Mass diffusivity estimate

Analysis of neutron data in terms of models that include lipid center-of-mass diffusion in a cylinder has led to estimates of the amplitudes of the lateral and out-of-plane motion and their corresponding diffusion constants. It is important to keep in mind that these diffusion constants are not derived from a Brownian dynamics model and are therefore not comparable to diffusion constants computed from simulations via the Einstein relation. Our comparison in the previous section of the Lorentzian line widths from simulation and neutron data has provided a direct, model-independent assessment of the integrity of the time scales of the dynamic processes predicted by the simulation. We estimate the amplimdes within the cylindrical diffusion model, i.e., the length (twice the out-of-plane amplitude) L and the radius (in-plane amplitude) R of the cylinder, respectively, as follows ... 

Figure 5. The same data as in figure 4b plotted together with the diffusion battery data. Note, the CN counter cannot see any particle below 4.2 nm. According to rough mass balance estimate 1( - 108 small clusters per as could be present.

Diffusivity Estimation Method for Binary Gas Mixtures from Treybal, Mass-Transfer Operations, 3rd Edition... 

For integrating Eq. (4-9), vji= ei Er) should be known as a function of and operating variables. However, the momentum diffusivity is the only term we know, with essentially no systematic data for In the case of free turbulence of a homogeneous fluid, the diffusivity of a scalar quantity like heat and mass is estimated to be about two times that of momentum (S4) and the two diffusivities are not far apart for turbulent pipe flow (S8). However, such a relation is not available yet for gas-liquid bubble flow in bubble columns. Generally the local radial mass diffusivity may be expressed by a, with a being a numerical coefficient of order unity. 

Regardless of its complex architecture, any polymer relaxing with no topological constraints and no hydrodynamic interactions is well-represented by the Rouse model, with friction proportional to molar mass. To estimate the terminal response of randomly branched polymers, we apply this reasoning to the characteristic polymers, with size consisting of N monomers. The diffusion coefficient of these chains is given by the... 

To determine the species mass diffusion a concentration gradient is induced by assuming that the species number concentration is different at each of the planes zq,z, Z2. To estimate the viscosity we create a gradient in the z-momentum by assuming that the molecules at the plane zq are moving in the negative z-direction, at the plane z the molecules are stationary, and those at plane Z2 are moving in the positive z-direction. To induce a thermal conduction flux the three planes are taken to be at different temperatures. 

Figure 1.3 Mathcad routine to estimate gas-phase mass diffusivities using the Wilke-Lee equation.

Figure 1.4 Mathcad routine to estimate liquid-phase mass diffusivities...

The problem of estimating or correlating effective thermal conductivities, k ff, for porous media is much more difficult than the corresponding mass transport problem. However, it turns out that this is a very important parameter. One reason for the difficulty is that, while for mass diffusion the solid forms a barrier between the... 

For most latex films, a simpler approach to data analysis is preferable. One approach which we have employed in the past is to by to estimate the extent of mixing due to diffusion from comparison of the fluorescence decay curves. In terms of Fick s laws in spherical geometry, the fraction of mass diffusing across the initial interface after time t is given by /s(t) = mt/m, where m =... 

From the basic equations of momentum, energy, and mass diffusion effects, and radial and axial convection, with or without chemical reaction. Additionally, we evaluate also the parameters that cause the deviation from ideal behavior and we adopt criteria to estimate the effects of radial and axial dispersion on the reactor. 

In a separate experiment, a sample particle is allowed to freely diffuse in the fluid, while its center of mass is estimated at regular time intervals (30 ms suffices for a micron-sized particle in water at room temperature) using the particle-tracking algorithm. 

For a 350-(xm reactive PS particle, an order of magnitude estimate of the diffusion time of 20 min is obtained for an upper limit of mass diffusivity of 10 cm /s. This is based on the following equation for the diffusion time (fd), size scale (A.), and diffusivity (D) ... 

The Weisz-Prater criterion makes use of observable quantities like -Ra)p, the measured global rate (kmol/kg-s) dp, the particle diameter (m) pp, the particle density (kg/m ) Dg, the effective mass diffusivity (m /s) and the surface concentration of reactant (kmol/m ). The intrinsic reaction rate constant ky need not be known in order to use the Weisz-Prater criterion. If external mass transfer effects are eliminated, CAb can be used, and the effective diffusivity can be estimated using catalyst and fluid physical properties. The criterion can be extended to other reaction orders and multiple reactions by using the generalized Thiele modulus, and various functional forms are quoted in the literature [17, 26, 28]. 

The Arrhenius plot of 1/r for benzophenone in poly(methyl acrylate) (PMA) showed another break at 40 °C (above T of PM A), which corresponds to the crossover of k j given by Eq. (14) from a diffusion-controlled to an activation-controlled reaction. The diffusion coefficient D for reacting carbonyl groups calculated from the values of 1/t and B also showed a break at each transition temperature, as exemplified in Fig. 8 for PMMA, polystyrene, and polycarbonate. It should be iK>ted that D in Fig. 8 refers to the reacting functional groups but not to the molecule. The diffusion proc at temperatures below T would be caused by rotation of the benzojdienone molecule and by the cooperative motion of a few successive monomer units of the matrix polymer. Nevertheless, the values of D in these polymers at 100 °C are comparable to the value of D = 5.6 x 10 an /s for mass diffusion of ethylbenzene in polj tyrene at 30 °C. The reaction radius R was estimated to be 3-5 A. The transition temperatures... 

Vapor in humidified rooms frequently diffuse through a plaster wall and condenses in the surrounding insulation. Estimate the mass diffusion rate of water through 3 by 5 m wall 10 mm thick. Room and insulation water vapor pressures are 0.03 and 0 bar. Diffusivity of water in the dry wall is 10 m /sec. Water solubility in the solid is 5 x 10 kmole/mbar. 

Estimation of model parameters (e.g., mass diffusivity) from experimental data... 

Since the degree of coupling is directly proportional to the product Q D k), the error level of the predictions of q is mainly related to the reported error levels of Q values. The polynomial fits to the thermal conductivity, mass diffusivity, and heat of transport for the alkanes in chloroform and in carbon tetrachloride are given in Tables C1-C6 in Appendix C. The thermal conductivity for the hexane-carbon tetrachloride mixture has been predicted by the local composition model NRTL. The various activity coefficient models with the data given in DECHEMA series may be used to estimate the thermodynamic factors. However, it should be noted that the thermodynamic factors obtained from various molecular models as well as from two sets of parameters of the same model might be different. 

Considering its electrical and magnetic properties, ScSe like ScS and ScTe may be regarded as a monovalent metal in which the conduction electron density n corresponds to one electron per formula unit. Theoretically, n = 2.54x 10 cm" for nominal stoichiometric ScSe, Zhuze et al. [3]. The carrier density n = 1 x 10 cm" was calculated from the minimum In the diffuse reflection spectrum (at 2.26 eV) of ScSe obtained by the metal hydride method. Similarly, the effective free carrier mass m = 1.00 mo, the mobility of free carriers = 2.5 cm V" s" and the relaxation time t = 5.3x 10" s were obtained for this sample, Obolonchik et al. [5]. The reflection spectrum for a Bridgman-single crystal gives t = 2.2 x 10" s calculated with use of the Drude theory. The optical effective mass was estimated to be m = 2.9 mo [3]. 

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