Law of Fick

Exactly the same mechanism determines diffusion processes. Using the first law of Fick we have a diffusion current. 

This constant diffusion flow according to the first law of Fick can be considered to be analogous to the irreversible flow given by Eq. (41). In Eq. (52) z is a function of time alone. In the case that z depends on space in the sense that the velocity of the... 

The laws of Fick are concerned with the concentration and the change of concentration with respect to space and time. In this paper we are interested in the number of molecular displacements. If we calculate the change of concentration we must use the laws of Fide. The diffusion constant in all cases is given by... 

In this section we have presented the first example of two-point boundary value problems that occur in chemical/biological engineering. The axial dispersion model for tubular reactors is a generalization of the plug flow model for tubular reactors which removes some of the limiting assumptions of plug flow. Our model includes additional axial diffusion terms that are based on the simple physics laws of Fick for mass and of Fourier for heat dispersion. 

According to the first law of Fick about a uni-dimentional flow, the mass dm transferred through an area of cross section A for time dr is proportional to the concentration gradient of the substance across film thickness dC/dh... 

A commonly used approach to simplify the mathematical description of diffusion is to introduce some kind of effective diffusion coefficients (Dej) being formally related to one corresponding concentration gradient only, i.e. the law of Fick... 

In work on the three-component diffusion theory, the volume fractions Y[= cv) are found to be the concentration units in which an explicit solution of the problem stated above, i.e. a determination of the friction coefficients from diffusion studies, is possible. Hence, there is a theoretical interest in seeing the analogous treatment for two components. Applying Eq. (4), the flow (8) provides the second law of Fick... 

Diffusion currents are the electrolytic currents controlled by the diffusion rate of the depolarizer from the bulk solution to the electrode surface and are caused by the concentration gradient due to the depletion of the active substance in the close vicinity of the electrode surface. Consequently, the rate of the electrode reaction must be high enough to obtain currents that are controlled by diffusion only. Therefore, the first and second laws of Fick may be applied, and taking into account the initial and boundary concentration conditions the final Ilkovic equation may be obtained ... 

For the first law of Fick, the application of relation [5.8] gives, by clarifying the gradient and the components of flux, and by supposing the coefficient of diffusion independent of the direction (isotropic diffusion)... 

Consider two cylinders having the same axis and the same height, with radii r and r-g (Figure 5.13). A species diffuses through the annulus limited by these two cyhnders under the action of a gradient of eoncentration imposed by the concentrations and Cg at the two cylindrical surfaces. These concentrations remain constant. We apply the steady state condition to the law of Fick taken in form [5.22], which leads to... 

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. 

Equimolar Counterdiffusion in Binary Cases. If the flux of A is balanced by an equal flux of B in the opposite direction (frequently encountered in binary distillation columns), there is no net flow through the film and like is directly given by Fick s law. In an ideal gas, where the diffusivity can be shown to be independent of concentration, integration of Fick s law leads to a linear concentration profile through the film and to the following expression where (P/RT)y is substituted for... 

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

A few simple equations describe most appHcations of barrier polymers. Equation 1 is an adaptation for films of Fick s First Law. 

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) ... 

The phenomenological aspects of diffusional mass transfer in adsorption systems can be described in terms of Fick s 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 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... 

Diffusion rates for liquids in an elastomer are easily measured by absorption (immersion) testing, a simple process as indicated in Figure 23.6. An initially weighed immersed sheet sample of elastomer is removed from the liquid periodically, rapidly dabbed with tissue paper, reweighed, and replaced. A plot of mass increase versus root time is drawn (also see Figure 23.6), root time being chosen due to the form of appropriate solutions of Fick s laws. 

A solution of Fick s 2nd Law often used for absorption testing is... 

Figure 4 Schematic representation of a small section of a diffusion profile illustrating the application of Fick s law to determine the concentration change in the central volume element as a result of the fluxes (F) across the two planes at L and R (see text for details).

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