Diffusion coefficient emulsions

The oil droplets in a certain benzene-water emulsion are nearly uniform in size and show a diffusion coefficient of 3.75 x 10 cm /sec at 25°C. Estimate the number of benzene molecules in each droplet. 

Fig. 4.5.5 Pulsed field gradient sequences to obtain velocity and diffusion data (a) spin-echo (PGSE) and (b) stimulated-echo (PGSTE). The application of imaging gradients C Gy and Gz allows the measurement of velcocity maps and spatially-resolved diffusion coefficients and size distribution in emulsions.

Koizumi and Higuchi [18] evaluated the mass transport of a solute from a water-in-oil emulsion to an aqueous phase through a membrane. Under conditions where the diffusion coefficient is expected to depend on concentration, the cumulative amount transported, Q, is predicted to follow the relationship... 

In that case the self diffusion coefficient - concentration curve shows a behaviour distinctly different from the cosurfactant microemulsions. has a quite low value throughout the extension of the isotropic solution phase up to the highest water content. This implies that a model with closed droplets surrounded by surfactant emions in a hydrocarbon medium gives an adequate description of these solutions, found to be significantly higher them D, the conclusion that a non-negligible eimount of water must exist between the emulsion droplets. 

In some cases, e.g. the oxidation of hydrocarbons by potassium permanganate (Meyer and Saam, Ber. xxx. 1935, 1897), the hydrolysis of emulsions of esters in water CGoldschmidt, Zeit. Phys. Ghem. xxxi. 235, 1899), and the dissmution of arsenious oxide (Drucker, Zeit. Phys. Ghem. xxxvi. 693, 1901), the actual chemical reaction between solvent and solute appears to be slower than the process of diffusion, and thus the rate of chemical action is independent of the diffusion coefficient. 

TABLE 1 Concentrations, Distribution Coefficients, and Diffusion Coefficients of FeCp-X in NB/Water Emulsions... 

Figure 23. The lateral diffusion coefficient of adsorbed FITC-/8-lg in thin films as a function of added Tween 20. (a), o/w thin films formed from aqueous non-homogenized solutions of /3-lg at 3 mg/ml ( ), o/w thin films formed from 10% v/v n-tetradecane emulsion or emulsion subnatant samples of FITC-/3-lg, initial protein concentration 3 mg/ml ( ), a/w thin films formed from aqueous non-homogenized solutions of /3-lg at 0.2 mg/ml.

Packer and Rees [3] extended the work of Tanner and Stejskal by the development of a theoretical model using a log-normal size distribution function. Measurements made on two water-in-oil emulsions are used to obtain the self-diffusion coefficient, D, of the water in the droplets as well as the parameters a and D0 0. Since then, NMR has been widely used for studying the conformation and dynamics of molecules in a variety of systems, but NMR studies on emulsions are sparse. In first instance pulsed field gradient NMR was used to measure sdf-diffusion coefficients of water in plant cells (e.g. ref. [10]). In 1983 Callaghan... 

Recently, Li et al. [16] performed PFG-NMR experiments on oil-in D20 emulsions. D20, with similar chemical properties as H20, was chosen because the NMR resonance frequency of deuterium is quite different from that of hydrogen. Therefore they could select the experimental parameters so that only NMR signals from oil molecules are observed. In their calculations they assumed a log-normal distribution. Because of the very different diffusion coefficients of the two oils used, they were only able to obtain stable converged distribution parameters for the n-octane sample during the non-linear fitting procedure. 

Nomura et ol. (1972) solved Eqs. (112) to (118) on a digital computer and analyzed the particle formation in styrene emulsion polymerization where kf = 0 approximately held under normal conditions and found that the value of was 1.3 x 10. This value is about 10 times greater than that predicted by the diffusion theory which assumes that k, = 2jtDd and k2 = 2nDdp, and where D is the diffusion coefficient of a radical in the water phase. 

For emulsion-type vehicles equations similar to those used to describe germicidal behaviour in two-phase systems can be applied. If Dj and D2 are the diffusion coefficients of the medicament in the continuous and disperse phases respectively, and 02 the volume fractions of these two phases, and P is the partition coefficient of the dmg between the... 

Figure 4. Water self-diffusion coefficient D of the micro-emulsions and PEO solutions, normalized to that of the pure liquid water. The need for the additional factor (1-p) is described in the text. Also shown are predictions of the Maxwell and Hanai equations.

In contrast, in emulsions it can be seen that the molecules encounter the boundaries after parts of seconds given the length scales presented in Figure 5.9 and the diffusion coefficient of water. This means that the effect of dimensionality and cormectivity is not so pronounced for emulsion systems as for gel systems on a short time scale. Flowever, the effects of dimensionality and connectivity increase over longer time scales. 

To measure the droplet size distribution of the primary emulsion (W/O in W/O/W or O/W in O/W/O) that has a micron range (with an average radius of 0.5-1.0 pm), a dynamic light-scattering technique (also referred to as photon correlation spectroscopy PCS) can be apphed. Details of this method are described in Chapter 19. Basically, the intensity fluctuation of scattered light by the droplets as they undergo Brownian diffusion is measured from this, the diffusion coefficient of the droplets can be determined, and in turn the radius can be obtained by using the Stokes-Einstein equation. 

In the first studies of micro emulsions using NSE spectroscopy [18, 45], the q variations of the effective diffusion coefficients were afterwards fitted by expressions of the form given below... 

The spherical shell approach is mathematically simple but fails to provide accurate results for many systems of interest. Properties such as diffusion coefficients and permeabilities estimated with the spherical shell approach will vary with extraction. A more accurate and complex approach is to describe the emulsion globule as a heterogeneous media. The Internal phase droplets are uniformly dispersed throughout the membrane phase. While the Internal droplets have a size distribution, they are small enough compared to the globule that they can be considered as point sources or sinks. 

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