Diffusion absolute speed

For diffusion that we will assume in pseudo-steady state conditions, the absolute speed, which lepiesents the flow is given as ... 

For steady state (or close to steady state) diffusion, we can provide an expression for the absolute speed, which is the flow rate ... 

In a sedimentation equilibrium experiment the cell is rotated at a relatively low speed (typically 5000-10000 rpm) until an equilibrium is attained whereby the centrifugal force just balances the tendency of the molecules to diffuse back against the concentration gradient developed. Measurements are made of the equilibrium concentration profiles for a series of solutions with different initial polymer concentrations so that the results can be extrapolated to c = 0. A rigorous thermodynamic treatment is possible and enables absolute values ot Mwand Mz, to be determined. The principal restriction to the use of sedimentation equilibrium measurements is the long time required to reach equilibrium, since this is at least a few hours and more usually is a few days. 

Undeniably, the speed vector, by its size and directional character, masks the effect of small displacements of the particle. Another difference comes from the different definition of the diffusion coefficient, which, in the case of the property transport, is attached to a concentration gradient of the property it means that there is a difference in speed between the mobile species of the medium. A second difference comes from the dimensional point of view because the property concentration is dimensional. When both equations are used in the investigation of a process, it is absolutely necessary to transform them into dimensionless forms [4.6, 4.7, 4.37, 4.44]. 

The time-dependent temperature distribution in a transient experiment is governed by Eq. 4, and usually the related parameter, thermal diffusivity. is obtained. However, under certain circumstanees the solution to the heat equation contains the thermal conductivity as well as the thermal diffusivity, and by choosing a suitable method the diffusivity can be eliminated from the answer. The more important methods are the line and plane source heater methods and arc described below. These arc not Standard methods, but they can be used where speed is more imp .>rtant than absolute accuracy, to give a conductivity value more quickly than the Standard methods. They can also be used to compare a range of materials. 

O Equation (51.9) shows a to be a simple function of the absolute (molar) mass difference, (M — M). This is in contrast to most methods of isotope separation where a depends on the ratio of masses, or the ratio raised to some power. Centrifuge a values for UFg/ UFg at several peripheral speeds are shown in Tables 51.5 and 51.6. The values are far above those for gaseous diffusion. 

Displacement of atoms within solid phase. The atoms or ions must move for chemical reaction or structural changes of sohds. This phenomenon may have a variety of mechanisms. One mechanism among them is that an atom moves from normal lattice sites to ordered vacancies. As mentioned above, at all temperatm es except for the absolute zero degrees, there are always all kinds of vacancies in each crystal. In such cases, the diffusion speed of atoms is related with the concentration of the vacancy and the difficulty in the movement of atoms. Atom movement in a random direction is equivalent to the opposite movement of the vacancy. Therefore, in similar status, it can be considered as diffusion of vacancy. 

Changes in gas composition and other conditions have different impact on reduction rate of catalysts with different structures. When H2 content is increased, the exchange intensity of the diffusion in pores is increased. When a molecule moves, every component in the mixed gas independently diffuses in the speed of inverse square root proportion to the molecular weight. Therefore, under the same conditions, diffusion of H2 molecules in gas mixture (H2 and H2O) in the pores is faster than the diffusion of gaseous H2O in the opposite direction. As the result, the absolute pressure in pore rises continuously until the partial pressure gradient of H2 and H2O reaches the value of /Mh o/Mh = 300%). The diffusion equations for the two gas flows (H2 and H2O) can be established at this time, while the diffusion gradient in the pores is determined by the slowest step i.e., the diffusion of product H2O. 

From the kinetic theory of gases, we know that the mean speed of molecules is proportional to the square root of its absolute temperature. Millions of intermolecular collisions occur per second and are proportional to the concentration of molecules. In a gas of nonuniform composition, this random interaction results in molecular diffusion until the composition is uniform throughout. Similar diffusive transport processes occur in liquids and solids as well. Diffusion is thus one aspect of the transport pillar and is the subject of this handbook. It comprises rates of chemical transport within and between media. We assert that this topic has been the poor relation in environmental science. 

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