Diffusivity measurements

Diffusivity measures the tendency for a concentration gradient to dissipate to form a molar flux. The proportionality constant between the flux and the potential is called the diffusivity and is expressed in m /s. If a binary mixture of components A and B is considered, the molar flux of component A with respect to a reference plane through which the exchange is equimolar, is expressed as a function of the diffusivity and of the concentration gradient with respect to aji axis Ox perpendicular to the reference plane by the fpllqvving relatipn 6 /... 

Other important characterization techniques include electrophoresis measurements of droplets [11, 12] (see Section XIV-3C), infrared absorption of the constituent species [13], and light or x-ray scattering. NMR self-diffusion measurements can be used to determine droplet sizes in W/0 emulsions [14]. 

Stepisnik J 1981 Analysis of NMR self-diffusion measurements by a density-matrix oaloulation Physica B/C 104 350-64... 

Karger J, Pfeifer FI and Fleink W 1988 Prinoiples and applioation of self-diffusion measurements by nuolear magnetio resonanoe Adv. Magn. Res. 12 1-89... 

The success of transport models must be measured by their ability to describe the results of flow and diffusion measurements in porous media. 

Proposed flux models for porous media invariably contain adjustable parameters whose values must be determined from suitably designed flow or diffusion measurements, and further measurements may be made to test the relative success of different models. This may involve extensive programs of experimentation, and the planning and interpretation of such work forms the topic of Chapter 10, However, there is in addition a relatively small number of experiments of historic importance which establish certain general features of flow and diffusion in porous media. These provide criteria which must be satisfied by any proposed flux model and are therefore of central importance in Che subject. They may be grouped into three classes. 

Chen-Chen Their correlation was based on diffusion measurements of 50 combinations of conditions with 3 to 4 replicates each and exhibited an average error of 6 percent. In this correlation, = Vg/[0.9724 (V, /g -I- 0.04765)] and = the liquid molar volume at the... 

Atwood and Goldstein [16] examined the effect of pressure on solute diffusivity and an example of some of their results is shown in Figure 7. It is seen that the diffusivity of the solutes appears to fall linearly with inlet pressure up to 40 MPa and the slopes of all the curves appear to be closely similar. This might mean that, in column design, diffusivities measured or calculated at atmospheric pressure might be used after they have been appropriately corrected for pressure using correction factors obtained from results such as those reported by Atwood and Goldstein [16]. It is also seen that the... 

From the molecular point of view, the self-diffusion coefficient is more important than the mutual diffusion coefficient, because the different self-diffusion coefficients give a more detailed description of the single chemical species than the mutual diffusion coefficient, which characterizes the system with only one coefficient. Owing to its cooperative nature, a theoretical description of mutual diffusion is expected to be more complex than one of self-diffusion [5]. Besides that, self-diffusion measurements are determinable in pure ionic liquids, while mutual diffusion measurements require mixtures of liquids. 

Popular methods for mutual diffusion measurements in fluid systems are the Taylor dispersion method and interferometric methods, such as Digital Image Holography [13, 14]. 

The surface diffusivity Ds is computed (conservatively) from the diffusivity measurements of Lewis and Gomer44 for O on Pt(lll) and Pt(110) near 400°C. They described their data via the equation ... 

Gral4n N (1944) Sedmentation and Diffusion Measurements on Cellulose and Cellulose Derivatives. PhD Thesis, University of Uppsala, Uppsala, Sweden... 

Another important factor in diffusion measurements that is often encountered in NMR experiments is the effect of time on diffusion coefficients. For example, Kinsey et al. [195] found water diffusion coefficients in muscles to be time dependent. The effects of diffusion time can be described by transient closure problems within the framework of the volume averaging method [195,285]. Other methods also account for time effects [204,247,341]. 

Table XXIX.—Molecular Weights of Poly-(Methyl Methacrylate) Fractions from Sedimentation and Diffusion Measurements ...

Equations (29), (30), and (10) might be applied to the elucidation of the frictional coefficient in a manner paralleling the procedure applied to the intrinsic viscosity. One should then determine/o (from sedimentation or from diffusion measurements extrapolated to infinite dilution) in a -solvent in order to find the value of Kf, and so forth. Instead of following this procedure, one may compare observed frictional coefficients with intrinsic viscosities, advantage being taken of the relationships already established for the viscosity. Eliminating from Eqs. (18) and (23) we obtain ... 

Due to the inherent variability of these assays either by agar-plate diffusion measurement or turbidimetry measurement, the fiducial hmits are calculated according... 

Independent self-diffusion measurements [38] of molecularly dispersed water in decane over the 8-50°C interval were used, in conjunction with the self-diffusion data of Fig. 6, to calculate the apparent mole fraction of water in the pseudocontinuous phase from the two-state model of Eq. (1). In these calculations, the micellar diffusion coefficient, D ic, was approximated by the measured self-dilfusion coefficient for AOT below 28°C, and by the linear extrapolation of these AOT data above 28°C. This apparent mole fraction x was then used to graphically derive the anomalous mole fraction x of water in the pseudocontinuous phase. These mole fractions were then used to calculate values for... 

Comparison between xf a as determined on the basis of Eq. (3.1.15) from the microscopically determined crystallite radius and the intracrystalline diffusivity measured by PFG NMR for sufficiently short observation times t (top left of Figure 3.1.1), with the actual exchange time xintra resulting from the NMR tracer desorption technique, provides a simple means for quantifying possible surface barriers. In the case of coinciding values, any substantial influence of the surface barriers can be excluded. Any enhancement of xintra in comparison with x a, on the other side, may be considered as a quantitative measure of the surface barriers. 

R M. Cotts, M. J. R. Hoch, T. Sun, J.T. Markert 1989, (Pulsed field stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems), J. Magn. Reson. 83, 252. 

The oil and water response in Figure 3.6.7 could easily be distinguished in this example with kerosene as the oil. If the oil was a crude oil with a broad distribution of relaxation times, the oil may have non-zero response at relaxation times shorter than the Tx cut-off. This could result in mistaking a part of the oil response as BVI. The correct approach in this case is to use diffusion measurements to distinguish between water and oil. This will be discussed under fluid identification (Section 3.6.9). 

E. O. Stejskal, J. E. Tanner 1965, (Spin diffusion measurements Spin echoes in the presence of a time-dependent field gradient),/. Chem. Phys. 42 (1), 288—292. 

W. J. Goux, L. A. Verkruyse, S. J. Salter 1990, (The impact of Rayleigh-Benard convection on NMR pulsed-field-gra-dient diffusion measurements), J. Mag. Reson. 88, 609. 

L. F. Gladden 2003, (Applications of fast diffusion measurement using Difftrain), /. Mag. Reson. 161, 112. 

K. G. Hollingsworth, A. J. Sederman, C. Buckley, L. F. Gladden, M. L. Johns 2004, (Fast emulsion droplet sizing using NMR self-diffusion measurements), /. Colloid Interface Sci. 274, 244. 

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