Diffusion-thermo effect

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. 

Differences in the chemical potential caused by a temperature gradient are called thermodiffusion, whereas the inverse effect where temperature differences are caused by a gradient of the chemical potential is called the diffusion-thermo effect. Such couplings between currents are common. The most well known is the thermoelectric effect which is caused by a coupling of entropy and charge currents. 

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. 

By definition of the mass-average velocity v of the mixture, all diffusional mass fluxes with respect to v must sum to zero. Hence, Ja = —jn for binary mixtures. The final expression for the molecular flux of thermal energy in binary mixtures, neglecting the diffusion-thermo (i.e., Dufour) effect, is... 

Fourier s law and the interdiffusional fluxes are considered, but the diffusion-thermo (i.e., Dufour) effect is neglected in (30-17). Since contributions from convective transport are insignificant at extremely low Peclet numbers for heat and mass transfer within the catalytic pores, the previous balances reduce to... 

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. 

Kinetic analysis of PP compositions thermo-oxidative degradation at heating rates of 3, 5 and lOK/min. was carried out using NETZSCH Thermokinetics software in order to provide an extra evidence of the diffusion-stabilizing effect of nanoclay structure. 

R. Daou, J. Daou, and J. Dold, The effect of heat loss on flame edges in a no-premixed counterflow within a thermo-diffusive model, Combust. Theory Model. 8(4) 683-699, 2004. 

When both hydrodynamic and thermo-diffusive effects are simultaneously taken into account, it is found that the growth rate a of wrinkling is given by the roots of the dispersion relation [11,12] ... 

In principle the deviation <5 can be determined by the use of usual analytical chemistry or a highly sensitive thermo-balance. These methods, however, are not suitable for very small deviations. In these cases the following methods are often applied to detect the deviation physico-chemical methods (ionic conductivity, diffusion constant, etc.), electro-chemical methods (coulometric titration, etc.), and physical methods (electric conductivity, nuclear magnetic resonance, electron spin resonance, Mossbauer effect, etc.), some of which will be described in detail. 

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... 

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). 

In thermally non-homogeneous supercritical fluids, very intense convective motion can occur [Ij. Moreovei thermal transport measurements report a very fast heat transport although the heat diffusivity is extremely small. In 1985, experiments were performed in a sounding rocket in which the bulk temperature followed the wall temperature with a very short time delay [11]. This implies that instead of a critical slowing down of heat transport, an adiabatic critical speeding up was observed, although this was not interpreted as such at that time. In 1990 the thermo-compressive nature of this phenomenon was explained in a pure thermodynamic approach in which the phenomenon has been called adiabatic effect [12]. Based on a semi-hydrodynamic method [13] and numerically solved Navier-Stokes equations for a Van der Waals fluid [14], the speeding effect is called the piston effecf. The piston effect can be observed in the very close vicinity of the critical point and has some remarkable properties [1, 15] ... 

Similar phenomena such as diffusion potential and thermal diffusion potential in systems where ion transport is involved are also of considerable interest. Coupling of flow of ions relative to solvent is involved in the development of diffusion potential, while in the case of thermal diffusion potential, coupling of flow of ions and energy flow is involved. In such situations, the effective transference number as compared to Hittorf transference number is affected. Interesting experimental results have been reported in the context of galvanic cells (thermo-cells), in which the two electrodes are not at the same temperature where results have been interpreted in terms of thermodynamics of irreversible processes [3]. 

For simpler phenomena such as thermo-osmosis, electro-kinetic phenomena, thermal diffusion and Dufour effect, the linear thermodynamics of irreversible processes is valid in a wide range as indicated by the experimental results discussed in Chapters 3-5. It may be noted that Onsager relations for thermal diffusion can be proved by ETT [2]. 

We hope that this brief review has given the reader a general feeling of the development and application of CE in the separation of nucleic acids. With the advent of capillary array electrophoresis and microchip electrophoresis, as well as remarkable improvements in separation matrices, CE has become a standardized and cost-effective technique in the separation of nucleic acids. Novel thermo-responsive polymer solutions combine the merits of different monomers, and offer the possibility to fine-tune the desirable properties of polymer molecular architecture and chemical composition. Artificial entropic trapping systems obviate the use of viscous polymer solutions, and even offer fast, unattended, miniaturized, and multiplexed platforms. Optimizing the geometry of these electrophoretic systems to both increase the separation and reduce the diffusion (band broadening) is the main topic for future research. 

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