Diffusion thermal

The effect of thermal diffusion or Soret diffusion was originally predicted by Soret for liquid solutions. In 1917 the effect was also predicted for mixtures of gases by Enskog, and by Chapman and Dootson. Basically, thermal diffusion can provoke a separation of the components of a mixture under influence of a thermal gradient. There is some relationship between thermal diffusion and the movements of particles in a thermal gradient, known as thermophoresis. A particle suspended in a fluid subjected to a thermal gradient will exhibit collisions from hot molecules at one side and cold molecules from the other side. Thus there will be a net force of the 

The following simple mathematical description of the thermal diffusion itself is rather straightforward. The mass flux due to thermal diffusion has been described by Bird, Stewart and Lightfoot160 and Wahl165  

Therefore, in a two component mixture one component will diffuse to the cold region (the heavier one ie. WF6) and the other component to the hot zone (the lighter one ie. H2). This thermal diffusion is of course opposed by ordinary diffusion  

For a two component mixture A and B and using some assumptions one can derive that the amount of separation of A is  

In a binary mixture consisting of two gaseous components A and B subject to a temperature gradient, the flux due to thermal diffusion is given by GREW and 

Equation 10.57. with a positive value of Djh, applies to the component which travels preferentially to the low temperature end of the system. For the component which moves to the high temperature end, Dn is negative. In a binary mixture, the gas of higher raoieculai weight has the positive value of and this therefore tends towards the lower temperature end of the system. 

If two vessels each containing completely mixed gas, one at temperature T and the other at a temperature Ti, axe connected by a lagged non-conducting pipe in which there are no turbulent eddies (such as a capillary tube), then under steady state conditions, the rate of transfer of A by thermal diffusion and molecular diffusion must be equal and opposite, or  

The relative magnitudes of the thermal diffusion and diffusion effects are represented by the dimensionless ratio  

If lemperature gradients are small, Cr may be regarded as effectively constant. Furthermore, Kabt is a function of composition, being approximately proportional to the product It is therefore useful to work in terms of the thermal diffusion facror a, where  

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 column. Thermal diffusion remained a scientific curiosity until 1938, when Clusius and Dickel [C5] developed their thermal diffusion column, which made possible useful separations in simple equipment. In the Qusius-Dickel column the mixture to be separated is 

For most isotopes it is preferable to work with gases rather than liquids, because the higher diffusion coefficients result in higher separative capacity. The optimum pressure is usually near atmospheric. However, when was first found to be fissionable, Nier [N3] attempted to separate it by thermal diffusion of UFe vapor at low pressure without success, so that it was necessary to work with the liquid at high pressures [Al] to obtain useful separation. The optimum spacii between hot and cold surfaces is a few millimeters for gases and fraction of a millimeter for liquids. 

The degree of separation obtainable in thermal diffusion (the difference in composition between hot and cold walls) is much less than in other diffusion processes, so that use of a column to multiply the composition difference is practically essential. The stage type of thermal diffusion has been used only to measure the thermal diffusion coefficient and is never used for practical separations. In some thermal diffusion columns, htu s are as low as 1.5 cm, and as many as 800 stages of separation have been obtained from a sin e column. Even with such a great increase in separation, it is often necessary to use a tapered cascade of thermal diffusion columns for isotopic mixtures, to minimize hold-up of partially enriched isotopes and to reduce equilibrium time. 

Isotopes separated. Table 14.24 gives examples of some of the highest reported concentrations of separated isotopes that have been obtained by thermal diffusion. Most of these separations were on a small laboratory scale. The high purity to which scarce isotopes such as C, N, and 0 have been concentrated is a notable feature of these examples of thermal diffusion. The feasibility of concentrating rare isotopes of intermediate mass, such as Ne and A, by thermal diffusion is also noteworthy. These separations are facilitated by the large number of stages obtainable from a single thermal diffusion column. 

Because the magnitude of the gravitational fractionation depends on the thickness of the fim layer, which in turn is correlated to ambient temperature during fim accumulation, Craig and Wiens (1996) suggested the use of noble gas ratios in ice as a paleothermometer. Indeed, isotope ratios of N2 and Ar in trapped air have recently been successfully employed to quantify past temperature changes, yet based on an additional fractionating effect, namely thermal diffusion. 

The fractional difference 5 (in per mil) of the isotope ratio f at temperature T to the ratio fo at temperature To is given by (Chapman and Cowling 1970)  

The occurrence of thermal diffusion in nature was first observed by Severinghaus et al. (1996) for soil gas in sand dunes. The fractionation of soil air by water vapor diffusion, gravitational settling, and thermal diffusion studied by these authors may also have a small effect on dissolved noble gases in ground water, and hence the calculation of noble gas paleotemperatures. However, these comparatively minor effects have not yet been further studied in the soil-air-ground-water system. 

Severinghaus et al. (1998) demonstrated that thermal fractionation of the air in polar fim layers can be detected and separated from the gravitational effect by high precision analysis of and Ar/ Ar ratios. Rapid temperature changes at the surface induce 

2 kyr BP. The latter studies were based on N2 isotopes only and focused on the calibration of the paleothermometer. 

If the transport of sulphur via the gas phase is prevented, then the transport of silver in the Ag2 S also ceases under steady state conditions. A concentration gradient (i. e. an activity gradient) is built up, and the well-known Soret effect [11] is observed. An even simpler situation arises if the chemical potential of the silver in the sample is maintained constant and equal, for example, to the standard potential of pure silver. The flux of silver is then proportional to the temperature gradient dT/dx, to the mobility of the silver ions, and to the sum of the heat of solution heat of transfer of the silver in the Ag2 S. In view of 

If a temperature gradient is maintained in a binary gaseous mixture, a concentration gradient is established with the light component collecting preferentially at the hot end and the heavier one at the cold end. This phenomenon, known as the Soret effect, may be used as the basis of a separation technique of commercial significance in the separation of isotopes. 

Conversely, when mass transfer is occurring as a result of a constant concentration gradient, a temperature gradient may be generated this is known as the Dufour effect. 

Heating the inner wire (or tube) and cooling the outer wall of a column produces a convective flow pattern, as shown, descending along the cold wall and rising along the heated wire. 

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

ACS Symposium Series American Chemical Society Washington, DC, 1975. 

Th 39 4.9 Pa l[u Np 1 6693 ILEl. Pu liAm Cm. .. TOTAL ESTIMATED WEIGHT (grom) THOUSANDS OF TANK-HOURS  

These two relations, called the Saxen relations, were obtained originally by kinetic considerations for particular systems, but by virtue of the formalism of nonequilibrium thermodynamics we see their general validity. 

The interaction between heat and matter flows produces two effects, the Soret effect and the Dufour effect. In the Soret effect, heat flow drives a flow of matter. In the Dufour effect, concentration gradients drive a heat flow. The reciprocal relations in this context can be obtained by writing the entropy production due to diffusion and heat flow  

This expression, however, does not quite separate the thermal and concentration gradients as we would like, because the term V X t contains the gradient of T (due to the fact that is a function of T, Uk and p). The explicit form of Vp can be written using the relation 

Here we have used the fact that dp — 0 because the system is assumed to be in mechanical equilibrium. Substituting (16.8.4) into (16.8.1) we obtain 

using the relation g = h — Ts, it is easily seen that + Tsk = hk where hk = dh/dnk)p j is the partial molar enthalpy. With this identification, a heat current that takes into account matter current can be defined as 

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This definition is in terms of a pool of liquid of depth h, where z is distance normal to the surface and ti and k are the liquid viscosity and thermal diffusivity, respectively [58]. (Thermal diffusivity is defined as the coefficient of thermal conductivity divided by density and by heat capacity per unit mass.) The critical Ma value for a system to show Marangoni instability is around 50-100. 

Fig. XVIII-22. Schematic illustration of the steps that may be involved in a surface-mediated reaction initial adsorption, subsequent thermalization, diffusion and surface reaction, and desorption. (From Ref. 199 copyright 1984 by the AAAS.)...

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... 

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 ... 

Thermal transpiration and thermal diffusion will not be considered here, but it would be incorrect to assume that their influence is negligible, or even small in all circumstances. Recent results of Wong et al. [843 indi cate that they may Influence computed values of the effectiveness factor iby as much as 30. An account of thermal transpiration and thermal diffu-Ision is given in Appendix I. 

When developing the dusty gas model flux relations in Chapter 3, the thermal diffusion contributions to the flux vectors, defined by equations (3.2), were omitted. The effect of retaining these terms is to augment the final flux relations (5.4) by terms proportional to the temperature gradient. Specifically, equations (5.4) are replaced by the following generalization... 

It is also interesting to examine the relative importance of thermal transpiration and thermal diffusion in the two limiting cases. From equations (A. 1.12) and (A. 1.13)... 

Finally, let us return to the question of the practical importance of thermal diffusion and thermal transpiration in modeling reactive catalyst... 

Fig. 4. Thermal diffusivity of silicon-based stmctural ceramics (a) reaction-bonded SiC (b) hot-pressed and sintered SiC (c) hot-pressed (1% MgO,...

Prandt/Number. The Prandtl number, Pr, is the ratio of the kinematic viscosity, V, to the thermal diffusivity, a. 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

Gaseous diffusion and thermal diffusion data may be found in References 8 and 9. 

In the oxidation process, a layer of dopant is apphed to the surface of sihcon and patterned sihcon dioxide for subsequent thermal diffusion into the sihcon. The masking property of the Si02 is based on differences in rates of diffusion. Diffusion of dopant into the oxide is much slower than the diffusion into the sihcon. Thus, the dopants reach only the sihcon substrate. Oxide masks are usually 0.5—0.7 p.m thick. 

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