Thermal diffusion effects

Thermal transpiration and thermal diffusion effects have been neglected in developing the dusty gas model, and will be neglected throughout the rest of the text. The physics of these phenomena and the justification for neglecting them are discussed in some detail in Appendix I. 

Thermal diffusion effects will be neglected throughout, so the flux relations are given by equations (3.17) - (3.19), which are repeated here for convenience ... 

Attempts to increase the size of nitrogen adsorption or desorption signals, by using larger sample cells, results in enhanced thermal diffusion signals due to the increased void volume into which the helium can settle. However, when krypton is used, no thermal diffusion effect is detectable in any of the sample cells shown in Fig. 15.10. 

The mass flux vector is also the sum of four components j (l), the mass flux due to a concentration gradient (ordinary diffusion) jYp), the mass flux associated with a gradient in the pressure (pressure diffusion) ji(F), the mass flux associated with differences in external forces (forced diffusion) and j,-(r), the mass flux due to a temperature gradient (the thermal diffusion effect or the Soret effect). The mass flux contributions may then be summarized ... 

Satterfield (S2, S3) carried out a number of interesting macroscopic studies of simultaneous thermal and material transfer. This work was done in connection with the thermal decomposition of hydrogen peroxide and yielded results indicating that for the relatively low level of turbulence experienced the thermal transport did not markedly influence the material transport. However, the results obtained deviated by 10 to 20 from the commonly accepted macroscopic methods of correlating heat and material transfer data. The final expression proposed by Satterfield (S3), neglecting the thermal diffusion effect (S19) in the boundary layer, was written as... 

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. 

All terms of the transport equations are retained and included in the solution. This is significant because both thermal diffusion effects and the ion drag affect the calculated performance. Boundary conditions for these equations have electron retaining sheaths at the edges of the plasma. Electrode area ratios and electron reflectivities are included in the boundary conditions also. Electron back emission from the collector is in the collector side boundary conditions, but ion emission from the emitter has been neglected. 

It seems most likely that the equilibrium data of Berkowitz-Mattuck and Buchler (2) are in error, since no satisfactory compromise in the flow rates of the inert carrier gas could be found such that saturation was achieved while eliminating thermal diffusion effects. Under these conditions the simple equations relating partial pressures to the masses transported during the transpiration experiment are now longer valid. Furthermore, the authors assumed that under the conditions of their experiment only dimer LiOH would be formed. The work of Berkowitz et al. (2 ) clearly establishes the existence of a trimer at water pressures some 100 times lower than those employed by Berkowitz-Mattuck and Buchler (3). 

In an ideal cold wall reactor the only hot object in the reactor is the wafer surface. All other parts are well below a temperature where deposition can occur. For the H2/WF6 chemistry this temperature may be as low as 130°C [Schmitz266] and for the SiH4/WF6 chemistry even lower in order to prevent tungsten deposition. Therefore, large temperature gradients can exist in cold wall reactors which creates other difficulties such as temperature non-uniformity across the wafer and thermal diffusion effects (vide infra). In the next sections we will address some of these issues. 

Develop the film model for simultaneous mass and energy transfer including Soret and Dufour effects. Use the Toor-Stewart-Prober linearized theory in developing the model. An example of a process where thermal diffusion effects cannot be ignored is chemical vapor deposition. Use the model to perform some sample calculations for a system of practical interest. You will have to search the literature to find practical systems. To get an idea of the numerical values of the transport coefficients consult the book by Rosner (1986). 

The diffusion-thermal effect or the Dufour energy flux eff describes the tendency of a temperature gradient under the influence of mass diffusion of chemical species. Onsager s reciprocal relations for the thermod3mamics of irreversible processes imply that if temperature gives rise to diffusion velocities (the thermal-diffusion effect or Soret effect), concentration gradients must produce a heat flux. This reciprocal effect, known as the Dufour effect, provides an additional contribution to the heat flux [89]. 

Premixed flames may be influenced by the Darrieus-Landau hydrodynamic instability [1, 2] when the chemical heat release is sufficiently large. Hydrodynam-ically unstable premixed flames are not always observed, however, because of stabilizing influences of buoyancy and thermal diffusion. The long-wavelength flame-surface wrinkles are attenuated by buoyancy for downward propagating flames, and thermal-diffusive effects stabilize small-wavelength wrinkles when the... 

The change of pD with temperature and pressure, and thermal diffusion effects, are neglected. 

When heat flows through a mixture initially of uniform composition, small diffusion currents are set up, with one component transported in the direction of heat flow, and the other in the opposite direction. This is known as the thermal diffusion effect. The existence of thermal diffusion was predicted theoretically in 1911 by Enskog [El, E2] from the kinetic theory of gases and confirmed experimentally by Chapman [Cl, C2] in 1916. It is not surprising that the effect was not discovered sooner, because it is very small. For example, when a mixture of 50 percent hydrogen and 50 percent nitrogen is held in a temperature gradient between 260 and 10°C, the difference in composition at steady state is only 5 percent. In isotopic mixtures the effect is even smaller. 

Thermal diffusion effect. When a composition gradient dy/dr and a temperature gradient dr/dr occur together in a stationary gas mixture, the usual diffusion mass velocity —Dp byjZr is modified by the thermal diffusion effect so that the mass velocity in the r direction becomes... 

Figure 14.40 shows the most accurate measurements of the thermal diffusion effect in UF vapor at low pressure, by Kirch and Schutte [K2]. Results are plotted both as k, for comparison with other gases in Fig. 14.39, and as the thermal diffusion constant y. The very low values, under 0.00005, explain Nier s [N3] inability to detect a thermal diffusion effect in UF5 vapor. The thermal diffusion coefficient 7 is so much smaller than the analogous parameter in gaseous diffusion, Qq 1 = 0.0043, that vapor-phase thermal diffusion caimot compete economically with gaseous diffusion for uranium enrichment. 

A contribution which Professor Emmett identifies as being one of the most satisfying of his career resulted from work at the Fixed Nitrogen Laboratory. It concerned thermal-diffusion effects in equilibrium measurements. The problem that confronted Paul Emmett in 1930 is shown in Figure 2. Indirect... 

Figure 2. Thermal Diffusion Effects in Equilibrium Measurements.

The terms containing a = VlnT Eqs. (13.1), (13.2) and (13.3) do not seem to have been presented before they may be omitted when isothermal systems are being considered. According to Eq. (13.2) there may be a drift of the center of mass associated with thermal gradients - that is, a thermal diffusion effect. This effect is discussed further in Sects. 15 and C.3. 

This convective flow Is super-imposed upon the radial concentration gradient produced by the thermal diffusion effect. The... 

Although Dj appears to be independent of the size and conformation of the polymer chain, it is not independent of the polymer composition. Whereas Dj for polystyrene in THF at room temperature is 0.92 x 10 cm s K it is largerfor PMM Ain THF, 1.27 x 10 cm s K and smaller for polyisoprene, 0.51 X 10 cm s K There is also a considerable dependence of Dj on the solvent employed, which means that solvent composition may potentially play a role in enhancing or suppressing the thermal diffusion effect. In preliminary studies it has been observed that Dj for copolymers assumes an intermediate value between the two parent polymers. 

The key point in these studies is that the presence of flow introduces non-thermal diffusion effects that can be related to the hydrod5mamic viscosity and to hydrodynamic interactions between particles in the case of concentrated suspensions. These effects may modify the fluctuation-dissipation relations and, consequently, the corresponding expressions for the thermal energy and other state variables like pressure or chemical potential. This may lead to what is known as nonequUibrium state equations (Onuki, 2004). 

In the case of the hydrogen-air flames containing 20, 30, and 41% hydrogen, Dixon-Lewis (1979a) found including the hydrogen-atom thermal diffusion effect to be approximately equivalent to increasing si) by 15%. 

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