Diffusion temperature determination

The spatially periodic temperature distribution produces the corresponding relxactive index distribution, which acts as an optical phase grating for the low-power probing laser beam of the nonabsorbed wavelength in the sample. The thermal diffusivity is determined by detecting the temporal decay of the first-order diffracted probing beam [°o exp(-2t/x)] expressed by... 

We have applied FCS to the measurement of local temperature in a small area in solution under laser trapping conditions. The translational diffusion coefficient of a solute molecule is dependent on the temperature of the solution. The diffusion coefficient determined by FCS can provide the temperature in the small area. This method needs no contact of the solution and the extremely dilute concentration of dye does not disturb the sample. In addition, the FCS optical set-up allows spatial resolution less than 400 nm in a plane orthogonal to the optical axis. In the following, we will present the experimental set-up, principle of the measurement, and one of the applications of this method to the quantitative evaluation of temperature elevation accompanying optical tweezers. 

In the case of heterogeneous surface burning of a particle, consideration must be given to the question of whether diffusion rates or surface kinetic reaction rates are controlling the overall burning rate of the material. In many cases, it cannot be assumed that the surface oxidation kinetic rate is fast compared to the rate of diffusion of oxygen to the surface. The surface temperature determines the rate of oxidation and this temperature is not always known a priori. Thus, in surface combustion the assumption that chemical kinetic rates are much faster than diffusion rates cannot be made. 

Diffusive exchange of isotopes, affecting temperature determination (thermometry)... 

The surface tension is found from an empirical formula and is a function of temperature (determined in the thermochemical submodel). The surrounding pressure P is determined in the resin flow or compaction submodels. The pressure within the void is determined by the partial pressures of the water vapor and air within the void. The mass of water vapor within the void changes during processing and can be described by Fickian diffusion across the void-composite interface [29], Once the mass of vapor inside the void and the pressure at the location are known, the change in void size can readily be calculated from Equation 13.19. Changes in void size are halted when the resin has solidified. 

In contrast to the critical temperature Tc, the spinodal temperature Tsp is well below the binodal temperature for off-critical mixtures and can hardly be reached due to prior phase separation. The diffusion coefficients in the upper left part of Fig. 8 have been fitted by (23) with a fixed activation temperature determined from Dj. The binodal points in Fig. 8 mark the boundary of the homogeneous phase at the binodal. The spinodal temperatures Tsp are obtained as a fit parameter for every concentration and together define the (pseudo)spinodal line plotted in the phase diagram in Fig. 7. The Soret coefficient is obtained from (11) and (23) as... 

Calculation and results. For each temperature we calculated the HMX molecular center-of-mass self-diffusion coefficient determined as ... 

The F uptake of flint takes a much longer time than that for bone. Fluorine diffusion into the depth of flint material is controlled by defect clusters. The diffusion coefficient determined by implanting a model compound (amorphous silica bombarded with heavy ions and hydrated at 100°C) is 9.10—21 cm2/s at room temperature. The corresponding penetration depth of F under ambient conditions in a 1000-year-old artefact can be estimated via x — (Dt)1/2 = 0.17. im [50], Thus, F accumulates only in the first micrometre of the surface. The surface of ancient flint artefacts can be altered by dissolution. The occurrence of this phenomenon is especially important in basic media. However, in some cases, the thickness of the dissolved layer can be neglected compared to the F penetration depth at low temperatures. Therefore, Walter et al. [35] proposed relative dating of chipped flint by measuring the full width at half maximum (FWHM) of F diffusion profiles in theses cases. 

Figure 4. Probability density functions of temperature for Ht-air turbulent diffusion flame determined at various radial positions 134 mm downstream of the fuel line tip according to procedures indicated in Figure 3. The measurement positions are drawn schematically in the center of the figure to correspond to the radial positions r on the scale at the RHS.

Figure 8. Nitrogen concentration vs. temperature, determined from Raman data at position shown in Hi-air turbulent diffusion flame. The solid theoretical curve, corresponding to adiabatic conditions, was obtained by replotting the information in Figure 7. The theoretical point for stoichiometric combustion ( = 1) is shown on this curve as a filled-in circle. These Raman data were not corrected for optical background at the Raman spectral band position.

Figure 9. Nitrogen concentration vs. temperature, determined from Raman data at position shown in Ht-mr turbulent diffusion flame. These Raman data were corrected approximately for optical background at the Raman spectral band position.

Figure 9. CARS spectra of Ht in a flat Hi-air diffusion flame at several temperatures determined from the identified Q-branch transitions...

The electrical conductivity of sapphire in a particular crystallographic direction was found to be 1.25mSm 1 at 1773 K. An independent experiment on the same material at the same temperature determined the oxygen tracer diffusion coefficient to be 0.4nm2s 1, the diffusion occurring by a vacancy mechanism. Do these data favour oxygen ion movement as the dominant charge transport mechanism (Relative atomic masses, A1 = 27 and 0=16 density of sapphire, 3980 kgm-3.)... 

The process of particle collision is governed by physical factors such as diffusion, temperature, fluid shear, particle and fluid density, and the size of particles and aggregates. Whether particles will adhere when they collide is considered to be a function of conditions at the interface between the two solid particles and the fluid medium. Chemical interactions at the solid-liquid interface are responsible for the development of surface charge and potential, the electric diffuse layer, and hydration and hydrophobic effects which determine the probability of particle attachment. 

Studies carried out with the aim of developing models to estimate migration include a study by Aurela and Ketoja (2002). They estimated the diffusion rate of model compounds (butanol, ethanol, butyl acetate and tetrahydrofuran) in air at room temperature. They then measured the diffusion of these substances through papers with different grammages (and hence, porosities) produced from birch Kraft pulp. The model compounds were not in contact with the test papers and hence transferred via the gas phase. They concluded that the diffusion constants determined in air could be used in random walk simulation to predict migration in a fibre network. Random walk simulations are a mathematical means of modelling processes based on probability distribution and are often applied to investigate diffusion processes. 

Procedure Transfer 5.0 mL of the test preparation to a 25-mL volumetric flask, add 5.0 mL of indicator solution dilute with water to volume, mix, and allow to stand for 1 h in diffuse light at ambient temperature. Determine the absorbance of this solution in a 1-cm cell with a suitable spectrophotometer, at the wavelength of maximum absorbance (620 nm), against a blank consisting of 5.0 mL of 0.1 N hydrochloric acid, 5.0 mL of indicator solution and 15.0 mL of water. The absorbance should not be greater than that produced by 5.0 mL of a solution containing 2.21 (ig of sodium fluoride per milliliter of 0.1 N hydrochloric acid, when treated in the same manner as the test preparation (10 ppm). 

The results in this study have demonstrated clearly that the rate of adsorption and desorption of ethane at low concentrations on 4A molecular sieves in the absence of binder is controlled by intracrystalline diffusion of the ethane. Furthermore, the diffusion process may be characterized by Pick s law and an effective diffusivity dependent only on temperature, and applicable to both adsorption and desorption. It may be expected, therefore, that such micropore diffusion also determines the rates of ethane sorption with commercial 4A pellets containing clay... 

From the temperature dependence of the excimer-to-monomer fluorescence intensity ratio I /I, for Py and IPy(3)IPy on reversed-phase Si-C. g, the activation energy E of surface diffusion was determined, using [2]. Values for E of 19 and 40 kJ/mol were found... 

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