Molecular diffusivity at different

Gases diffuse at different rates. If one piece of cotton wool is soaked in concentrated ammonia solution and another is soaked in concentrated hydrochloric acid and these are put at opposite ends of a dry glass tube, then after a few minutes a white cloud of ammonium chloride appears (Figure 1.14). This shows the position at which the two gases meet and react. The white cloud forms in the position shown because the ammonia particles are lighter and have a smaller relative molecular mass (Chapter 4, p. 62) than the hydrogen chloride particles (released from the hydrochloric acid) and so move faster. 

Figure 4 shows all the experimental Cq data for the short screws and the corresponding values calculated from Figure 2. Molecular diffusivities at the various temperatures were taken from Figure 3, and the equilibrium values from Figure 5. The scatter is not too bad, and indicates that the model fairly well predicts the effect of rotational speed, throughput rate, and molecular diffusivity on devolatilization performance. The data also indicate that the geometry efficiency, p (which were different for the two screws) has some merit, and provides a convenient means for comparing the relative efficiency of different screw designs.

Perhaps the simplest basis for separation of two gases is molecular size. Gases of different molecular weights have different diffusion coefficients and will diffuse at different rates through the membrane. For membranes having pores whose diameter is comparable or smaller than the mean-free path of gas molecules, the diffusion coefficient is inversely proportional to the square-root of molecular weight ... 

In contrast to the X and A type zeolites, the framework of ZSM-5 is of non-cubic structure. Hence, as a consequence of the interrelation between zeolite structure and molecular mobility, molecular diffusion in different crystallographic directions has to proceed at different rates so that, strictly speaking, molecular diffusion must be described by a diffusion tensor rather than by the diffusion coefficient, i.e. a scalar quantity. 

Although the molecules of a single-phase liquid system may differ, and may diffuse at different rates, they will ultimately achieve a random distribution within the confines of the system. Particulate and granular components do not usually have the constant properties of molecular species and can differ widely in physical characteristics. Thus a mixing motion which depends on identical particulate properties is unlikely to achieve its objective. More commonly such a mixer would produce a grading or segregation of... 

A polymer solution is submitted to ultrafiltration through a series of membranes of different porosity. The rate of diffusion depends on the molecular size and the degree of permeability of the membranes. It is possible to isolate fractions with varying molecular weights at different times. 

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). 

The problems that arise when experiments are carried out in a greatly reduced scale can be overcome if the Reynolds number is high and the flow pattern is governed mainly by fully developed turbulence. It is possible to ignore the Reynolds number, the Schmidt number, and the Prandtl number because the structure of the turbulence and the flow pattern at a sufficiently high level of velocity will be similar at different supply velocities and therefore independent of the Reynolds number. The transport of thermal energy and mass by turbulent eddies will likewise dominate the molecular diffusion and will therefore also be independent of the Prandtl number and the Schmidt number. 

Hydrodynamic Dispersion Macroscopic dispersion is produced in a capillar) even in tlie absence of molecular diffusion because of the velocity profile produced by the adherence of the fluid to tlie wall. Tlris causes fluid particles at different radial positions to move relative to one anotlier, witli tlie result tliat a series of mixing-cup samples at tlie end of tlie capillary e.xhibits dispersion. 

The parameter D is known as the axial dispersion coefficient, and the dimensionless number, Pe = uL/D, is the axial Peclet number. It is different than the Peclet number used in Section 9.1. Also, recall that the tube diameter is denoted by df. At high Reynolds numbers, D depends solely on fluctuating velocities in the axial direction. These fluctuating axial velocities cause mixing by a random process that is conceptually similar to molecular diffusion, except that the fluid elements being mixed are much larger than molecules. The same value for D is used for each component in a multicomponent system. 

At a close level of scrutiny, real systems behave differently than predicted by the axial dispersion model but the model is useful for many purposes. Values for Pe can be determined experimentally using transient experiments with nonreac-tive tracers. See Chapter 15. A correlation for D that combines experimental and theoretical results is shown in Figure 9.6. The dimensionless number, udt/D, depends on the Reynolds number and on molecular diffusivity as measured by the Schmidt number, Sc = but the dependence on Sc is weak for... 

The use of excess inert electrolyte so as to reduce differences in transport properties of the solution at the electrode surface and in the bulk. In such a solution, the ionic diffusivity of the reacting ion, for example, Cu2 + or Fe(CN)g, should be employed in the interpretation of results, and not the molecular diffusivities of the compounds, for example, CuS04 or K3Fe(CN)6. 

These experiments were carried out with the copper deposition reaction, which creates a large density difference at high concentrations. The diffus-ivity data used were the diaphragm cell data of Cole and Gordon (C12a). These data, as correlated by Fenech (F3), were also used in later work on horizontal electrodes. The question whether molecular diffusivity data are adequate for the work in question, has been discussed in Section IV,C.5... 

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