Effect Soret

The SORET effect, or thermal diffusion, obeys the following law  

The superscript T indicates that the matter transport due to the SORET effect is the 

The thermal diffusion intervenes mainly at low temperature for light species, like H and 

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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. 

Walker D. and DeLong S.E. (1984) A small Soret effect in spreading center gabbros. Contrib. Mineral. Petrol. 85, 203-208. 

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 ... 

Equations (4.16) and (4.17) are examples of the so-called cross effects whereby a force Ac can induce fluxes j) despite that X = 0. Another example of a cross effect is thermotransport in which temperature gradients (fluxes of heat) induce fluxes of atomic species, j,. An application of this concept is the steady state demixing of a (closed solid) solution system, which has been exposed to a temperature gradient (heat flux). This is the Ludwig-Soret effect originally observed with fluid systems. 

Demixing in Temperature Gradients (Ludwig-Soret Effect)... 

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]. 

Most data about the Ludwig-Soret effect of polymers in solution have been obtained from thermal field-flow fractionation (TFFF), developed by Giddings and coworkers [17,18]. TFFF is one member of the family of field-flow fractionation techniques, which are all characterized by a laminar flow of the polymer solution or colloidal suspension within a relatively narrow channel. An external field, which may be gravitation, cross-flow, or temperature as in TFFF, is applied... 

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... 

We have outlined how TDFRS not only provides a useful tool for the study of the Ludwig-Soret effect in multicomponent liquids, but can also contribute valuable pieces of information towards solving the puzzles encountered in polymer analysis. Though TDFRS is conceptually simple, real experiments can be rather elaborate because of the relatively low diffraction efficiencies, which require repetitive exposures and a reliable homodyne/heterodyne signal separation. As an optical scattering technique it has much in common with PCS, and the diffusion coefficients obtained in the hydrodynamic limit (q —> 0) for monodisperse solutions are indeed identical. 

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],... 

The focused laser beam is scanned along an arbitrary path within the xy-plane as sketched in Fig. 10. The perspective view with the cross section through the scan path shown in Fig. 10a visualizes the color-coded concentration change due to the Soret effect according to the numerical simulation discussed later on. On the right hand side a phase contrast micrograph is shown where the word Soret has been written into the polymer blend. 

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... 

Jd is the mass current caused by gradients of the chemical potential p( = pA - Pb) and Jt is the mass current due to the Soret effect in an inhomogeneous temperature field T [76]... 

In this section it will be demonstrated how spinodal decomposition patterns in the two phase region can locally be manipulated in a controlled way by heating a polymer blend PDMS/PEMS by a focused laser beam. It will also be shown that the essential spatial and temporal phenomena, as observed in the experiments, can only be reproduced in numerical simulations if thermodiffusion (Soret effect) is taken into account in the basic equations. 

Fig. 18 Temporal evolution of a pattern in a polymer blend at T = 37.2°C < Tc which was exposed locally to laser light during the period 0 < t < 200 s. Images are taken at t = 0 (A), t = 300 s (B), and t = 700 s (C). The corresponding images (a-c) are obtained by simulations with and the images (ia — y) without taking the Soret effect into account. Figure from [119]. Copyright (2005) by The American Physical Society...

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. 

Zimmerman, G. and Muller, U., Bernard Convection. in a Two-Component System with Soret Effects , Int. J. Heat Mass Transfer. Vol. 35. pp. 2245-2256, 1991... 

Soret effect — When a temperature gradient is applied to an homogeneous mixture of two or more components there is a partial separation of the components by -> migration along the temperature gradient. This phenomenon, known as Soret effect, occurs in condensed phases (i.e., liquids and solids) [i]. Another term that is used to describe the Soret effect is thermo diffusion, which has been observed for either mixtures of gases or liquids and solid solutions [ii]. For electrolytic solutions in a temperature gradient, ions move from a location... 

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