

Diffusion/reaction stoichiometry

Diffusion/reaction, flat interface

Diffusive transport/reaction regime

Diffusive/advective transport /reaction

Diffusive/advective transport /reaction equation

Diffusivity reactions

Diffusivity reactions

Dimensionless Form of the Generalized Mass Transfer Equation with Unsteady-State Convection, Diffusion, and Chemical Reaction

ENZDYN - Dynamic Diffusion and Enzymatic Reaction

ENZDYN - Dynamic Diffusion with Enzymatic Reaction

ENZSPLIT- Diffusion and Reaction Split Boundary Solution

Effective diffusivity model endothermic reactions

Effectiveness factor for first-order irreversible reaction-diffusion system

Equations of diffusion and reaction

Example Reaction and Diffusion

Experimental systems diffusion with first-order reaction

F Diffusion in a Sphere with Fast Reaction - Singular Perturbation Theory

Facilitated diffusion fast reaction limit

Film Diffusion and Chemical Reaction

First-order reaction, with diffusion

Flat plate catalyst pellets diffusion/reaction

Flow reaction, with axial diffusion

Front Propagation 4 Reaction-Diffusion Fronts

Gasification reactions diffusion control

General Reaction Kinetics Diffusion Resistance as the Rate-Determining Step

Heterogeneous reactions Diffusion

Heterogeneous reactions external diffusion effects

Heterogeneous reactions. Rates of diffusion

Hyperbolic reaction-diffusion equations

I Molecular diffusion and reaction rates

Infrared laser-enhanced diffusion cloud reactions

Intermacromolecular diffusion controlled reaction

Intraparticle diffusion reaction networks

Intraparticle diffusion reaction rate

Ionic reactions Diffusion control

Kinetic equations for reactions with diffusion

Kinetic equations of reactions without diffusion

Kinetic expressions derived for diffusion limited reactions

Kinetics of diffusion-controlled reactions

Laws reaction-diffusion equations

Ligand binding reaction diffusion processes

Linear reaction diffusion system, stationary solution

Mass diffusion with catalytic surface reaction

Mass diffusion with homogeneous reaction

Mechanisms of chemical ageing reaction-diffusion coupling

Modeling diffusion with reaction

Modeling diffusion without reaction

Models of reactions with diffusion and their analysis

Molecular Diffusion Plus Convection and Chemical Reaction

Molecular diffusion and reaction rate

Multi-Component Reaction-Diffusion Systems

Natural selection, reaction-diffusion process

Neutrality condition, reaction-diffusion process

Nonisothermal heterogeneous autocatalytic reactions-diffusion system

Nonisothermal reaction-diffusion systems

Nonlinear macrokinetics in a reaction-diffusion system

One-dimensional reaction-diffusion

Organic Reactions under Diffusion Control at Electrodes

Oscillating reactions diffusion

Oxygen diffusion/reaction coupling

Oxygen reduction reaction limiting diffusion current densities

Partially Diffusion Controlled Reactions

Partially Diffusion Controlled Reactions Neutral Species

Phenomenological Derivation of the Reaction-Diffusion Equation

Polymers reaction-diffusion system models

Population density, reaction-diffusion process

Pore Diffusion Resistance and Effective Reaction Rate

Pore Diffusion and Chemical Reaction

Preservatives reaction-diffusion interaction

Propagating reaction-diffusion fronts

Pseudo-diffusion reactions

Pulping reactions diffusion

Rate constant for) diffusion controlled reactions

Reaction Versus Diffusion

Reaction and Diffusion in a Catalyst Particle

Reaction and diffusion in the catalytic washcoat

Reaction diffusion control model

Reaction diffusion definition

Reaction diffusion estimation

Reaction diffusion from composition data

Reaction diffusion prediction

Reaction diffusion reactivity- ratios

Reaction diffusion solvent effects

Reaction diffusion substituent effects

Reaction diffusion system model

Reaction diffusion template effects

Reaction diffusion terminal model

Reaction diffusion, in biofilms

Reaction dynamics, ionic liquids diffusion

Reaction effective diffusivity

Reaction fast relative to the film diffusion time

Reaction kinetics diffusion equation

Reaction mechanism diffusion-controlled

Reaction parameters pore diffusion

Reaction rate pore diffusion effect

Reaction rates, diffusion controlled limit

Reaction space, proton diffusion between

Reaction space, proton diffusion between membranes

Reaction too slow to occur within the diffusion film

Reaction with Configurational Diffusion

Reaction with Diffusion in Complicated Pore Structures

Reaction with Pore Diffusion

Reaction, flow and diffusion

Reaction-Diffusion Fronts in Complex Structures

Reaction-Diffusion Fronts in General Heterogeneous Media

Reaction-Diffusion Fronts on Fractals

Reaction-Diffusion Systems with Two Intermediates

Reaction-convection-diffusion

Reaction-diffusion Dynamics inside Pores

Reaction-diffusion cells

Reaction-diffusion coupling

Reaction-diffusion degradation model

Reaction-diffusion equation

Reaction-diffusion equation , model

Reaction-diffusion equation , model system

Reaction-diffusion equation boundaries

Reaction-diffusion equation general form

Reaction-diffusion equation generalized

Reaction-diffusion equation with electric field

Reaction-diffusion fronts

Reaction-diffusion manifold

Reaction-diffusion manifold method

Reaction-diffusion master equation

Reaction-diffusion modeling

Reaction-diffusion pattern

Reaction-diffusion problem

Reaction-diffusion problem cylindrical pellet

Reaction-diffusion process

Reaction-diffusion process nonequilibrium thermodynamics

Reaction-diffusion regime

Reaction-diffusion regime mass transfer time

Reaction-diffusion sequence

Reaction-diffusion system apparatus

Reaction-diffusion systems

Reaction-diffusion systems generalized chemical kinetics

Reaction-diffusion systems with decaying catalyst

Reaction-diffusion systems, mesoscopic

Reaction-diffusion, pore water profile

Reaction-diffusion—transport system

Reaction/diffusion model mixing theory

Reactions and Anomalous Diffusion

Reactions and diffusion during cooling

Reactions in Highly-Rarefied and Diffusion Flames Reaction

Reactions rate-limited by a diffusion process

Reactions, noncatalytic diffusion models

Relaxation time diffusion reaction

Response Experiments for Reaction-Diffusion Systems

Response theory, reaction-diffusion process

Reversible diffusion-controlled reactions

Self-diffusion coefficients reactions

Separate determination of reaction-diffusion constants

Series Solutions for Diffusion with a Second Order Reaction

Simultaneous Diffusion and Chemical Reaction

Simultaneous diffusion and reaction

Slice Partially Diffusion Controlled Reactions

Smoluchowski equation, diffusion controlled reactions

Solid-state reactions diffusion

Solution of the reaction-diffusion equations

Sorption, diffusion, and catalytic reaction

Spatially distributed systems and reaction-diffusion modeling

Sphere diffusion with fast reaction

Spherical catalyst pellets diffusion/reaction

Statistical mechanics reaction-diffusion processes

Steady-State Diffusion with Homogeneous Chemical Reaction

Steady-state mass diffusion with catalytic surface reaction

Steady-state mass diffusion with homogeneous chemical reaction

Stochastic theory reaction diffusion system

Surface Reaction and Diffusion-Controlled Crack Growth

Surface diffusion and reactions

Surface diffusion/reaction coupling

The Fisher-Kolmogorov model of reactions with diffusion

The relative magnitude of chemical and diffusion reaction rates

Thermodynamic and Stochastic Theory of Reaction Diffusion Systems

Time-dependent diffusion coefficient electron-transfer reactions

Transport limitation by reaction-diffusion interaction

Turing Instabilities in Hyperbolic Reaction-Diffusion Equations

Turing Instabilities in Reaction-Diffusion Systems with Temporally or Spatially Varying Parameters

Turing Instabilities in Standard Reaction-Diffusion Systems

Turing Instability in the Standard Brusselator Reaction-Diffusion System

Two-Variable Reaction-Diffusion Systems

Unimolecular reactions diffusion theory

Unsteady State Diffusion with a First-Order Reaction

Variable Reaction-Diffusion Equations

Variable Reaction-Diffusion Systems

Waves Propagating Reaction-Diffusion Fronts

What is a Diffusion-Controlled Reaction

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