Soret effect, concentration gradients

Another well-known example is the coupling between mass flow and heat flow. As a result, an induced effect known as thermal diffusion (Soret effect) may occur because of the temperature gradient. This indicates that a mass flow of component A may occur without the concentration gradient of component A. Dufour effect is an induced heat flow caused by the concentration gradient. These effects represent examples of couplings between two vectorial flows. The cross-phenomenological coefficients relate the Dufour and Soret effects. In order to describe the coupling effects, the thermal diffusion ratio is introduced besides the transport coefficients of thermal conductivity and dififusivity. 

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... 

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. 

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 ... 

The diffusion caused only by the temperature gradient is called the thermal diffusion (Soret effect). When the concentration gradient vanishes, Eq. (7.6) reduces to... 

As the second application of irreversible thermodynamics we consider the Soret effect (1893) for a two-component system a flow of particles under the influence of a temperature gradient produces a gradient in concentration. We are ultimately interested in the magnitude of this effect under steady state conditions. Let J0, Jlt J2 be the entropy and particle fluxes... 

Like other FFF subtechniques, materials are retained in thermal FFF as a result of their field-induced concentration at one wall of the channel. In thermal FFF, that field is a temperature gradient. Several terms are used to express the movement of material in response to a temperature gradient, including thermal diffusion, thermodiffusion, thermophoresis, and the Soret effect. The term thermodiffusion is used here, as it has been adopted by the scientific committee for The International Symposium on Thermodiffusion, which is devoted to the scientific study of this phenomenon. 

In general, the diffusive mass flux is composed of diffusion due to concentration gradients (chemical potential gradients), diffusion due to thermal effects (Soret diffusion) and diffusion due to pressure and external forces. It is possible to include the full multicomponent model for concentration gradient driven diffusion (Taylor and Krishna, 1993 Bird, 1998). In most cases, in the absence of external forces, it is... 

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]. 

The latter serves as a reminder that the kinetic theory predicts the cross effects like the transport of mass resulting from a temperature gradient (thermal diffusion). It can also be shown that the theory predicts transport of energy resulting from a concentration gradient (the diffusion-thermo effects). These second-order effects are often referred to as the Soret - and Dufour effects. Unfortunately, no shortcuts are available as these terms do not appear when applying simple kinetic theory, only the more rigorous solution methods resolve these properties. 

Standard notations in thermodynamics and fluid mechanics are used in Eqs. (1-4). The mass diffusion velocity V] consists of contributions from both concentration (i.e.. Pick s law) and temperature (i.e., Soret effect) gradients. 

The coefficients and are related to coeflEcients of heat conductivity and diffusion. Coefficients Li characterize the phenomenon of thermo-diffusion (the Soret effect). Coefficients Lqh describe the reverse phenomenon consisting in the occurrence of heat flux due to the concentration gradient (the Dufour effect). 

A temperature gradient AT induces a concentration gradient A w through the Soret effect such that [ 19,20]... 

Diffusion is the transport of matter caused by a concentration gradient. Matter is transported from areas of high concentration towards those of low concentration, i.e. in the opposite direction to the concentration gradient. The corresponding law is FICK s law. Two other phenomena of molecular transport of matter exist one results from a temperature gradient, this is the SORET effect the other is due to a pressure gradient and is called barodiffusion. These two diffusion fluxes are negligible with respect to pick s diffusion in most cases. 

The term in the mass flux involving the temperature gradient describes the Soret (or thermal-diffiisiori) effect the term on the right side of Eq. (31) involving the concentration gradient describes the Dufour (or diffusion-thermo) effect. 

Chapters 5 and 6 deal with systems where interaction between temperature gradient, concentration gradient and potential gradients without any barrier are involved. In these chapters, theoretical and experimental studies relating to thermal diffusion, Dufour effect, Soret effect, thermal diffusion potential, thermo-cells, precipitation and dissolution potential have been described. Physical implications of the experimental results have also been described. 

Thermal diffusion/Soret effect Establishment of steady concentration gradient due to fixed temperature gradient. 

An even more potent concept comes from the Onsager reciprocal relations, which states that there is a coupling between conjugate force-flux pairs. For example, mass transfer of species by diffusion in an aqueous solution causes a change in concentration, which is accompanied by heat consumption or release due to the heat of dilution. This sets up a thermal gradient, which causes heat flow. The resulting link between heat flux and isothermal diffusion is the Dufour effect. Its conjugate is the Soret effect, which is the diffu-sional mass flux linked to heat flow. The Soret effect has been coupled with... 

This simple formula directly expresses the relationship between water vapour flux and the driving force for mass transfer across the membrane (i.e., the water vapour pressure difference between feed and permeate side). However, in this process heat is also transferred, and thus heat and mass transfer are intimately linked with the consequent development of both concentration and temperature profiles. Moreover, the temperature difference across the membrane while creating a thermal gradient in the fluid phase induces mass transfer, due to the Soret effect. 

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... 

Measurements at temperatures different from ambient temperature may be influenced by the Soret effect observed at low electrolyte concentrations. Placing a solution from ambient temperature to a thermostat creates a concentration gradient caused by an initial temperature gradient [42]. The cell conductance reaches a stable value within an hour however, correct values may be reached only within several days. The effect should be eliminated by a well-designed circulation of solution and stirring. 

We should note that if an initially homogeneous solution is heated, concentration gradients will arise from the Soret effect (14). This is due to the temperature dependence of the solute s chemical potential. For a polymer solution in a thermal gradient, the polymer molecules may migrate toward the lower temperature region. The Soret effect is usually small. However, the Soret coefficient is typically 100 times larger for macromolecules than for small molecules (15,16). 

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