Molecular diffusion 1.4 INDEX

Recent Uses of Solid-Surface Luminescence Analysis in Environmental Analysis. Vo-Dinh and coworkers have shown very effectively how solid-surface luminescence techniques can be used for environmentally important samples (17-22). RTF has been used for the screening of ambient air particulate samples (17,18). In addition, RTF has been employed in conjunction with a ranking index to characterize polynuclear aromatic pollutants in environmental samples (19). A unique application of RTF reported recently is a personal dosimeter badge based on molecular diffusion and direct detection by RTF of polynuclear aromatic pollutants (20). The dosimeter is a pen-size device that does not require sample extraction prior to analysis. 

The coefficient Ex is called the turbulent (or eddy) diffusion coefficient it has the same dimension as the molecular diffusion coefficient [L2 1]. The index x indicates the coordinate axis along which the transport occurs. Note that the turbulentjliffusion coefficient can be interpreted as the product of a mean transport distance Lx times a mean velocity v = (Aa At) l Egex, as found in the random walk model, Eq. 18-7. 

In Equation (9.6), x is the direction of flux, nt [mol m-3 s 1 ] is the total molar density, X [1] is the mole fraction, Nd [mol m-2 s 1] is the mole flux due to molecular diffusion, D k [m2 s 1] is the effective Knudsen diffusion coefficient, D [m2 s 1] is the effective bimolecular diffusion coefficient (D = Aye/r), e is the porosity of the electrode, r is the tortuosity of the electrode, and J is the total number of gas species. Here, a subscript denotes the index value to a specific specie. The first term on the right of Equation (9.6) accounts for Knudsen diffusion, and the following term accounts for multicomponent bulk molecular diffusion. Further, to account for the porous media, along with induced convection, the Dusty Gas Model is required (Mason and Malinauskas, 1983 Warren, 1969). This model modifies Equation (9.6) as ... 

A Function of the index of refraction Dim Molecular diffusivity of species / in a mixture... 

Costin, C.D., Synovec, R.E., A microscale-molecular weight sensor probing molecular diffusion between adjacent laminar flows by refractive index gradient detection. Anal. Chem. 2002, 74, 4558 1565. 

We showed in Chapter 18 that the molecular diffusion term on the RHS of (18.1) can be neglected in atmospheric flows. In Chapter 18 we used index notation, for example, S(ujCi)/Sxj. Here we use both vector and index notation. The three wind velocity components can be denoted ( i, u2,u ),(uxi uy, u7), or (u,v,w) in Cartesian coordinates, and each of these notations has been used at various points in the book. 

The exchange molecular diffusion between residual monomer of gel-polymer matrix (monomer with high value of refractive index) and monomer-diffuser (monomer with more low value of refractive index relatively to matrix monomer) ... 

For laminar flow - flow in which the layers of fluid are stratified across which there is no mixing apart from that due to molecular diffusion - Stokes Law (Stokes, 1851) applies. Firstly, however, it is necessary to define an index of the flow to indicate whether it is laminar or turbulent. This is done through the... 

In addition to CN and ON, the smoke point (SP), which is the maximum smoke-free laminar diffusion flame height, has been employed widely to evaluate the tendency of different fuels to form soot. This tool was first applied to kerosenes, later diesel, and then jet engine fuels.19,20 Researchers have tried to relate smoke points of pure compounds to their molecular structure. It was found that the inverse of smoke point, which measures the potential of a fuel to form soot, increases from n-paraffins to iso-paraffins to alkylbenzenes to naphthalenes.21,22 Since smoke points vary with experimental conditions, the concept of a threshold soot index (TSI), which is calculated from the smoke point, molecular weight, and experimental constants, has been used to compare the soot-formation tendencies of different fuel molecules.23... 

It is fortunate that theory has been extended to take into account selective interactions in multicomponent systems, and it is seen from Eq. (91) (which is the expression used for the plots in Fig. 42 b) that the intercept at infinite dilution of protein or other solute does give the reciprocal of its correct molecular weight M2. This procedure is a straightforward one whereby one specifies within the constant K [Eq. (24)] a specific refractive index increment (9n7dc2)TiM. The subscript (i (a shorter way of writing subscripts jUj and ju3) signifies that the increments are to be taken at constant chemical potential of all diffusible solutes, that is, the components other than the polymer. This constitutes the osmotic pressure condition whereby only the macromolecule (component-2) is non-diffusible through a semi-permeable membrane. The quantity... 

Absolute methods provide the molecular weight and the degree of polymerization without any calibration. Their calculation from the experimental data requires only universal constants such as the gas constant and Avogadro s number, apart from readily determinable physical properties such as density, refractive index, etc. The most important methods in use today are mass spectrometry, osmometry, light scattering, and - to some extent - sedimentation and diffusion measurements. Also, some chemical and spectroscopic methods (determination of end-groups) are important because of their relative simplicity. 

The physical properties of solvents greatly influence the choice of solvent for a particular application. The solvent should be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapor pressure, temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity, also need to be considered. Electrical, optical, and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant, too. Furthermore, molecular... 

Relative rates of sulfate reduction and methanogenesis in lakes of varying trophic status are claimed to indicate that sulfate reduction rates are limited by the supply of sulfate (4, 5, 13). According to this hypothesis, at high rates of carbon sedimentation, rates of sulfate reduction are limited by rates of sulfate diffusion into sediments, and methanogenesis exceeds sulfate reduction. In less productive lakes, rates of sulfate diffusion should more nearly equal rates of formation of low-molecular-weight substrates, and sulfate reduction should account for a larger proportion of anaerobic carbon oxidation. Field data do not support this hypothesis (Table II). There is no relationship between trophic status, an index of carbon availability, and rates of anaerobic... 

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