Laws of diffusion

Diffusion occurs down a concentration gradient as shown in Fig. 9. Fick demonstrated that the diffusive flux is proportional to the magnitude dc/dx of the concentration gradient of the diffusing solute 

The constant of proportionality is negative (because a positive value of dc/dx induces a diffusive flux towards negative x values) and its absolute value is called the diffusion coefficient, D 

Mobilities of various ions at infinite dilution in aqueous solutions at 25°C [17] 

Values of diffusion coefficients for several species in various media at 25°C [18] 

Known as Fick s first law, eqn. (23) is one of the most important equations in electrochemistry. 

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Fick s law of diffusion A law relating the rate of diffusion of a substance in a given direction to the gradient of its concentration. 

Graham s law of diffusion This law states that the rates at which two gases diffuse are inversely proportional to their densities, i.e. 

LID) see Ref. 139. In this last method, a small area, about 0.03 cm radius, is depleted by a laser beam, and the number of adatoms, N(t), that have diffused back is found as a function of time. From Pick s second law of diffusion ... 

We have shown that the contribution of the through micropores to diffusion in a porous catalyst may be increased substantially in the presence of a chemical reaction, but it must be emphasized that this is not a consequence of any real modification of the laws of diffusion in the micropores. 

Graham s Law of Diffusion. The rates at which gases diffuse under the same conditions of temperature and pressure are inverseiy proportionai to the square roots of their densities ... 

When the concentration of the solute is low, the measured diffusion profiles are predictable from Eick s second law of diffusion ... 

The rate of diffusion of the carbon atoms is given by Fick s laws of diffusion. In one dimension,... 

When a relatively slow catalytic reaction takes place in a stirred solution, the reactants are suppHed to the catalyst from the immediately neighboring solution so readily that virtually no concentration gradients exist. The intrinsic chemical kinetics determines the rate of the reaction. However, when the intrinsic rate of the reaction is very high and/or the transport of the reactant slow, as in a viscous polymer solution, the concentration gradients become significant, and the transport of reactants to the catalyst cannot keep the catalyst suppHed sufficientiy for the rate of the reaction to be that corresponding to the intrinsic chemical kinetics. Assume that the transport of the reactant in solution is described by Fick s law of diffusion with a diffusion coefficient D, and the intrinsic chemical kinetics is of the foUowing form... 

In this context, the relative terms far, short, small, and large can be defined as follows. Fick s second law of diffusion dictates that the distance, 5, that a species having a diffusion coefficient, D, may diffuse within a period of time, t, is given by (12) ... 

Diffusion-controlled mass transfer is assumed when the vapor or liquid flow conforms to Tick s second law of diffusion. This is stated in the unsteady-state-diffusion equation using mass-transfer notation as... 

Transport across tire direction of flow can be determined using Pick s hrst law of diffusion for dre flux of material in particles/cm sec in a steady, time-independent state... 

The protection potential can be evaluated kinetically for such cases [10,21]. It is assumed that the concentration of metal ions on the metal surface is Cq. The weight loss rate follows from the first law of diffusion ... 

If the PBR is less than unity, the oxide will be non-protective and oxidation will follow a linear rate law, governed by surface reaction kinetics. However, if the PBR is greater than unity, then a protective oxide scale may form and oxidation will follow a reaction rate law governed by the speed of transport of metal or environmental species through the scale. Then the degree of conversion of metal to oxide will be dependent upon the time for which the reaction is allowed to proceed. For a diffusion-controlled process, integration of Pick s First Law of Diffusion with respect to time yields the classic Tammann relationship commonly referred to as the Parabolic Rate Law ... 

The Dunwald—Wagner equation, based on the application of Ficks second law of diffusion into or out of a sphere (radius r) [477], can be written... 

Derive the Cottrell equation by combining Fick s first law of diffusion with the tune-dependent change of the concentration gradient during a potential-step experiment. 

If the rate of a reaction is governed by the encounter frequency, it is said to be diffusion-controlled. This frequency imposes an upper limit on the rate of reaction that can be evaluated by the use of Fick s laws of diffusion. The mathematical expression of this phenomenon was first presented by von Smoluchowski.2 We shall adopt a simple approach,3,4 although more rigorous derivations have been given.5... 

The quantity of solute B crossing a plane of area A in unit time defines the flux. It is symbolized by J, and is a vector with units of molecules per second. Fick s first law of diffusion states that the flux is directly proportional to the distance gradient of the concentration. The flux is negative because the flow occurs in a direction so as to offset the gradient ... 

Fick s Law of diffusion is normally expressed in molar units or ... 

It may be noted that equation 10.86 is identical to equation 10.30. (Stefan s Law) and. Stefan s law can therefore also be derived from Maxwell s Law of Diffusion. 

It is shown in Chapter 10, from Fick s Law of diffusion, that the rate of diffusion of a constituent A in a mixture is proportional to its concentration gradient. 

A crystal is suspended in fresh solvent and 5% of the crystal dissolves in 300 s. How long will it take before 10% of the crystal has dissolved Assume that the solvent can be regarded as infinite in extent, that the mass transfer in the solvent is governed by Fick s second law of diffusion and may be represented as a unidirectional process, and that changes in the surface area of the crystal may be neglected. Start your... 

On the assumption that the oxygen transfer can be represented by a surface renewal model, obtain the appropriate equation for mass transfer by starting with Tick s second law of diffusion and calculate ... 

If transport across this film is controlled by diffusion then from Pick s Second Law of Diffusion,... 

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