Thermal diffusivity of liquids

Many other methods for separating isotopes have been described. A partial list includes membrane and membrane pervaporation, thermal diffusion of liquids, mass diffusion, electrolysis and electro-migration, differential precipitation, solvent extraction, biological microbial enrichment, and more. Although not discussed in... 

Since the length scales associated with the thermal lens are on the order of 10 to 1000 times the grating constant, their characteristic time scale interferes with polymer diffusion within the grating. Such thermal lensing has been ignored in many FRS experiments with pulsed laser excitation [27,46] and requires a rather complicated treatment. A detailed discussion of transient heating and finite size effects for the measurement of thermal diffusivities of liquids can be found in Ref. [47]. 

In conventional crystallization processes, supersaturation (and hence nucleation) are caused by a thermal perturbation. Because of the inherently low thermal diffusivities of liquids, this approach is ahva3rs accompanied by the existence of temperature non-uniformities within the supersaturated liquid. This, in turn, gives rise to rather wide product size distributions. In the rapid expansion of a highly compressible supercritical mixture, on the other hand. 

DETERMINING THE THERMAL CONDUCTIVITIES AND THERMAL DIFFUSIVITIES OF LIQUIDS BY THE PROBE METHOD. 

A PERIODIC HEATING METHOD FOR THE DETERMINATION OF THE THERMAL DIFFUSIVITY-OF LIQUIDS. PH.D. THESIS. 

Thus at small Pol the growth rate of the oscillations is negative and the capillary flow is stable. The absolute value of sharply increases with a decrease of the capillary tube diameter. It also depends on the thermal diffusivity of the liquid and the vapor, as well as on the value of the Prandtl number. 

The Prandtl number of a liquid (PrL) is defined as the ratio of the kinematic viscosity to the thermal diffusivity of the liquid ... 

T is the temperature of the liquid pool (degree), as is the thermal diffusivity of the soil (area/time), and t is the time after spill (time). 

The large fluctuations in temperature and composition likely to be encountered in turbulence (B6) opens the possibility that the influence of these coupling effects may be even more pronounced than under the steady conditions rather close to equilibrium where Eq. (56) is strictly applicable. For this reason there exists the possibility that outside the laminar boundary layer the mutual interaction of material and thermal transfer upon the over-all transport behavior may be somewhat different from that indicated in Eq. (56). The foregoing thoughts are primarily suppositions but appear to be supported by some as yet unpublished experimental work on thermal diffusion in turbulent flow. Jeener and Thomaes (J3) have recently made some measurements on thermal diffusion in liquids. Drickamer and co-workers (G2, R4, R5, T2) studied such behavior in gases and in the critical region. 

Secondly, the model of thermal diffusion does not allow one to explain the independence of the reaction rate on temperature observed for many low-temperature electron transfer processes. Indeed, the thermal diffusion of molecules in liquids and solids is known to be an activated process and its rate must be dependent on temperature. True, at low temperatures when activated processes are very slow, diffusion itself can be assumed to become a non-activated process going on via a mechanism of nuclear tunneling, i.e. by tunneling transitions of atoms over very short (less than 1 A) distances. A sequence of such transitions can, in principle, result in a diffusional approach of reagents in the matrix. Direct tunneling of the electron, whose mass is less than that of an atom by a factor of 10 or 104, can, however, be expected to proceed much faster. 

B. Havskjold, T. Ikeshoji and S. Kjelstrup Ratkje, On the Molecular Mechanism of Thermal Diffusion in Liquids, Mol. Phys. 80 (1993) 1389 B. Havskjold and S. Kjelstrup Ratkje, Criteria for Local Equilibrium in a System with Transport of Heat and Mass, J. Stat. Phys. 78 (1995) 463. 

Dj for the polymer solution is not well understood. There are several theories of polymer thermal diffusion in liquids. Extensive reviews have been done by Schimpf and colleagues in several publications [4,9]. As an example, the radiation pressure theory of Gaeta and Scala shows that Dj is proportional to the cross-sectional area of the solute molecules [10] ... 

The heat-transfer rate is found to be substantially higher under conditions of agitation. The heat transfer is usually said to occur by combined conductive and convective modes. A discussion and explanation are given by Holt [Chem. Eng., 69(1), 110 (1962)]. Prediction of [/ by Eq. (11-48) can be accomplished by replacing a by a, the effective thermal diffusivity of the bed. To date so httle work has been performed in evaluating the effect of mixing parameters that few predictions can be made. However, for agitated liquid-phase devices Eq. (18-19) is applicable. Holt (loc. cit.) shows that this equation can be converted for solids heat transfer to yield... 

A major disadvantage of the Si(Li) counter is that it must be operated at the temperature of liquid nitrogen (77°K = — 196°C) in order to minimize (1) a constant current through the detector, even in the absence of x-rays, due to thermal excitation of electrons in the intrinsic region, and (2) thermal diffusion of lithium, which would destroy the even distribution attained by drifting. Even when not... 

With the development of specific equipment and processes by which thermal be diffusion is now carried out, separation of substances from their mixtures can often carried out more cheaply by this method, if applicable, than by other separation techniques. Amongst the successful separations effected by thermal diffusion are those of the isotopes of helium and the isotopes of chlorine gas. The method had also been used to effect separation of the isotopes of uranium during the years of World War II in the U.S.A. Constituent hydrocarbons can easily be separated from their mixture by liquid-phase thermal diffusion, because interaction between molecules of different hydrocarbons is practically non-existent and, consequently, each hydrocarbon molecule of the mixture acts independently under the influence of the applied temperature gradient. Another use of thermal diffusion of special interest is its applicability to the separation of mixtures of liquids of close boiling points and of mixtures of isomers, into their respective components. 

The layer of glacial melt shown in Figure 16.1 will be near 0°C while the seawater in this location, a Chilean fjord, is several degrees warmer. Thermal diffusion in liquids is much faster than molecular diffusion, so temperatures near the interface will equilibrate much sooner than salinity. Use this fact to speculate as to the cause of the line of white froth in Figure 16.1. 

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. 

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