Pick’s law

The second of Pick s laws expresses the change in concentration of a species at a point as a fimction of time due to difflision (figure B 1.28.2). Plence, the one-dimensional variation in concentration of material within a volume element bounded by two planes v and x + dx during a time interval dt is expressed by dc fx.,t)ldt) = D... 

Figure Bl.28.2. Pick s laws of dififiision. (a) Pick s first law, (b) Pick s second law.

Under diffusion controlled conditions tire reaction rate depends, tlien, only on tire supply of 02(g) to the surface which is detennined by Pick s law ... 

The driving force in diffusion involves differences in the concentration of the diffusing substance. The molecular diffusion of a gas into a hquid is dependent on the characteristics of the gas and the hquid, the temperature of the hquid, the concentration deficit, the gas to hquid contact area, and the period of contact. Diffusion may be expressed by Pick s law (13,14) ... 

Physically, diffusion occurs because atoms, even in a solid, are able to move - to jump from one atomic site to another. Figure 18.4 shows a solid in which there is a concentration gradient of black atoms there are more to the left of the broken line than there are to the right. If atoms jump across the broken line at random, then there will be a net flux of black atoms to the right (simply because there are more on the left to jump), and, of course, a net flux of white atoms to the left. Pick s Law describes this. It is derived in the following way. 

Either the and the two e s diffuse outward through the film to meet the 0 at the outer surface, or the oxygen diffuses inwards (with two electron holes) to meet the at the inner surface. The concentration gradient of oxygen is simply the concentration in the gas, c, divided by the film thickness, x and the rate of growth of the film dx/dt is obviously proportional to the flux of atoms diffusing through the film. So, from Pick s Law (eqn. (18.1)) ... 

The plot in Fig. 13 shows the bleed emissions that were measured after a 24 hour soak. Two eanisters were tested, one loaded with a wood granular carbon with a mean particle diameter of 1.27 mm, the second with a wood pellet carbon with a mean particle diameter of 2.10 mm. Both carbon samples had equal BWC of 11.4 g/lOOml. Although both earbons had the same BWC, the larger pellet earbon had lower bleed emissions. These diffusion results are expected in light of Pick s Law. 

Dispersion The movement of aggregates of molecules under the influence of a gradient of concentration, temperature, etc. The effect is represented by Pick s law with a dispersion coefficient substituted for molecular diffusion coefficient. The rate of transfer = -Dg(dC/3z). 

Consider a binary mixture consisting of components A and B. If component A moves with a velocity of v and the component B with a velocity of v there is a force against the motion of component A that is proportional to the velocity difference (5 a. Vfj). This is the physical content of Pick s law in the steady-state condition. 

In a steady-state case at constant pressure [p Pa+ Pb constant). Pick s law (Eq. (4.273)) is valid ... 

Chemicals have to pass through either the skin or mucous membranes lining the respiratory airways and gastrointestinal tract to enter the circulation and reach their site of action. This process is called absorption. Different mechanisms of entry into the body also greatly affect the absorption of a compound. Passive diffusion is the most important transfer mechanism. According to Pick s law, diffusion velocity v depends on the diffusion constant (D), the surface area of the membrane (A), concentration difference across the membrane (Ac), and thickness of the membrane (L)... 

Pick s law States that the molecular diffusion of water vapor in a gas without appreciable displacement of the gas is analogous to the conduction of heat, and is governed by a similar type of law. 

Rabt Ratio of transport rate by thermal diffusion to that by Pick s law ... 

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 governed by Pick 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. Obtain an expression for the mass transfer rate across the gas-liquid interface in terms of the molecular diffusivity, 1), the first order reaction rate constant k. the film thickness L and the concentration Cas of solute in a saturated solution. The reaction is initially carried our at 293 K. By what factor will the mass transfer rate across the interface change, if the temperature is raised to 313 K7... 

This section derives a simple version of the convective diffusion equation, applicable to tubular reactors with a one-dimensional velocity profile V (r). The starting point is Equation (1.4) applied to the differential volume element shown in Figure 8.9. The volume element is located at point (r, z) and is in the shape of a ring. Note that 0-dependence is ignored so that the results will not be applicable to systems with significant natural convection. Also, convection due to is neglected. Component A is transported by radial and axial diffusion and by axial convection. The diffusive flux is governed by Pick s law. 

Diffusion of the fluid into the bulk. Rates of diffusion are governed by Pick s laws, which involve concentration gradient and are quantified by the diffusion coefficient D these are differential equations that can be integrated to meet many kinds of boundary conditions applying to different diffusive processes. ... 

The relationship between the diffusional flux, i.e., the molar flow rate per unit area, and concentration gradient was first postulated by Pick [116], based upon analogy to heat conduction Fourier [121] and electrical conduction (Ohm), and later extended using a number of different approaches, including irreversible thermodynamics [92] and kinetic theory [162], Pick s law states that the diffusion flux is proportional to the concentration gradient through... 

We are now ready to consider some soUd state reactions that relate more directly to the real world. These include the tarnishing reaction and Pick s Laws of Diffusion. Both of these scientific areas have been rigorously studied because of their importcmce in revealing how diffusion mechanisms are related to everyday solid state reactions which occur on a daily basis. 

GP 9] [R 16[ The extent of external transport limits was made in an approximate manner as for the internal transport limits (see above), as literature data on heat and mass transfer coefficients at low Peclet numbers are lacking [78]. Using a Pick s law analysis, negligible concentration differences from the bulk to the catalyst sur-... 

In accordance with Pick s Law, diffusive flow always occurs in the direction of decreasing concentration and at a rate, which is proportional to the magnitude of the concentration gradient. Under true conditions of molecular diffusion, the constant of proportionality is equal to the molecular diffusivity of the component i in the system, D, (m /s). For other cases, such as diffusion in porous matrices and for turbulent diffusion applications, an effective diffusivity value is used, which must be determined experimentally. 

Each film is in stagnant or laminar flow, such that mass transfer across the films is by a process of molecular diffusion and can therefore be described by Pick s Law. 

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