Fick s law

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. 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

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,... 

Molecular transport concerns the mass motion of molecules in condensed and gaseous phases. The mass motions are driven primarily by temperature. As time progresses, the initial mass motion results in concentration gradients. In the condensed phase, dow along concentration gradients is described by Fick s law. 

The limiting current density /) for the transport of species i to the reacting site is given from Fick s law by ... 

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... 

For an ion to move through the lattice, there must be an empty equivalent vacancy or interstitial site available, and it must possess sufficient energy to overcome the potential barrier between the two sites. Ionic conductivity, or the transport of charge by mobile ions, is a diffusion and activated process. From Fick s Law, J = —D dn/dx), for diffusion of a species in a concentration gradient, the diffusion coefficient D is given by... 

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

Assuming Dj is constant, and in particiilar that it is independent of Q, and that the concentrations in the fliiid phases are in equilibrium with the membrane. Fick s law may be written ... 

The dislocation cannot glide upwards by the shearing of atom planes - the atomic geometry is wrong - but the dislocation can move upwards if atoms at the bottom of the half-plane are able to diffuse away (Fig. 19.2). We have come across Fick s Law in which diffusion is driven by differences in concentration. A mechanical force can do exactly the same thing, and this is what leads to the diffusion of atoms away from the... 

Diffusion plays an important part in peak dispersion. It not only contributes to dispersion directly (i.e., longitudinal diffusion), but also plays a part in the dispersion that results from solute transfer between the two phases. Consider the situation depicted in Figure 4, where a sample of solute is introduced in plane (A), plane (A) having unit cros-sectional area. Solute will diffuse according to Fick s law in both directions ( x) and, at a point (x) from the sample point, according to Ficks law, the mass of solute transported across unit area in unit time (mx) will be given by... 

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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 kinetics of transport depends on the nature and concentration of the penetrant and on whether the plastic is in the glassy or rubbery state. The simplest situation is found when the penetrant is a gas and the polymer is above its glass transition. Under these conditions Fick s law, with a concentration independent diffusion coefficient, D, and Henry s law are obeyed. Differences in concentration, C, are related to the flux of matter passing through the unit area in unit time, Jx, and to the concentration gradient by,... 

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

A deep pool of ethanol is suddenly exposed to an atmosphere of pure carbon dioxide and unsteady state mass transfer, governed by Fick s Law, takes place for 100 s. What proportion of the absorbed carbon dioxide will have accumulated in the 1 mm layer closest to the surface in this period ... 

The case of a sphere of pure liquid of radius ro being suddenly immersed in a gas, when the whole of the mass transfer resistance lying within the liquid, is now considered. It will be assumed that mass transfer is governed by Fick s law and that angular symmetry exists. 

In a steady-state process, a gas is absorbed in a liquid with which it undergoes an irreversible reaction. The mass transfer process is governed by Fick s law, and the liquid is sufficiently deep for it to be regarded as effectively infinite in depth. On increasing the temperature, the concentration of reactant at the liquid surface CAi falls to 0.8 times its original value. The diffusivity is unchanged, but the reaction constant increases by a factor of 1.35. It is found that the mass transfer rate at the liquid surface falls to 0.83 times its original value. What is the order of the chemical reaction ... 

A pure gas is absorbed into a liquid with which it reacts. The concentration in the liquid is sufficiently low for the mass transfer to be covered by Fick s Law and the reaction is first-order with respect to the solute gas. It may be assumed that the film theory may be applied to the liquid and that the concentration of solute gas falls from the saturation value to zero across the film. The reaction is initially carried out at 293 K. By what factor will the mass transfer rate across the interface change, if the temperature is raised to 313 K ... 

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 solute diffuses from a liquid surface at which its molar concentration is C, into a liquid with which it reads. The mass transfer rate is given by Fick s law and the reaction is first order with respect to the solute, fn a steady-state process the diffusion rate falls at a depth L to one half the value at the interface. Obtain an expression for the concentration C of solute at a depth z from the surface in terms of the molecular diffusivity D and the reaction rate constant k. What is the molar flux at the surface ... 

The charge consumed by oxidation swelling under diffusion control, once the structure is relaxed, depends on the anodic potentials applied at each moment. The process can be quantified by Fick s law ... 

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. 

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