Chemical diffusion, coefficient

The numerical value of each of these constants depends on temperature due to the temperature dependence of the diffusion coefficients, chemical reaction rate constant, and equilibrium constant. 

System variables. Viscosity, density and thermal conductivity of the liquid, interfacial tension, diffusion coefficients, chemical reaction rate constants Operating variables. Impeller speed, gas flow rate, liquid volume, pressure Equipment variables. Impeller type and diameter, geometry of the equipment. 

If tlie diffusion coefficients of tlie chemical species are sufficiently different, new types of chemical instability arise which can lead to tlie fonnation of chemical patterns and ultimately to spatio-temporal chaotic behaviour. 

The Turing mechanism requires that the diffusion coefficients of the activator and inlribitor be sufficiently different but the diffusion coefficients of small molecules in solution differ very little. The chemical Turing patterns seen in the CIMA reaction used starch as an indicator for iodine. The starch indicator complexes with iodide which is the activator species in the reaction. As a result, the complexing reaction with the immobilized starch molecules must be accounted for in the mechanism and leads to the possibility of Turing pattern fonnation even if the diffusion coefficients of the activator and inlribitor species are the same 62. 

Another class of instabilities that are driven by differences in the diffusion coefficients of the chemical species detennines the shapes of propagating chemical wave and flame fronts [65, 66]. 

Before pursuing the diffusion process any further, let us examine the diffusion coefficient itself in greater detail. Specifically, we seek a relationship between D and the friction factor of the solute. In general, an increment of energy is associated with a force and an increment of distance. In the present context the driving force behind diffusion (subscript diff) is associated with an increment in the chemical potential of the solute and an increment in distance dx ... 

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 the former case, the rate is independent of the diffusion coefficient and is determined by the intrinsic chemical kinetics in the latter case, the rate is independent of the rate constant k and depends on the diffusion coefficient the reaction is then diffusion controlled. This is a different kind of mass transport influence than that characteristic of a reactant from a gas to ahquid phase. 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Penetration theoiy often is used in analyzing absorption with chemical reaction because it makes no assumption about the depths of penetration of the various reacting species, and it gives a more accurate result when the diffusion coefficients of the reacting species are not equal. When the reaction process is veiy complex, however, penetration theoiy is more difficult to use than film theory, and the latter method normally is preferred. 

The dispersion coefficient is orders of magnitude larger than the molecular diffusion coefficient. Some rough correlations of the Peclet number are proposed by Wen (in Petho and Noble, eds.. Residence Time Distribution Theory in Chemical Tngineeiing, Verlag Chemie, 1982), including some for flmdized beds. Those for axial dispersion are ... 

If samples of two metals widr polished faces are placed in contact then it is clear that atomic transport must occur in both directions until finally an alloy can be formed which has a composition showing die relative numbers of gram-atoms in each section. It is vety unlikely that the diffusion coefficients, of A in B and of B in A, will be equal. Therefore there will be formation of an increasingly substantial vacancy concentration in the metal in which diffusion occurs more rapidly. In fact, if chemically inert marker wires were placed at the original interface, they would be found to move progressively in the direction of slowest diffusion widr a parabolic relationship between the displacement distance and time. 

At any plane in a Raoultian alloy system parallel to die original interface, the so-called chemical diffusion coefficient Dchem. which determines the flux of atoms at any given point, and is usually a function of the local composition so that according to Darken (1948), Dchem is given by... 

The chemical diffusion coefficient at any concentration C in the experimental diffusion profile is dren given by... 

This analysis makes possible the determination of a chemical diffusion coefficient from experimental data having made no use of a model, and which takes no account of tire atomic mechanism of diffusion, and assumes tlrat the same chemical diffusion coefficient applies to each component of the alloy. 

The materials problems in the construction of microchips are related to both diffusion and chemical interactions between the component layers, as shown above. There is probably a link between drese two properties, since the formation of inter-metallic compounds of medium or high chemical stability frequently leads to tire formation of a compound ban ier in which tire diffusion coefficients of both components are lower than in the pure metals. 

The technology of silicon and germanium production has developed rapidly, and knowledge of die self-diffusion properties of diese elements, and of impurity atoms has become reasonably accurate despite die experimental difficulties associated widi die measurements. These arise from die chemical affinity of diese elements for oxygen, and from die low values of die diffusion coefficients. 

Bailey, R. G. and Chen. H. T., Predicting Diffusion Coefficients In Binary Gas Systems," Chemical Engineering, March 17, 1975, p. 86. 

Compound and Chemical Formula Specific Gravity or Density Solubility in 100 Parts Diffusion Coefficient in Air (cm /sec) Melting Point, C Boiling Point, C... 

Chemical Boiling Point C Desnity gm/cm Viscosity cP is-c Water Solubi- lity rag/L Vapor Pressure nun Hg Diffusion Coefficient, cnP/day ... 

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