Thermal diffusion, Soret effect

The first and the second terms on the right-hand side of Equation (2.8) represent the effect of electrotransfer of the diffusing ions and the Soret effect (thermal diffusion due to temperature gradients), respectively. The electrical force is given by... 

Ludwig-Soret effect Soret effect Thermal diffusion Thermodiffusion... 

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 thermodiffusion, - Soret effect Thermal electroanalysis — is an analytical method... 

The first effect, thermal diffusion, is exemplified by the two experiments shown in Fig. 21.5-1. In the first, a tall column of salt solution is heated at the top and cooled at the bottom. The salt s concentration is initially uniform, but later becomes more concentrated near the bottom of the tube. This experiment was originally made in 1856 by Tick s mentor, Carl Ludwig more complete experiments were later made by Charles Soret, after whom this effect is named. A similar experiment, shown schematically in Fig. 

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 e.m.f. of a thermogalvanic cell is the result of four main effects (a) electrode temperature, (b) thermal liquid junction potential, (c) metallic thermocouple and (d) thermal diffusion gradient or Soret. 

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 ... 

Thermal diffusion, also known as the Ludwig-Soret effect [1, 2], is the occurrence of mass transport driven by a temperature gradient in a multicomponent system. While the effect has been known since the last century, the investigation of the Ludwig-Soret effect in polymeric systems dates back to only the middle of this century, where Debye and Bueche employed a Clusius-Dickel thermogravi-tational column for polymer fractionation [3]. Langhammer [4] and recently Ecenarro [5, 6] utilized the same experimental technique, in which separation results from the interplay between thermal diffusion and convection. This results in a rather complicated experimental situation, which has been analyzed in detail by Tyrrell [7]. 

Concentration grating Due to the Ludwig-Soret effect, the temperature grating is the driving force for a secondary concentration grating, which starts to build up and is superimposed upon the thermal one. Its temporal and spatial evolution is obtained from the one-dimensional form of the extended diffusion equation... 

Keywords Cahn-Hilliard model Diffusion Nonlinear dynamics Pattern selection Polymer blends Soret effect Spinodal decomposition Thermal diffusion... 

Since there had not been any measurements of thermal diffusion and Soret coefficients in polymer blends, the first task was the investigation of the Soret effect in the model polymer blend poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS). This polymer system has been chosen because of its conveniently located lower miscibility gap with a critical temperature that can easily be adjusted within the experimentally interesting range between room temperature and 100 °C by a suitable choice of the molar masses [81, 82], Furthermore, extensive characterization work has already been done for PDMS/PEMS blends, including the determination of activation energies and Flory-Huggins interaction parameters [7, 8, 83, 84],... 

A modified Cahn-Hilliard (CH) model [114] is used for the theoretical analysis of the impact of thermal diffusion on phase separation by taking into account an inhomogeneous temperature distribution, which couples to a concentration variation via the Soret effect. The Flory-Huggins model is used for the free energy of binary polymer-mixtures. The composition is naturally measured in terms of volume fraction 0 of a component A, which can be related to the weight fraction c by... 

Our simulations clearly demonstrate that without thermally driven mass diffusion the spatial variation of the control parameter b(T) due to the local laser heating does not provide the typical pattern evolution observed in the experiments. It is crucial to take the Soret effect in the basic equations into account in order to reproduce the phenomena observed in an experiment with local heating. 

The movement of macromolecules in a temperature gradient is always in the direction from the hot to the cold region [43,197]. This movement is caused by thermal diffusion, exploited as the driving force in Th-FFF, and called the Soret effect, known already for over 50 years [201-203]. The transport (Eq. (1)) has to be extended by a term taking the thermal diffusion into account. Thus the flux density Jx can be expressed by [34,194] ... 

Solute Thermal diffusion (Soret effect), Ad = —D scfJT, where s is the Soret coefficient Diffusion, = -DeVci Electrophoresis Hyper filtration, Jco = -CfCrKVh, where h is the hydraulic head... 

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. 

Simultaneous heat and mass transfer plays an important role in various physical, chemical, and biological processes hence, a vast amount of published research is available in the literature. Heat and mass transfer occurs in absorption, distillation extraction, drying, melting and crystallization, evaporation, and condensation. Mass flow due to the temperature gradient is known as the thermal diffusion or Soret effect. Heat flow due to the isothermal chemical potential gradient is known as the diffusion thermoeffect or the Dufour effect. The Dufour effect is characterized by the heat of transport, which represents the heat flow due to the diffusion of component / under isothermal conditions. Soret effect and Dufour effect represent the coupled phenomena between the vectorial flows of heat and mass. Since many chemical reactions within a biological cell produce or consume heat, local temperature gradients may contribute in the transport of materials across biomembranes. 

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... 

These equations obey the Onsager reciprocal relations, which state that the phenomenological coefficient matrix is symmetric. The coefficients Lqq and Lu arc associated with the thermal conductivity k and the mutual diffusivity >, respectively. In contrast, the cross coefficients Llq and Lql define the coupling phenomena, namely the thermal diffusion (Soret effect) and the heat flow due to the diffusion of substance / (Dufour effect). 

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. 

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 inverse of the Dufour effect is the production of mass fluxes due to temperature gradients this is referred to as thermal diffusion or the Soret effect. To account for this effect, we need to augment the generalized Maxwell-Stefan diffusion equations in the following manner ... 

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]. 

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. 

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