Back diffusion coefficients

Figure 4. Computed distributions for samples partly crystallized at 125°C and quenched. DL = diffusion coefficient of additive in liquid pm2 sec"1 DS = back diffusion coefficient G = spherulite growth rate pm sec"1.

In dilute solutions, tire dependence of tire diffusion coefficient on tire molecular weight is different from tliat found in melts, eitlier entangled or not. This difference is due to tire presence of hydrodynamic interactions among tire solvent molecules. Such interactions arise from tire necessity to transfer solvent molecules from tire front to tire back of a moving particle. The motion of tire solvent gives rise to a flow field which couples all molecules over a... 

Elementary Theory of the Front-to-Back q-count Ratio for Wire Screens. The use of wire screens for measurement of unattached fraction of 218Po hinges on two factors. It is necessary to know how much 218 Po deposits on the screen (as a function of diffusion coefficient and other parameters) and how this deposit is distributed around each wire. The latter point is important because a particles from the decay of 218Po on the back of a wire cannot penetrate the wire to be counted from the front. Experiments to investigate these are discussed later. 

The EOD coefficient, is the ratio of the water flux through the membrane to the proton flux in the absence of a water concentration gradient. As r/d,3g increases with increasing current density during PEMFC operation, the level of dehydration increases at the anode and normally exceeds the ability of the PEM to use back diffusion to the anode to achieve balanced water content in the membrane. In addition, accumulation of water at the cathode leads to flooding and concomitant mass transport losses in the PEMFC due to the reduced diffusion rate of O2 reaching the cathode. 

As intuitively expected, the rate of transfer across the interface depends on the difference in the liquid-phase concentrations at the interface and in the bulk and on the diffusion coefficient in the liquid. In addition, it depends inversely on the time of exposure of the liquid to the gas because of the increasing importance of reevaporation back to the gas phase at longer times. When cl bulk = 0, Eq. (EEE) becomes... 

To evaluate fission product release in a reactor, it is necessary to supply the appropriate particle geometry, diffusion coefficients, and distribution coefficients. This is a formidable task. To approach this problem, postirradiation fission product release has been studied as a function of temperature. The results of these studies are complex and require considerable interpretation. The SLIDER code without a source term has proved to be of considerable value in this interpretation. Parametric studies have been made of the integrated release of fission products, initially wholly in the fueled region, as a function of the diffusion coefficients and the distribution coefficients. These studies have led to observations of critical features in describing integrated fission product releases. From experimental values associated with these critical features, it is possible to evaluate at least partially diffusion coefficients and distribution coefficients. These experimental values may then be put back into SLIDER with appropriate birth and decay rates to evaluate inreactor particle fission product releases. Figure 11 is a representation of SLIDER simulation of a simplified postirradiation fission product release experiment. Calculations have been made with the following pertinent input data ... 

Unsteady State Diffusion. The apparatus, experimental procedures, and the computational procedures used to calculate the diffusion parameter D /r (where D is the diffusion coefficient and r is the diffusion path length) have been described in detail previously (6, 8). A differential experimental system was used to avoid errors caused by small temperature fluctuations. In principle, the procedure consisted of charging the sample under consideration with argon to an absolute pressure of 1204 12 torr (an equilibrium time of about 24 hours was allowed) and then measuring the unsteady state release of the gas after suddenly reducing the pressure outside the particles back to atmospheric. 

The lifetime T and diffusion coefficient D of photoinjected electrons in DSC measured over five orders of magnitude of illumination intensity using IMVS and IMPS.56) fis proportional to the r m, indicating that the back reaction of electrons with I3 tnay be second order in electron density. On the other hand, D varied with C0 68, attributed to an exponential trap density distribution of the form Nt(E) <=< exp[ P(E - Ec)l(kBT) with 0.6. Since T and D vary with intensity in opposite senses, the calculated electron diffusion length L = (JD-z)m does not change linearly with the irradiance. 

As organic and aqueous phases are macroscopically separated by the membrane, HFM offer several hydrodynamic advantages over other contactors, such as the absence of flooding and entrainment, or the reduction of feed consumption (160, 161). The flowsheets tested in HFM were similar to those developed for centrifugal contactor tests. Computer codes based on equilibrium (162) and kinetics data, diffusion coefficients (in both phases and in the membrane pores), and a hydrodynamic description of the module, were established to calculate transient and steady-state effluent concentrations. It was demonstrated that, by selecting appropriate flow rates (as mass transfer is mainly controlled by diffusion), very high DFs (DI A 11 = 20,000 and DFrm = 830) could be achieved. Am(III) and Cm(III) back-extraction efficiency was up to 99.87%. 

The Doppler shift will vary from zero for zero scattering angle to maximum for back-scattering (0 = 180°). The width of the Doppler-broadened peak at half-height (Figure 3.9) is related to the diffusion coefficient by... 

Although a preindustrial project of ethanol production with immobilized cells goes back to the 1980s (8), its application is still limited because of technical problems related to the gel stability and even more to the mass-transfer resistance of the gel membrane (9). Specifically, both substrate and product counterdiffusion (in addition to the presence of cells inside the beads) could reduce the diffusion coefficients of glucose and ethanol up to 13.7 and 28.1%, respectively (10). 

Nmr methods have unrivalled potential to explore interfaces, as this account has striven to show. We have been able to determine the mobility of hydrated sodium cations at the interface of the Ecca Gum BP montmorillonite, as 8.2 ns. We have been able to measure the translational mobility of water molecules at the interface, their diffusion coefficient is 1.6 10 15 m2.s. We have been able to determine also the rotational mobility of these water adsorbate molecules, it is associated to a reorientational correlation time of 1.6 ns. Furthermore, we could show the switch in preferred reorientation with the nature of the interlayer counterions, these water molecules at the interface tumbling about either the hydrogen bond to the anionic surface or around the electrostatic bond to the metallic cation they bear on their back. And we have been able to achieve the orientation of the Ecca Gum BP tactoids in the strong magnetic field of the nmr spectometer. 

Thus in turbulent flow, the dispersion coefficient is independent of the diffusion coefficient, but in laminar flow, the dispersion coefficient depends inversely on the diffusion coefficient. This counterintuitive inverse dependence, the result of axial convection coupled with radial diffusion, is the foundation of the Goulay equation describing peak spreading in chromatography. We now return from this dispersion tangent back to diffusion and in particular, to mass transfer. 

The exciton migration within aggregates of cyanine dyes and the possibility of oxygen diffusion into the porous dye film result in a bulk generation of photocurrent [80]. Photoholes produced due to the oxidation of excitons by molecular oxygen diffuse to the back contact. The diffusion coefficient of charge carriers in dye layer (Dc) can be evaluated from the potential-step chronoamperometric measurements in the indifferent electrolyte. Considering dye film as a thin-layer cell, the current vs. time dependence can be described as follows [81] ... 

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