Thermal diffusion, described

The coefficients, L., are characteristic of the phenomenon of thermal diffusion, i.e. the flow of matter caused by a temperature gradient. In liquids, this is called the Soret effect [12]. A reciprocal effect associated with the coefficient L. is called the Dufour effect [12] and describes heat flow caused by concentration gradients. The... 

The foremnner of the modern methods of asphalt fractionation was first described in 1916 (50) and the procedure was later modified by use of fuller s earth (attapulgite [1337-76-4]) to remove the resinous components (51). Further modifications and preferences led to the development of a variety of fractionation methods (52—58). Thus, because of the nature and varieties of fractions possible and the large number of precipitants or adsorbents, a great number of methods can be devised to determine the composition of asphalts (5,6,44,45). Fractions have also been separated by thermal diffusion (59), by dialysis (60), by electrolytic methods (61), and by repeated solvent fractionations (62,63). 

Furzikov79 proposed a thermal model to describe the etching rate that led to an inverse square root dependence of the threshold fluence on a modified absorption coefficient, aeff, which includes possible changes in the singlephoton absorption coefficient owing to thermal diffusion. This inverse square root relation is given by... 

Many other methods for separating isotopes have been described. A partial list includes membrane and membrane pervaporation, thermal diffusion of liquids, mass diffusion, electrolysis and electro-migration, differential precipitation, solvent extraction, biological microbial enrichment, and more. Although not discussed in... 

The minns sign in Eq. (4.2) arises dne to the fact that in order for there to be heat flow in the +y direction, the temperatnre gradient in that direction must be negative—that is, lower temperature in the direction of heat flow. If the temperature gradient is expressed in units of K/m, and the heat flux is in J/m - s, then the thermal conductivity has units of J/K m s, or W/m K. A related quantity is the thermal diffusivity, which is often represented by the lowercase Greek letter alpha, a. Thermal diffusivity is defined as k/pCp, where k is the thermal conductivity, p is the density, and Cp is the heat capacity at constant pressure per unit mass. We will see in a moment why the term diffusivity is used to describe this parameter. We will generally confine our descriptions in this chapter to thermal conductivity. 

The thermal conductivity is also related to the specific heat capacity Cp as described in Eq. (7.5), where d is the density of the material and TD is the thermal diffusivity ... 

Certainly most surface chemistry occurs as adsorbates come together as a result of thermal diffusion on the surface. When both reagents are in thermal equilibrium with the surface before reacting, the surface chemistry is described as a Langmuir-Hinschelwood (LH) mechanism. Even most gas-surface reactions occur via this mechanism. However, when the product of the reaction also remains on the surface, no dynamic information is available. Therefore, the only LH reactions discussed in this chapter are when the product of the reaction is a gas phase species. One example already discussed extensively is associative desorption. Here, another well-studied example is considered. 

The phenomenon of diffusion may be used to separate various materials, Benedict and Halle et al in Kirk Othmer (Refs 12 27) describe several devices for diffusion separations, such as mass diffusion, thermal diffusion gas diffusion apparatuses... 

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[. 

An essential step forward was also the development of kinetic models for electron tunneling reactions in solids [20-25]. Kinetic equations corresponding to these models were found to describe experimental data rather accurately. The agreement of experimental data with theory together with the absence of the temperature dependence for the reaction rate (which rules out its control by thermal diffusion) and with the evidence of considerable... 

Some other pathological phenomena connected with the existence of hysteresis loop have been reported in the literature. Frank-Kamenetskii (32) described the Buben experimental results for difference of surface temperatures for both steady states for the reaction between hydrogen and air on a Pt wire. These observations indicate a difference up to 1000°C if hydrogen with an excess of air was used, while the maximum temperature difference amounts to 250°C for air in excess of hydrogen. Frank-Kamenetskii explained this phenomenon by the thermal diffusion effects. 

The transport coefficients have been measured by the transient holographic grating technique of Thermal Diffusion Forced Rayleigh Scattering (TDFRS) that has already been described in more detail in previous works [85-87] and will only be briefly sketched in the following (Fig. 1). 

The diffusion, thermal diffusion, and Soret coefficients for nine different PDMS concentrations from c = 0.09 to c = 0.9 have been measured between the binodal temperature and approximately 368 K. Figure 8 shows on the left side the diffusion and thermal diffusion coefficients. The temperature dependences of the latter are very well described as thermally activated processes according to (11) with a common activation temperature Ta = 1,395 K, which is very close to the 1,460 K obtained for the critical blend in Sect. 2. 

Sj = Dj/D and D = (MkBTc b )/v are the Soret and the diffusion coefficient, respectively. In the absence of thermal diffusion, (49) reduces to the well known Cahn-Hilliard equation, which belongs to the universality class described by model B [3], In fact, (49) gives a universal description of a system in the vicinity of a critical point leading to spinodal decomposition. 

There are many excellent differential scanning calorimeter systems available which can be used to measure the specific heat which, when combined with the sample density can be used to give c . The thermal diffusivity (which can be important for thermal imaging systems if the target is not reticulated) can be measured directly on a pyroelectric substrate using the laser intensity modulation method described by Lang [23],... 

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