Measurement Of Mass Diffusivity Research Articles

Measurement of mass diffusivity by light streak imaging

Mass diffusion relates to migration of one species in another and is a consequence of local heterogeneity of concentration distribution and energy. The present study describes an optical method based on the shadowgraph technique for measuring a binary mass diffusivity of a solute in a solvent using a collimated beam of light. The measurement technique exploits the principle that refraction of a light beam due to concentration gradient creates a sharp visible streak in an image. The streak is a bright, visible linear feature in a shadowgraph image and opens up a new method of diffusivity measurement. The movement of the streak with time is due to a finite mass diffusivity of a solute in a solvent. Experiments with glucose, salt and glycerin diffusion in water have been conducted within a time window obtained from the sensitivity analysis. The respective mass diffusivities are determined by the light streak as well as the linearized shadowgraph technique, and compared with the values reported in the literature. The proposed approach promises to yield a simple method of determining mass diffusivity in a variety of binary systems without explicit measurement of the species concentration.

Measurement of Mass Diffusivity Using Interferometry through Sensitivity Analysis

Mass diffusion of a solute in a solvent is realized in many applications. The extraction of transport properties from optical images has not received sufficient attention, though refractive index techniques for determination of the mass diffusion coefficient of a solute in a binary system have been discussed in the literature. The issue becomes important in experiments involving slow diffusion during which concentration gradients in parts of the domain are large. Accordingly, refractive index gradients are also large and higher order effects influence image formation. This weakness can be addressed by carrying out sensitivity analysis, wherein only that part of the data is analyzed which is highly sensitive to the experimental determination of diffusivity. In the context of interferometry, the present study reports fringe patterns obtained for the diffusion of NaCl and sucrose in deionized water at 25 °C. A Mach–Zehnder configuration of the interferometer has been employed. In an experiment, a layer of so...

Effect of Input Diffusivity in an Axisymmetric Mass Diffusivity Model for Liquid Metals with an Applied Magnetic Field

Depending on the magnitude of the diffusivity, convective contamination may result in erroneous measurement of mass diffusivity even in microgravity. The effect of natural or buoyant convection is numerically investigated for liquid germanium with an axisymmetric model using two different magnetic field strengths and four heat transfer conditions. Since the reported input diffusivity value may vary due to inaccuracies in measurements, an order of magnitude lower and higher input diffusivity from the base value of D0 = 2 x 10(-4) cm2/sec was used to evaluate the behavior of liquid germanium in the presence of a magnetic field. From the numerical results, the temperature nonuniformity and the flow velocities in the liquid vary according to the input diffusivity (i.e., an order of magnitude lower and higher than the base cases). The heat transfer pattern is important in achieving a larger temperature nonuniformity in the liquid during the experiments. A stronger magnetic field can tolerate a higher temperature nonuniformity as expected.

Experimental confirmation of the insensitivity of mass diffusion measurements to blockages and voids along the diffusion path

Using the real-time diffusion methodology first developed by Codastefano et al. [Rev. Sci. Instrum. 48, 1650 (1977)] we show that deviations from strictly one-dimensional transport (i.e., blockages and voids) widely cited in the literature as leading to erroneous results, have little effect on the measured diffusivity. In this methodology, radiotracer, initially located at one end of a cylindrical diffusion sample, is used as the diffusant. The sample is positioned in a concentric isothermal radiation shield with collimation bores located at defined positions along its axis. The intensity of the radiation emitted through the collimators is measured as a function of time using solid state detectors. Diffusivities are calculated from the signal difference between the detectors. These results were obtained using 114mIn radiotracer in benign indium. A 60% blockage was simulated by using a 2 mm source disk diffusing into 3 mm diameter host section. A void/bubble was simulated by inserting a 1 mm diameter by 1 mm long side plug into the sample 7 mm from the top (radiotracer section). The resulting self-diffusivities obtained were, for both modifications, comparable with other ground experiments. These results agree with numerical simulations. An analytical model describing the minimal effects of blockages and voids on the output diffusivity is presented.

The effects of collimator geometry and self-absorption on in-situ mass diffusion measurements

We consider a real-time methodology for determining self-diffusion coefficients at several temperatures utilizing a single sample, based on a radiotracer technique put forth by Codastefano, Di Zanza and Russo (Codastefano, P., Di Russo, A., Zanza, V. 1977. A new apparatus for accurate diffusion measurements in fluids. Reviews of Science Instrumentation 48, 1650–1653 (CDZ)) and recently optimized by our group (Jalbert, L.B., Banish, R.M., Rosenberger, F.E. 1997. Real-time diffusivity measurements in liquids at several temperatures with one sample. Physical Review E 57, 1727–1736 (JBR)). In this technique the evolution of the concentration distribution of the radiotracer is followed by shielding the source except for a pair of collimated apertures placed at mathematically advantageous positions along the diffusion axis. Radiation detectors at each collimator measure the intensity of radioactive tracer emission at each aperture, and the counting rate difference versus time leads to a determination of the diffusion coefficient. The effects of self-absorption of radiation in the source were previously treated by us using a one-dimensional approximation, which is a typical procedure. However, in order to obtain meaningful counting statistics in the detectors, the size of the collimator apertures must be large enough that the measured counting rate is actually an integral over a three-dimensional region of the source volume rather than an ideal point measurement. Here we consider, by a ray-tracing algorithm, the effects of this finite extent of the observed volume on the experimentally-determined diffusivity. Self-absorption effects are considered both for photon energies that have essentially no absorption in the sample (so that the entire thickness of the sample is effectively viewed) and for those that suffer sufficient self-absorption that the measured radiation comes from only a surface “skin-depth” (∼100 μm in extent). Collimation holes from ∼1 to ∼100% of the sample diameter are investigated. We find that neither the effects of self-absorption nor of the intrinsic three-dimensional geometry involved have a significant effect on the experimentally determined value of the diffusivity. In addition, linear concentration gradients along the diffusion axis do not influence the diffusivity measurement. A (quadratic) correction formula to determine the actual diffusion coefficient from the experimentally-obtained value is presented.

Diffusion of Sodium Chloride Through Chicken Eggshell in Relation to an Ancient Method of Egg Preservation

Egg salting is an ancient method of egg preservation dating back hundreds of years. The salting process brings additional taste and flavour which many Asian people enjoy. This process involves tanking intact eggs in a NaCl salt solution in a static situation which allows the salt to diffuse through eggshell into the egg white and yolk. Typically, this process would last more than 3 weeks at room temperature depending on how strong the taste required. Long-term salting would also induce certain fermentation to create authentic flavour and taste development. Despite the large quantity of these treated eggs are consumed daily, the process remains an art and quantitative data is non-existent. In this study, NaCl diffusion through egg shell has been investigated. The procedures and equipment used and the results of measurement of mass diffusivity of NaCl through egg shell are reported. The temperature dependence function of the diffusivity has been obtained.

Polymers bearing intramolecular photodimerizable probes for mass diffusion measurements by the forced Rayleigh scattering technique: synthesis and characterization

A new photochromic probe, bis(9-anthryl methyl) ether (BAME) derivative, was synthesized and introduced as an effective probe for forced Rayleigh scattering (FRS) measurement. It is shown that BAME and polystyrene labelled with BAME exhibit a large change in refractive index under irradiation of u.v. light (363.8 nm). The self-diffusion of BAME and polystyrene labelled with BAME (PSA) were measured in various solvents. Results of PSA in good, marginal and poor solvents are consistent with those obtained from quasi-elastic light scattering (QELS). Since the photodimerization reaction of anthracene has been extensively studied in solution and crystal as well as in polymer matrix, unfavourable multistep photochemical reactions can be avoided. One such unfavourable case, which involves a fluorescence quenching solvent CCl 4, is demonstrated. A temperature dependence study of polystyrene in semi-dilute theta solution by FRS has suggested that the non-exponential intensity decay is due to large concentration fluctuations in the solution. The well known photochemistry, large refractive index change and temperature stability have made BAME a very promising probe for FRS measurements.

On the application of forced Rayleigh light scattering to mass diffusion measurements

The newly developed forced Rayleigh light scattering (FRS) method has been applied to the measurement of anisotropic mass diffusion in well-aligned nematic samples of p-azoxy anisol (PAA) and p-methoxy benzilidene-p-n-butyl aniline (MBBA). Since both materials are photochromic and can thus be photochemically labeled, self-diffusion can be studied as well as impurity diffusion. In the latter case, the diffusing species was chosen to be methyl red (MR), which is photochromic but had also been used as a regular dye in optical tracer diffusion experiments. The FRS data for self-diffusion are shown to agree well with this earlier determination; a satisfactory result if one considers that MR and both PAA and MBBA have very similar molecular structures. They also agree to within 10% with the Franklin theory of self-diffusion in liquid crystals. On the other hand, the FRS measurements of impurity diffusion with photochemically labeled MR give diffusion coefficients that are considerably smaller. This discrepancy can, in principle, be explained through nonequilibrium thermodynamic considerations which show that the diffusion coefficient actually measured by FRS is different in the two cases of self- and impurity diffusion. However, the observed variation seems anomalously large. We tentatively suggest that photoactivated MR molecules tend to form aggregates, a problem apparently not encountered with photoexcited MBBA or PAA molecules. This demonstrates that, although FRS is undoubtedly a powerful technique to measure mass transport, the possibility of photoinduced spurious intermolecular interactions between the diffusing species must always be considered with care.

Binary Mass Diffusion Measurements in Nematic and Smectic Liquid Crystals by Forced Rayleigh Scattering

Abstract The binary mass diffusion constants of methyl red in 8CB were measured in the smectic A, nematic and isotropic phases by forced Rayleigh scattering (FRS). The diffusion constant parallel to the director orientation, D⊥, is always larger than the perpendicular one, D||, not only in the nematic but also in the smectic phase. The present result D|| > D⊥ in the smectic phase conflicts with that of methane diffusion, D|| & D⊥, obtained by NMR. The difference was ascribed not to the different method employed but to the different tracer molecules used. The temperature dependence shows nearly an Arrhenius type, but has sharp dip at T AN. The anomaly was attributed to the formation of cybotactic clusters of a smectic phase in a nematic medium and of a nematic phase in a smectic medium.

Mass diffusion measurements in liquid crystals by a novel optical method

Binary mass diffusion measurements have been performed in fluid media doped with photochromic dye molecules. A periodic concentration of tagged molecules is created by illuminating the sample with a fringe intensity pattern. The photo induced change of refractive index and/or absorption of the dye molecules creates an optical grating which is observed through Bragg diffraction of an auxiliary laser beam. When the flash excitation is switched off, this grating will relax since photoexcited molecules will diffuse into nonphotoexcited zones and vice versa. The main advantages of this method are that: (1) the duration of the experiment is strongly reduced compared to classical tracer methods since diffusion lengths, defined by the fringe spacing, are small (1–100 μm); (2) the possibility of studying anisotropic diffusion is readily available; and (3) small sample volumes are required. Results are reported on the diffusion of methyl red in a homogeneously aligned sample of MBBA. In the nematic phase, the diffusion is faster along the local optical axis than perpendicular, the anisotropic ratio D∥/D⊥ being 1.6±0.1 at 22 °C, in good agreement with previous tracer data. The temperature dependence yields an activation energy of 5.8±0.7 kcal/mole for D∥ and 6.0±0.8 kcal/mole for D⊥. In the isotropic phase, the activation energy is found to be 10±1.5 kcal/mole.