Thermal diffusion, coefficient

The dimensionless parameter Dpc / is called the Lewis number, which is the ratio of the diffusion coefficient of a gas through the mixture divided by the thermal diffusion coefficient of the gas mixture. 

The task of the problem-independent chemistry software is to make evaluating the terms in Equations (6-10) as straightforward as possible. In this case subroutine calls to the Chemkin software are made to return values of p, Cp, and the and hk vectors. Also, subroutine calls are made to a Transport package to return the ordinary multicomponent diffusion matrices Dkj, the mixture viscosities p, the thermal conductivities A, and the thermal diffusion coefficients D. Once this is done, finite difference representations of the equations are evaluated, and the residuals returned to the boundary value solver. 

The Chemkin package deals with problems that can be stated in terms of equation of state, thermodynamic properties, and chemical kinetics, but it does not consider the effects of fluid transport. Once fluid transport is introduced it is usually necessary to model diffusive fluxes of mass, momentum, and energy, which requires knowledge of transport coefficients such as viscosity, thermal conductivity, species diffusion coefficients, and thermal diffusion coefficients. Therefore, in a software package analogous to Chemkin, we provide the capabilities for evaluating these coefficients. ... 

Note Negative average error indicates that the correlation is conservative. The thermal diffusion coefficients of the reactor vendors proprietary grid geometries are not considered in this comparison. 

The mixing data were correlated by defining a thermal diffusion coefficient, a, such that... 

TRANFIT A Fortran Computer Code Package for the Evolution of Gas-Phase Multicomponent Transport Properties, Kee, R. J., Dixon-Lewis, G., Wamatz, J., Coltrin, M. E. and Miller, J. A. Sandia National Laboratories, Livermore, CA, Sandia Report SAND86-8246, 1986. TRANFIT is a Fortran computer code (tranlib.f, tranfit.f, and trandatf) that allows for the evaluation and polynomial fitting of gas-phase multicomponent viscosities, thermal conductivities, and thermal diffusion coefficients. 

When the liquid flow is initiated, the solute zone is carried downstream at a rate depending on the layer thickness, I, which can be related to the particle size, density, diffusion coefficient or thermal diffusion coefficient. 

Kg, gas film coefficient A, surface area of water body 7), diffusion coefficient of compound in air W, wind velocity at 2 m above the mean water surface v, kinematic viscosity of air a, thermal diffusion coefficient of air g, acceleration of gravity thermal expansion coefficient of moist air AP, temperature difference between water surface and 2 m height APv virtual temperature difference between water surface and 2 m height. 

Temperature (°C) Density (kg/m ) Kinematic viscosity (m /s) Thermal diffusion coefficient (m /s)... 

In these equations is the partial molal free energy (chemical potential) and Vj the partial molal volume. The Mj are the molecular weights, c is the concentration in moles per liter, p is the mass density, and z, is the mole fraction of species i. The D are the multicomponent diffusion coefficients, and the are the multicomponent thermal diffusion coefficients. The first contribution to the mass flux—that due to the concentration gradients—is seen to depend in a complicated way on the chemical potentials of all the components present. It is shown in the next section how this expression reduces to the usual expressions for the mass flux in two-component systems. The pressure diffusion contribution to the mass flux is quite small and has thus far been studied only slightly it is considered in Sec. IV,A,6. The forced diffusion term is important in ionic systems (C3, Chapter 18 K4) if gravity is the only external force, then this term vanishes identically. The thermal diffusion term is impor-... 

For the light molecules He and H2 at low temperatures (below about 50°C.) the classical theory of transport phenomena cannot be applied because of the importance of quantum effects. The Chapman-Enskog theory has been extended to take into account quantum effects independently by Uehling and Uhlenbeck (Ul, U2) and by Massey and Mohr (M7). The theory for mixtures was developed by Hellund and Uehling (H3). It is possible to distinguish between two kinds of quantum effects— diffraction effects and statistics effects the latter are not important until one reaches temperatures below about 1°K. Recently Cohen, Offerhaus, and de Boer (C4) made calculations of the self-diffusion, binary-diffusion, and thermal-diffusion coefficients of the isotopes of helium. As yet no experimental measurements of these properties are available. 

DiT Multicomponent thermal diffusion coefficients 3>ab Binary diffusion coefficients (37)... 

In this text we are concerned exclusively with laminar flows that is, we do not discuss turbulent flow. However, we are concerned with the complexities of multicomponent molecular transport of mass, momentum, and energy by diffusive processes, especially in gas mixtures. Accordingly we introduce the kinetic-theory formalism required to determine mixture viscosity and thermal conductivity, as well as multicomponent ordinary and thermal diffusion coefficients. Perhaps it should be noted in passing that certain laminar, strained, flames are developed and studied specifically because of the insight they offer for understanding turbulent flame environments. 

Here Dkj is the matrix of ordinary multicomponent diffusion coefficients, and Dj are the thermal diffusion coefficients. The vector dk represents the gradients in the concentration... 

Various forms of diffusion coefficients are used to establish the proportionality between the gradients and the mass flux. Details on determination of the diffusion coefficients and thermal diffusion coefficients is found in Chapter 12. Here, however, it is appropriate to summarize a few salient aspects. In the case of ordinary diffusion (proportional to concentration gradients), the ordinary multicomponent diffusion coefficients Dkj must be determined from the binary diffusion coefficients T>,kj. The binary diffusion coefficients for each species pair, which may be determined from kinetic theory or by measurement, are essentially independent of the species composition field. Calculation of the ordinary multicomponent diffusion coefficients requires the computation of the inverse or a matrix that depends on the binary diffusion coefficients and the species mole fractions (Chapter 12). Thus, while the binary diffusion coefficients are independent of the species field, it is important to note that ordinary multicomponent diffusion coefficients depend on the concentration field. Computing a flow field therefore requires that the Dkj be evaluated locally and temporally as the solution evolves. 

Here the are the gas-phase mole fractions, the K are the gas-phase mass fractions, W is the mean molecular weight of the gaseous mixture, Dkj is the ordinary multicomponent diffusion coefficient matrix, and the Dj are the thermal diffusion coefficients. 

No reliable mixture-averaged theory is available for computing the thermal diffusion coefficient D[. When thermal diffusion is important, the rigorous multicomponent theory described next should be used to obtain D[. 

Chapman-Enskog theory provides the basis for the multicomponent transport properties laid out by Hirschfelder, Curtiss, and Bird [178] and by Dixon-Lewis [103]. The multi-component diffusion coefficients, thermal conductivities, and thermal diffusion coefficients are computed from the solution of a system of equations defined by the L matrix [103], seen below. It is convenient to refer to the L matrix in terms of its nine block submatrices, and in this form the system is given by... 

Of special interest are dilute polymer solutions, where the thermal diffusion coefficient, Dr = Sr D, is independent of molar mass [11,21]. For the diffusion coefficient D, a scaling law D M a holds, with the exponent for linear flexible... 

Since the interferometer used for (dn / dT)c>p measurement is heated completely, and not just the cuvette, it has been made out of Zerodur (Schott, Mainz), which has a negligible thermal expansion coefficient. Precise values of the refractive index increments are crucial for the determination of the thermal diffusion coefficient and the Soret coefficient. The accuracy achieved for (dn / dc)ftP is usually better than 1 %, and the accuracy of (dn / dT)rp better than 0.1 %. 

T = (Dq2) 1 is the collective diffusion time constant, DT the thermal diffusion coefficient. In Eq. (18), the low modulation depth approximation c( M c0, resulting in c(x,t)(l-c(x,t)) c0(l-c0)y has been made, which is valid for experiments not too close to phase transitions. Eqs. (16) and (20) provide the framework for the computation of the temperature and concentration grating following an arbitrary optical excitation. 

The ratio of 6.8 for the two peak areas from stochastic TDFRS is close to the value of 5.9 as expected from the concentration ratio and the refractive index increments of the two PS, which depends on molar mass due to end-group effects. The thermal diffusion coefficient DT= 1.12 x 10 7 cm2 (sK) l is in excellent agreement with the value found previously in our laboratory [36]. 

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