Evaluation of the thermodynamic models for the thermal diffusion factor

Over the years, several thermodynamic models for the thermal diffusion factors for binary mixtures have been proposed. The goal of this paper is to test some of these models in combination with different equations of state. We tested the following models: those proposed by Rutherford and Drickamer in 1954, by Dougherty and Drickamer in 1955, by Haase in 1969, by Kempers in 1989 and 2002, and by Shucla and Firoozabadi in 1998. The calculated values of thermal diffusion factors were compared with a few sets of experimental data for hydrocarbon mixtures. For calculation of the partial molar properties we applied different thermodynamic models, such as the Soave-Redlich-Kwong and the Peng-Robinson equations of state. The necessity to try different thermo-dynamic models is caused by the high sensitivity of the thermal diffusion factors to the values of the partial molar properties. Two different corrections for the determination of the partial molar volumes have been implemented; the Peneloux correction and the correction based on the principle of corresponding states.     

Influence of isotopic substitution on the diffusion and thermal diffusion coefficient of binary liquids

The mutual mass diffusion coefficient (D) and the thermal diffusion coefficient ( D _T) of the liquids acetone, benzene, benzene-d ₁, benzene-d ₃, benzene-d ₅, benzene-d ₆, benzene- ¹³C₆, n-hexane, toluene, 1, 2, 3, 4-tetrahydronaphtalene, isobutylbenzene, and 1, 6-dibromohexane in protonated and perdeuterated cyclohexane have been measured with a transient holographic grating technique at a temperature of 25 ^°C. The mass diffusion coefficient shows a pronounced concentration dependence. Perdeuteration of cyclohexane only leads to marginal changes of the mass diffusion coefficient. The Stokes-Einstein equation describes the limiting tracer diffusion coefficients well if the solute molecule is smaller than the solvent. It is not capable to describe the small isotope effect of a few percent. On the other hand, the isotope effect, which is independent of concentration, is in agreement with the Enskog theory, that does not provide the absolute value of the mass diffusion coefficient of the liquid mixtures. The thermal diffusion coefficient of all the binary mixtures shows a moderate and almost linear concentration dependence. Its isotope effect, which is the change of D _T upon deuteration of cyclohexane, varies with mole fraction. The thermophoretic force acting on any tracer molecule in cyclohexane changes by the same amount when cyclohexane is perdeuterated, irrespective of the magnitude of the thermophoretic force before deuteration. This change of the thermophoretic force is equal but of opposite sign to the difference between the thermophoretic forces acting on cyclohexane and perdeuterated cyclohexane as tracers in any of the above liquids.     

恒流法测定热扩散系数

介绍了一种准确测定材料热扩散系数和导热系数 的方法－恒流法,该方法使用的仪器设备简单,测度时间短,准确度高,复现性好,适合于作学生分组实验,也宜于在生产实践和科学研究中广泛推广应用。     

The thermal diffusion factor of Ar-CO2 mixtures: New measurements and comparison with quantum calculations

New measurements for the thermal diffusion factor and for the diffusion coefficient derived from it are reported for the Ar-CO2 gaseous mixture at different temperatures and for various concentrations of the CO2 molecule. Several of the interaction potentials between the partners which have been suggested in the literature are examined, and quantum dynamics calculations are carried out to compare their performances using the infinite order sudden dynamic decoupling scheme. The present results are compared with other experiments and show clearly that, although one of the empirical potentials turns out to be the most realistic for describing such properties, a unique form of a multiproperty-tested potential energy surface for this system is still lacking.     

In vivo lipid diffusion coefficient measurements in rat bone marrow

The diffusion coefficient of lipids, D_l, within bone marrow, fat deposits and metabolically active intracellular lipids in vivo will depend on several factors including the precise chemical composition of the lipid distribution (chain lengths, degree of unsaturation, etc.) as well as the temperature. As such, D_l may ultimately prove of value in assessing abnormal fatty acid distributions linked to diseases such as cystic fibrosis, diabetes and coronary heart disease. A sensitive temperature dependence of D_l may also prove of value for MR-guided thermal therapies for bone tumors or disease within other fatty tissues like the breast. Measuring diffusion coefficients of high molecular weight lipids in vivo is, however, technically difficult for a number of reasons. For instance, due to the much lower diffusion coefficients compared to water, much higher b factors than those used for central nervous system applications are needed. In addition, the pulse sequence design must incorporate, as much as possible, immunity to motion, susceptibility and chemical shift effects present whenever body imaging is performed. In this work, high b-factor line scan diffusion imaging sequences were designed, implemented and tested for D_l measurement using a 4.7-T horizontal bore animal scanner. The gradient set available allowed for b factors as high as 0.03 μs/nm² (30,000 s/mm²) at echo times as short as 42 ms. The methods were used to measure lipid diffusion coefficients within the marrow of rat paws in vivo, yielding lipid diffusion coefficients approximately two orders of magnitude smaller than typical tissue water diffusion coefficients. Phantom experiments that demonstrate the sensitivity of lipid diffusion coefficients to chain length and temperature were also performed.     

用电子散斑干涉法测量材料热膨胀系数

 利用双光束电子散斑干涉法（ESPI）对试件受热变形进行了实时观测，针对一次实验过程中得到的图片较多（300～500幅）的特点，在图像处理时摒弃了以往的手动识别等位移线的办法，用MATLAB语言编写了批处理程序，能够在采集的大量散斑图片中自动快速准确地标定等位移线，得到相应的位移和应变，并结合实时测量的温度值，获得了45钢和LY12铝合金在不同温升率下的热膨胀系数及其随温度的变化。实验结果表明，在涉及的温升率范围内，温升率的改变对材料热膨胀系数的影响不明显，材料的热膨胀系数随温度的升高略有上升。     

Grain-boundary diffusion in nanocrystals with a time-dependent diffusion coefficient

A solution to the equation of grain-boundary diffusion is obtained under conditions where migration of the diffusant from the boundaries into the grains is absent and the diffusion coefficient decreases with time from an increased value to a value characteristic of equilibrium grain boundaries. The specific features of the grain-boundary diffusion in nanocrystals are qualitatively analyzed in terms of this solution.     

Influence of a magnetic field on diffusion and thermal diffusion in gaseous mixtures

The influence of a magnetic field on the transport properties of binary mixtures of a polyatomic and a noble gas is studied theoretically. Using an inverse operator technique, first thermal conductivity and viscosity are treated. Then diffusion and thermal diffusion are discussed in detail, with special emphasis on the composition dependence. A relation connecting the magnitudes of the field effects on thermal conductivity, diffusion, and thermal diffusion is derived. This relation is used to estimate the field effect on diffusion.     

The diffusion coefficient depends on absorption

The diffusion approximation is widely invoked to model the propagation of light in turbid media. When absorption is not weak in comparison with scattering, there is currently a controversy as to if, and how, the diffusion coefficient depends on absorption. Here it is shown that better agreement with random walk simulation is obtained if the photon-diffusion coefficient is taken as D=c/(3micro(s)(')+micro(a)) . One can reconcile this result with recent work advocating D=c/3micro(s)(') by noting that the diffusion equation must be correspondingly changed to a telegrapher's equation.     

Evaluation of cystic ovarian lesions using apparent diffusion coefficient calculated from reordered turboflash MR images.

Reordered snapshot fast low-angle shot images with, and without, diffusion-perfusion gradients were used for the evaluation of contents of cystic ovarian lesions. Sonographically detected 51 cystic ovarian lesions (13 endometrial cysts, 17 ovarian cysts, 7 serous cystadenomas, 6 mucinous cystadenomas, 8 malignant cystic ovarian tumors) were studied. T1- and T2-weighted images, reordered snapshot fast low-angle shot images with and without diffusion-perfusion gradients (b = 106 and 0 s/mm2, respectively) were obtained. Using these images, apparent diffusion coefficients (ADCs) were calculated in the cystic contents of these lesions. Endometrial cysts and malignant cystic ovarian tumors showed lower ADC values than ovarian cysts, serous cystadenomas and mucinous cystadenomas (p < 0.02). There was no distinct ADC difference among ovarian cysts, serous cystadenomas, mucinous cystadenomas (p > 0.2). In conclusion, diffusion-weighted magnetic resonance imaging is possible to be useful to evaluate cystic contents of ovarian lesions.     

Electrical conductivity and chemical diffusion coefficient measurements in single crystalline nickel oxide at high temperatures

Electrical conductivity measurements on nickel oxide have been performed at high temperatures (1273 K<T< 1673 K) and in partial pressures of oxygen ranging from Po₂ = 1.89 × 10^?4 atm to Po₂ = 1 atm. The $\text{po}{}_2{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}$ dependence of the conductivity decreases from about $\text{1}\text{4}$ for Po₂ = 1 atm to smaller values for lower partial pressures of oxygen. The activation enthalpy for conduction increases for decreasing oxygen partial pressures (from 22.5 kcal mol^?1 at Po₂ = 1 atm to 26.0 kcal mol^?1 for Po₂ = 1.89 × 10^?4 atm). This behaviour can be explained by the simultaneous presence of singly and doubly ionized nickel vacancies, with different energies of formation.Furthermore, chemical diffusion coefficient measurements have been performed in the same temperature range, using the conductivity technique, and leading to the result:

$\text{D}\text{?}\text{= 0.244 exp (?}\text{36,600}\text{RT}\text{) cm}{}^2\text{s}{}^{\mathrm{?1}}$

.     

Abdominal apparent diffusion coefficient measurements: effect of diffusion-weighted image quality and usefulness of anisotropic images

This study aimed to assess the effect of diffusion-weighted image (DWI) quality on abdominal apparent diffusion coefficient (ADC) measurements and the usefulness of anisotropic images. Twenty-six patients (10 men and 16 women; mean, 58.1 years) who underwent DW imaging and were diagnosed not to have any abdominal diseases were analyzed. Single-shot spin-echo echo-planar DW imaging was performed, and one isotropic and three orthogonal anisotropic images were created. ADCs were calculated for liver (four segments), spleen, pancreas (head, body, tail) and renal parenchyma. Image quality for each organ part was scored visually. We estimated the correlation between ADC and image quality and evaluated the feasibility of using anisotropic images. ADCs and image quality were affected by motion probing gradient directions in the liver and pancreas. A significant inverse correlation was found between ADC and image quality. The r values for isotropic images were −.46, −.48, −.70 and −.28 for the liver, spleen, pancreas and renal parenchyma, respectively. Anisotropic images had the best quality and lowest ADC in at least one organ part in 17 patients. DWIs with the best quality among isotropic and anisotropic images should be used in the liver and pancreas.     

New method for determining the thermal diffusion coefficient of thin films using ferroelectric crystals

A new method for determining the thermal diffusion coefficient of thin dielectric films deposited on a ferroelectric crystal detector is presented. The surface of the specimen was periodically heated by a rectangular modulated heat flow. The impact of the ratio of the film thickness to the detector thickness, as well as the film thermal diffusion coefficient on the shape of the system’s pyroelectric response is analyzed. Optimal conditions for the measurements are offered. Approbation of the method was carried out on an unannealed lead zirconate titanate (PZT) film deposited on a lithium tantalate crystal. The thermal diffusion coefficient of the specimen was α = 1.5 × 10⁻⁷ m²/s, which correlates with an independent estimation of this magnitude for polarized films.     

Computed and measured thermal diffusion factor for CO-He mixtures: a test of recent interaction potentials

Several anisotropic interaction potentials which describe the He–CO gaseous mixture were tested via the detailed analysis of recently measured thermal diffusion factors, as functions of both temperature and concentration. The calculations were carried out using the quantum treatment of collision dynamics via the infinite order sudden (IOS) coupling scheme between angular momenta, and further using two additional schemes of approximation to second order: the Chapman–Cowling and the Kihara expansions. The results made it possible to test the relative behaviour of the repulsive regions of the various interactions examined in this work, among which those given by the density functional approach for describing van der Waals forces turn out to give fairly realistic values for the anisotropy of the repulsive wall, but have difficulties in generating the well region correctly. These new calculations confirm also the reliability of an earlier multiproperty potential when treating transport properties at temperatures above 100 K, and therefore when examining features which do not depend much on the details of the attractive well.     

Self-diffusion coefficient of nematic liquid crystals from diffusion concentration gradient

A dynamic study of the mass transport by optical methods provides a new approach to evaluate the nematic self-diffusion coefficient. This value is obtained by extrapolation to C = 0 in an empirical relation D_C = D₀ exp (-βC), where D_C is the mass-corrected impurity diffusion coefficient and C is the local concentration of the diffusion profile.     

Diffusion-weighted MRI: influence of intravoxel fat signal and breast density on breast tumor conspicuity and apparent diffusion coefficient measurements

Promising recent investigations have shown that breast malignancies exhibit restricted diffusion on diffusion-weighted imaging (DWI) and may be distinguished from normal tissue and benign lesions in the breast based on differences in apparent diffusion coefficient (ADC) values. In this study, we assessed the influence of intravoxel fat signal on breast diffusion measures by comparing ADC values obtained using a diffusion-weighted single shot fast spin-echo sequence with and without fat suppression. The influence of breast density on ADC measures was also evaluated. ADC values were calculated for both tumor and normal fibroglandular tissue in a group of 21 women with diagnosed breast cancer. There were systematic underestimations of ADC for both tumor and normal breast tissue due to intravoxel contribution from fat signal on non–fat-suppressed DWI. This ADC underestimation was more pronounced for normal tissue values (mean difference=40%) than for tumors (mean difference=27%, P<.001) and was worse in women with low breast tissue density vs. those with extremely dense breasts (P<.05 for both tumor and normal tissue). Tumor conspicuity measured by contrast-to-noise ratio was significantly higher on ADC maps created with fat suppression and was not significantly associated with breast density. In summary, robust fat suppression is important for accurate breast ADC measures and optimal lesion conspicuity on DWI.     

Anomalous diffusion and thermal diffusion of light ions in a nonisothermal plasma

A turbulent state appearing upon the Cherenkov generation of slow ion acoustic waves by light ions and their induced scattering on heavy ions has been studied. The coefficients of the anomalous diffusion and thermal diffusion of light ions have been determined.     

The diffusion coefficient of a model with multiple collisions

A model Lorentz gas, in which each scatterer may be struck more than once, is analyzed, and the diffusion coefficient obtained explicitly as a function of the density of the scatterers.     

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266–281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.