Diffusion constant flux relationship

The flux is related both to an equiUbrium quantity, ie, the chemical activity, through the solubiUty and to a nonequilihrium coefficient D. In contrast, for an ideal membrane emphasizes the path length and the diffusion constant. Binding and heterogeneity of the membrane may compHcate these simple relationships. 

From this relationship the steady-state diffusion coefficient can be calculated. This kind of test can be used to compare the characteristics of different concretes with regard to chloride diffusion. A practical complication may be that concrete with low porosity may require a very long time to reach a constant flux. Values found for the steady-state effective chloride diffusion coefficient may vary from to 10 m /s for concrete with various binders and w/c [18, 19]. 

The important relationship in difflisional mass is Pick s law. It states that in diffusion the positive mass flux of component A is related to a negative concentration of ingredients. This law is valid for constant densities and for relatively low concentrations of component A in component B. The term binary mixture is used to describe a two-component mixture. A binary diffusivity constant of one component is a binary mixture. 

By inspection, the flux is directly proportional to the solubility to the first power and directly proportional to the diffusion coefficient to the two-thirds power. If, for example, the proposed study involves mass transport measurements for series of compounds in which the solubility and diffusion coefficient change incrementally, then the flux is expected to follow this relationship when the viscosity and stirring rate are held constant. This model allows the investigator to simulate the flux under a variety of conditions, which may be useful in planning experiments or in estimating the impact of complexation, self-association, and other physicochemical phenomena on mass transport. 

For single-component gas permeation through a microporous membrane, the flux (J) can be described by Eq. (10.1), where p is the density of the membrane, ris the thermodynamic correction factor which describes the equilibrium relationship between the concentration in the membrane and partial pressure of the permeating gas (adsorption isotherm), q is the concentration of the permeating species in zeolite and x is the position in the permeating direction in the membrane. Dc is the diffusivity corrected for the interaction between the transporting species and the membrane and is described by Eq. (10.2), where Ed is the diffusion activation energy, R is the ideal gas constant and T is the absolute temperature. 

Consider the reason for the appearance of the thermomechanical effect and its expected value. Let us say that two vessels, 1 and 2, are filled with some identical fluid (hquid or gas) and connected by a capillary, the fluids being held at preset constant temperatures T and T + dT. Let Jq desig nate the heat flux that passes through the capillary between the vessels, while Jg designates a potential fluid flux that diffuses through the same cap iUary (Figure 2.3). In accordance to the preceding deduced relationships (also see Section 1.5), the thermodynamic forces that initiate the fluxes are determined by the formula... 

Generally speaking, the single-gas flux through supported zeolite membranes, for a given temperature, depends on the sorption capacity of the gas on the zeolite pores and its equilibrium adsorption constant (Langmuir isotherm is often used to describe the relationship between the amount adsorbed and the gas-phase pressure), the gas diffusion coefficient, the thickness of the zeolite layer, the porosity of the support, and the pressure at the feed and permeate sides. 

Regime 1 has been described as erosion-enhanced oxidation, because the scale is thinner than it would have been in the absence of erosion, thus the scaling rate is enhanced. The scale grows under diffusion control but its outer surface is eroded at a constant rate by the erosive flux. This situation can be represented by the relationship given in Equation (9.1) ... 

We have discussed so far the Knudsen diffusivity and Knudsen flux for capillary as well as for porous medium. We have said that the flow of one species by the Knudsen mechanism is independent of that of the other species. The question now is in a constant total pressure system, is there a relationship that relates fluxes of all the species when the partial pressures are constrained by the constant total pressure condition. Let us now address this issue. 

Pick (5) observed a linear relationship between the flux of a species and its concentration gradient and defined the diffusion coefficient (being the proportionality constant). One of the most frequent formulation of Pick s law is... 

Usingk+ and k. equal to 500 M s and 5 x 10 M s (7), we find =2.5 xlO" an s and Li =2.25 x lO" cm. The thickness of the reaction layer in the acidic solution is 1 A, which is not surprising for this fast reaction. Both and Dm are much lower than typical diffusion coefficients in water, but both of Aese coefficients were calculated independently. Dm is based on the experimental flux dependence on membrane thickness, while D is calculated using its relationship to the transport resistance and reaction constants. The low values for diffusion coefficients in this case cannot be explained only by the influence of the porous support used in these experiments. For example diffusion coefficients of dichlorobenzoquinone (14) and different nonelectrolytes (75) in similar membranes were >10 cm s. It seems that an aggregation processes, vvdiich usually are not taken into account (16) but are important for long chain fa acids, are responsible for the decrease of the diffusion coefficient of oleic acid both in water and the membrane. 

Another analogous relationship is that of mass transfer, represented by Pick s law of diffusion for mass flux, J, of a dilute component, I, into a second fluid, 2, which is proportional to the gradient of its mass concentration, mi. Thus we have, J = p Du Vmt, where the constant Z)/2 is the binary diffusion coefficient and p is density. By using similar solutions we can find generalized descriptions of diffusion of electrons, homogeneous illumination, laminar flow of a liquid along a spherical body (assuming a low-viscosity, non-compressible and turbulent-lree fluid) or even viscous flow applied to the surface tension of a plane membrane. 

The constant of proportionality D is called the diffusion coefficient, which is expressed in m s , c is the concentration in m and hence / is expressed in m s . The negative sign in this expression indicates that the direction of diffusion is opposite to the concentration gradient. This means that diffusion happens from a high- to a low-concentration region. This relationship between concentration gradient and flux is called Pick s first law and is formally identical to the Fourier law that relates thermal flux to temperature gradient. 

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