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The Diffusion

4 n 2) depending on whieh one of the two is the prevalent one, aeeording to the dimensional distribution of the dispersed particles. [Pg.61]


A diffusion mechanism is also used in dialysis as a means of separating colloids from crystalloids. The rate of diffusion of molecules in gels is practically the same as in water, indicating the continuous nature of the aqueous phase. The diffusion of gases into a stream of vapour is of considerable importance in diffusion pumps. [Pg.137]

Diffusivity measures the tendency for a concentration gradient to dissipate to form a molar flux. The proportionality constant between the flux and the potential is called the diffusivity and is expressed in m /s. If a binary mixture of components A and B is considered, the molar flux of component A with respect to a reference plane through which the exchange is equimolar, is expressed as a function of the diffusivity and of the concentration gradient with respect to aji axis Ox perpendicular to the reference plane by the fpllqvving relatipn 6 /... [Pg.136]

The value of coefficient depends on the composition. As the mole fraction of component A approaches 0, approaches ZJ g the diffusion coefficient of component A in the solvent B at infinite dilution. The coefficient Z g can be estimated by the Wilke and Chang (1955) method ... [Pg.136]

First, the plane n(x,y) coincides with the diffuser mean plane of G, IT (x ,y ). When G is translated a distance x and rotated an angle Aa respect to the y axis of Il (x ,y ), we ob-a null movement of the speckle pattern on a circumference of center C and radius R ... [Pg.657]

A CCD camera is located in the II(t, ) plane. It records the first speekle pattern and proeesses it digitally. After this, the diffuser G is rotated and trtinslated (Figure I). [Pg.658]

Therefore, the ultrasonic testing method in the diffusion joint of the dissimiler materials shall considered the influence of the interference with the reflective wave. [Pg.839]

On the other hand, the reliability of the product improves, too, if each state of the plasticity deformation, the creep deformation, and the diffusion joint in the solid phase diffusion bonding as the bonding process, is accurately understood, and the bonding process is controlled properly. [Pg.849]

There is also a traffic between the surface region and the adjacent layers of liquid. For most liquids, diffusion coefficients at room temperature are on the order of 10 cm /sec, and the diffusion coefficient is related to the time r for a net displacement jc by an equation due to Einstein ... [Pg.57]

Here (D is the diffusion coefficient and C is the concentration in the general bulk solution. For initial rates C can be neglected in comparison to C/ so that from Eqs. IV-59 and IV-60 we have... [Pg.150]

The quantity 1 /k is thus the distance at which the potential has reached the 1 je fraction of its value at the surface and coincides with the center of action of the space charge. The plane at a = l//c is therefore taken as the effective thickness of the diffuse double layer. As an example, 1/x = 30 A in the case of 0.01 M uni-univalent electrolyte at 25°C. [Pg.173]

By analogy with the Helmholtz condenser formula, for small potentials the diffuse double layer can be likened to an electrical condenser of plate distance /k. For larger yo values, however, a increases more than linearly with o, and the capacity of the double layer also begins to increase. [Pg.173]

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. [Pg.179]

In the case of a charged particle, the total charge is not known, but if the diffuse double layer up to the plane of shear may be regarded as the equivalent of a parallel-plate condenser, one may write... [Pg.184]

The effect known either as electroosmosis or electroendosmosis is a complement to that of electrophoresis. In the latter case, when a field F is applied, the surface or particle is mobile and moves relative to the solvent, which is fixed (in laboratory coordinates). If, however, the surface is fixed, it is the mobile diffuse layer that moves under an applied field, carrying solution with it. If one has a tube of radius r whose walls possess a certain potential and charge density, then Eqs. V-35 and V-36 again apply, with v now being the velocity of the diffuse layer. For water at 25°C, a field of about 1500 V/cm is needed to produce a velocity of 1 cm/sec if f is 100 mV (see Problem V-14). [Pg.185]

Derive the general equation for the differential capacity of the diffuse double layer from the Gouy-Chapman equations. Make a plot of surface charge density tr versus this capacity. Show under what conditions your expressions reduce to the simple Helmholtz formula of Eq. V-17. [Pg.215]

The interaction of an electrolyte with an adsorbent may take one of several forms. Several of these are discussed, albeit briefly, in what follows. The electrolyte may be adsorbed in toto, in which case the situation is similar to that for molecular adsorption. It is more often true, however, that ions of one sign are held more strongly, with those of the opposite sign forming a diffuse or secondary layer. The surface may be polar, with a potential l/, so that primary adsorption can be treated in terms of the Stem model (Section V-3), or the adsorption of interest may involve exchange of ions in the diffuse layer. [Pg.412]

Reference 115 gives the diffusion coefficient of DTAB (dodecyltrimethylammo-nium bromide) as 1.07 x 10" cm /sec. Estimate the micelle radius (use the Einstein equation relating diffusion coefficient and friction factor and the Stokes equation for the friction factor of a sphere) and compare with the value given in the reference. Estimate also the number of monomer units in the micelle. Assume 25°C. [Pg.490]

The repulsion between oil droplets will be more effective in preventing flocculation Ae greater the thickness of the diffuse layer and the greater the value of 0. the surface potential. These two quantities depend oppositely on the electrolyte concentration, however. The total surface potential should increase with electrolyte concentration, since the absolute excess of anions over cations in the oil phase should increase. On the other hand, the half-thickness of the double layer decreases with increasing electrolyte concentration. The plot of emulsion stability versus electrolyte concentration may thus go through a maximum. [Pg.508]

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. [Pg.589]

The rate of dissolving of a solid is determined by the rate of diffusion through a boundary layer of solution. Derive the equation for the net rate of dissolving. Take Co to be the saturation concentration and rf to be the effective thickness of the diffusion layer denote diffusion coefficient by . [Pg.592]

Figure A2.4.9. Components of the Galvani potential differenee at a metal-solution interfaee. From [16], A2.4.5.2 INTERFACIAL THERMODYNAMICS OF THE DIFFUSE LAYER... Figure A2.4.9. Components of the Galvani potential differenee at a metal-solution interfaee. From [16], A2.4.5.2 INTERFACIAL THERMODYNAMICS OF THE DIFFUSE LAYER...
Figure A3.6.13. Density dependence of die photolytic cage effect of iodine in compressed liquid n-pentane (circles), n-hexane (triangles), and n-heptane (squares) [38], The solid curves represent calculations using the diffusion model [37], the dotted and dashed curves are from static caging models using Camahan-Starling packing fractions and calculated radial distribution fiinctions, respectively [38],... Figure A3.6.13. Density dependence of die photolytic cage effect of iodine in compressed liquid n-pentane (circles), n-hexane (triangles), and n-heptane (squares) [38], The solid curves represent calculations using the diffusion model [37], the dotted and dashed curves are from static caging models using Camahan-Starling packing fractions and calculated radial distribution fiinctions, respectively [38],...
Kramers H A 1940 Brownian motion in a field of force and the diffusion model of chemical reactions Physica 7 284-304... [Pg.865]


See other pages where The Diffusion is mentioned: [Pg.150]    [Pg.150]    [Pg.204]    [Pg.109]    [Pg.84]    [Pg.833]    [Pg.834]    [Pg.854]    [Pg.175]    [Pg.176]    [Pg.176]    [Pg.178]    [Pg.287]    [Pg.333]    [Pg.400]    [Pg.519]    [Pg.580]    [Pg.711]    [Pg.359]    [Pg.689]    [Pg.721]    [Pg.846]    [Pg.1109]    [Pg.1529]    [Pg.1685]    [Pg.1837]    [Pg.1924]   


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A Multicomponent Diffusion in the Presence of Reaction

A comparison of the phenomenological diffusion coefficients

A critique of the diffusion equation and molecular pair treatments

An Expression for the Diffusion Potential

An Often-Used Device for Solving Electrochemical Diffusion Problems The Laplace Transformation

An example of a convective-diffusion system the rotating disc electrode

Analysis of Diffusion Reactions in the Solid State

Analysis of Diffusion in the A, B, and C Regimes

Analytical Solutions of the diffusion equation

Analytical solution of the grain boundary diffusion problem

Application to the diffusion of salts in solution

Approximate neglect of pressure variations in the intermediate diffusion range

Approximate value of the diffusivity

Approximation of the Diffusive Transport Terms

Arrhenius plots of the diffusion coefficients

Atomic migration and the diffusion coefficient

B Diffusion of Gas Through the Lamellae

Bounds for the diffusion constant

Brownian Motion, Levy Flight, and the Diffusion Equations

C Quantitation of the Transferred Product and Diffusion

Calculation of the Diffusion Potential

Capacity of the diffuse electric double layer

Change of Entropy and the Diffusion Process

Characteristic time of the diffusion

Choice of the Diffusion Interaction Mode

Concentration dependence of the diffusion coefficient

Conclusions on the Diffusion Process

Conductivity, Transference Numbers, and the Diffusion Potential

Control Volume Alternative to the Theory of Diffusive Burning

Controlling Molecular Diffusion in the Fluidic Lipid Bilayer

Cumulative Uptake by Diffusion for the Semi-Infinite Domain

Current, Poor Oxygen Diffusivity in the CCL

Determination of the diffusion coefficient

Different Forms of the Diffusion Equation

Diffuse Part of the Double Layer

Diffuse Reflectance Spectroscopy (DRS) in the Visible UV Region

Diffuse layer at the interface

Diffuse part of the edl

Diffusion Boundary Layer Near the Surface of a Drop (Bubble)

Diffusion Boundary Layer Near the Surface of a Particle

Diffusion Coefficients of Both Oxygen and Any Ions in the Sensing Material Should Be Minimized

Diffusion Fluxes and the Sherwood Number

Diffusion Motion of the Rouse Chain

Diffusion Obstacles Inside the ZSM-5 Framework by Pulsed-Field Gradient NMR

Diffusion Parameters of the System

Diffusion Path Stochastization in the Two-Phase Region

Diffusion The movement of a substance

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 coefficient in the

Diffusion coefficient of the cation

Diffusion coefficient of the charge carriers

Diffusion constant, dependence on the

Diffusion in polymers - The classical approach

Diffusion in polymers - The computational approach

Diffusion in the High-Field Regime

Diffusion in the Region of a Critical Point

Diffusion in the Stationary Phase

Diffusion in the extracellular space

Diffusion in the matrix

Diffusion on the Surface of a Micelle

Diffusion processes in the photo-oxidation of polymers

Diffusion through the membrane

Diffusion through the product

Diffusion through the product layer

Diffusion within the catalyst pellet

Diffusivities from the

Diffusivity of the Oxide Ion in Perovskite Oxides

Diffusivity of the reactant molecule

Diffusivity, Mobility and Conductivity The Nernst-Einstein Relation

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

Does Helium Diffuse Through the Upper Crust

Effect of sucrose on the bimolecular diffusion constant

Effects of Rotational Diffusion on Fluorescence Anisotropies The Perrin Equation

Effects of intraparticle diffusion on the experimental parameters

Elimination of diffusion contribution to the overpotential in chronoamperometry and chronopotentiometry

Elimination of diffusion contributions to the overpotential by impedance spectroscopy

Equations for the diffusive flux (Ficks law)

Equimolar Counterdiffusion and Diffusion through a Stagnant Film The Log-Mean Concentration Difference

Estimate the Diffusivity of Hydrogen

Estimating the Diffusion Depth and Time to Approach Steady State

Estimation of the diffusion coefficient

Exchange is controlled by bulk diffusion into the support

Experimental study of the rotational diffusion constant

Experiments for the Direct Observation of Proton Spin-Diffusion

Factors Affecting the Diffusion of Proteins

Fick Diffusion Coefficients for the System Acetone-Benzene-Methanol

Ficks Laws and the Diffusion Equations

Flow and Diffusion in the Mobile Phase

Flow and diffusion in the reactor

From the diffusion equation to escape and survival probabilities

General Reaction Kinetics Diffusion Resistance as the Rate-Determining Step

Generalization of the Nonlinear Phase Diffusion Equation

Gouy-Chapman theory of the diffuse electrical double-layer

How Can the Diffusion Coefficient Be Related to Molecular Quantities

How does one obtain a quick estimate of the distance moved by diffusing atoms

Hydrodynamic repulsion and the diffusion equation

Intrinsic Diffusion Coefficient The Kirkendall Effect

Laminar Flow and Diffusion in a Pipe The Graetz Problem for Mass Transfer

Lead users in the diffusion process

Limiting Diffusion Resistance of the Disperse Phase

Long-range transfer and the diffusion equation

Luminosity evolution and the diffuse background

Mass Transport in Binary Mixtures and the Diffusion Equation

Metals in the Universe and diffuse background radiation

Modelling the diffusion coefficient D for all solvents simultaneously

Modelling the diffusion coefficient D for solvents other than water

Modelling the diffusion coefficient D for water as solvent

Molecular weight of the diffusant

No Peaks The Interpretation of Diffuse Scattering

Non-equilibrium distribution of adsorbing ions along the diffuse layer

Nucleation in the Diffusion Zone of a Ternary System

Numerical Solution of the Lumped Pore Diffusion Model

Numerical Solution of the diffusion equation

On the Diffusivity of Vitamin E in UHMWPE

On the Dispersion of a Solute by Diffusion, Convection, and Exchange between Phases

Origin of the diffusion in a solid

Oxygen Transport Loss in the Gas Diffusion Layer

Parameters in the Atmospheric Diffusion Equation

Passive diffusion through the membrane

Perfectly mobile equilibria the mean diffusion coefficient

Phenomenological Derivation of the Reaction-Diffusion Equation

Physical derivation of the multicomponent diffusion equation

Plasticizer diffusion rate and the methods of study

Poisson-Boltzmann theory of the diffuse double layer

Polymer Blend and Diffusion of the Synthetic Macromolecules

Potential in the diffuse layer

RET in the Rapid-Diffusion Limit

Radial diffusion in the sphere

Reaction and diffusion in the catalytic washcoat

Reaction fast relative to the film diffusion time

Reaction too slow to occur within the diffusion film

Reconciliation of Apparent Contradictions in the Diffusion Model for Water Radiolysis According to Schwarz

Reducing the Eddy Diffusion Term

Reducing the Effect of Longitudinal Diffusion

Rotational Diffusion of Liquid Crystals in the Nematic Phase

Scaling and Convergence to the Diffusion Process

Scaling of the Diffusion Equation

Solution of the Atmospheric Diffusion Equation for an Instantaneous Source

Solution of the Multicomponent Diffusion Equations

Solution of the Transient Gas-Phase Diffusion Problem Equations

Solution of the Transient Gas-Phase Diffusion Problem Equations (11.4) to

Solution of the diffusion equation when Le

Solution of the reaction-diffusion equations

Solution to the Diffusion Equation with a Step in Concentration

Solution-Diffusion Model for the Transport of Binary Gas Mixtures

Solutions of the Radial Diffusion Equation

Solutions of the Steady-State Atmospheric Diffusion Equation

Solutions of the diffusion equation

Solutions of the diffusion equation parallel flux

Solutions to the Diffusion Equation

Solutions to the diffusion equation with no solute elimination or generation

Solutions to the diffusion equation with solute binding and elimination

Solving the Diffusion Equations

Some Cases for which there is no Solution of the Diffusion Equation

Some Properties of the Nonlinear Phase Diffusion Equation

Some simple solutions to the diffusion equation at steady state

Techniques for Measurement of the Diffusion Coefficient

Temperature Variation of the Diffusion Coefficient

Temperature dependence of the diffusion constant

The Arnold diffusion cell

The Binary Diffusion Equations

The Brusselator with diffusion

The Combined Slowing-down and Diffusion Equation

The Concentration of Reactants in Each Phase is Affected by Diffusion

The Concept of Augmented Diffusivity by Convection

The Convective Diffusion Equation

The Diffuse Double Layer

The Diffusion Categories

The Diffusion Domain Approach

The Diffusion Layer

The Diffusion Layer Model

The Diffusion Model and Dispersion in a Straight Tube

The Diffusion Process

The Diffusion Quantum Monte Carlo Method

The Diffusion Spectrum

The Diffusion Theory of Adhesion

The Diffusive Flux Vectors for a Mixture of Chemical Species

The Diffusivity Tensor for Steady-State Shear and Elongational Flows

The Discretized Diffusion Equation

The Effect of B-Site Cation on Oxygen Diffusivity

The Effect of Diffusion Limitation

The Effective Diffusion Coefficient

The Effective Diffusivity—Closing Remarks

The Fisher-Kolmogorov model of reactions with diffusion

The Free Energy of a Diffuse Double Layer

The Gas-Diffusion Layer

The General Equations of Diffusion and Flow in a Straight Tube

The Gross View of Nonsteady-State Diffusion

The Implications of Using Diffusive or Convective Control

The Influence of Impurity upon Diffusion Constants

The Lagrangian density for diffusion

The Longitudinal Diffusion, or (B), Term

The Maxwell-Stefan theory for zeolite diffusion

The Measurement of Solute Diffusivity and Molecular Weight

The Multicomponent Diffusion Equations

The Nemst diffusion layer

The Nernst diffusion layer and dimensionless variables

The Oregonator with diffusion

The Oxygen Tracer Diffusion Coefficient

The Phenomena of Diffusion

The Phenomenon of Hydrodynamic Diffusion

The Problem of Diffusion

The Rate Equation for Film Diffusion

The Relation to Diffusion and Brownian Motion

The Role of Molecular Diffusivity

The Rotational Diffusion Model

The Self-diffusion Coefficient of Xe in Elastomers

The Simplest Classical Solution for Diffusion in a Plate

The Solution and Diffusion of Gases in Elastic Polymers

The Solution-Diffusion Model

The Time-Dependent Diffusion Equation

The Translational Diffusion Coefficient

The Transport Diffusivities

The Two Bulb Diffusion Cell

The action of diffusion

The cellular origins of relaxation and diffusion contrast

The chemical diffusion coefficient and its derivation for special cases

The combination of external mass transfer and internal diffusion

The differential equations of diffusion

The diffuse field

The diffusion and desorption processes

The diffusion battery method for aerosol particle size determination

The diffusion coefficient

The diffusion coefficient varies with time

The diffusion couple technique in phase diagram determination

The diffusion equation

The diffusion equation assumptions and applications

The diffusion of an isolated pair

The diffusion of oxygen in polymers

The diffusion phenomenon

The diffusion tensor

The effective diffusivity

The extended ZGB-model incorporating diffusion and desorption processes

The inelastic diffusion length

The international diffusion of innovation

The measurement of diffusion coefficients in simple oxides

The propagator for one-dimensional diffusion

The relationship between D and diffusion distance

The relationship between diffusion constant and specific surface

The relative magnitude of chemical and diffusion reaction rates

The role of vacancies in surface diffusion

The significance of diffusion coefficients

The spatial diffusion of innovations

The theory of convective diffusion

The time dependence of diffusion

Thermal diffusivity in the gas phase

Thermal diffusivity of the condensed

Thermal diffusivity of the condensed phase

Thickness of the Nernst diffusion layer

Thickness of the diffusion boundary layer

Thickness of the diffusion layer

Timescale of the diffusion

Towards the diffusion equation analysis

Transition from the Diffusion to Inertial Ranges

Transport Limitations and the Thiele Diffusion Modulus

Turing Instability in the Standard Brusselator Reaction-Diffusion System

Two Bulb Diffusion Cell A Test of the Effective Diffusivity

Using the Diffusion Coefficient

Variation of the sample profile along its travel convective and diffusive phenomena

Variational Interpretation of the Diffusion Equation

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