Diffusion transport rates

Mass evaporation rate = diffusion transport rate to the air Heat transfer rate = energy required to vaporize... 

Solute Molecular weight Apparent diffusion coefficient in the presence of structured flow system Enhanced diffusion transport rate" Linear transport rate (10 8 m s 1)... 

In this equation, ,/ and mi/2 are the masses of the two isotopes making up RZ1, and the terms are condensation coefficients for the two isotopes, which are determined experimentally and are typically close to 1. Equation (7.2.1) is valid if a is independent of the evolving composition of the evaporating liquid, and the diffusive transport rate is fast enough to keep the liquid homogeneous. The last condition is violated in solids, where diffusion is very slow relative to the evaporation rate, so solids do not undergo Rayleigh distillation. 

The diffusion rates of fluids, particularly gases, throagh porous solid materials are of particular interest because of the common practice of using porous solids as catalysts and adsorbents. Diffusions transport rates within the pores may limit the rates by which such procesms occur. 

Diffusive transport rates through a polymeric phase are vety important to membrane reparation processes such as reveres osmosis, ultrafiltration, and gus permeation. See Chapters 18-21 fordiscossion of msmbrane processes. Here, diffusion coefficients of solutes within a polymeric material are discussed. 

The flexibility of the SDF fluid transport system in nano-and micrometer thin channels enables to exploit numerous other possible applications, especially if a high degree of spatial confinement or an increase in the diffusion transport rates is required. Vankrunkelsven et al. used the SDF system for the size separation of macromolecules and micro-particles in nano- and micrometer deep channels using micro-steps [7] (Fig. 2). The separation of 0.5 and 1.0 xm carboxylated polysterene beads mixtures of Staphylococcus aureus and Saccharomyces cerevisiae, and mixtures of Saccharomyces cerevisiae and Escherichia coli cells in a micro- or nanochannel that is only slightly larger than the molecules themselves and is narrowed in a stepped structure. 

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or pie2ometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

Nonporous Dense Membranes. Nonporous, dense membranes consist of a dense film through which permeants are transported by diffusion under the driving force of a pressure, concentration, or electrical potential gradient. The separation of various components of a solution is related directiy to their relative transport rate within the membrane, which is determined by their diffusivity and solubiUty ia the membrane material. An important property of nonporous, dense membranes is that even permeants of similar size may be separated when their concentration ia the membrane material (ie, their solubiUty) differs significantly. Most gas separation, pervaporation, and reverse osmosis membranes use dense membranes to perform the separation. However, these membranes usually have an asymmetric stmcture to improve the flux. 

For weU-defined reaction zones and irreversible, first-order reactions, the relative reaction and transport rates are expressed as the Hatta number, Ha (16). Ha equals (k- / l ) where k- = reaction rate constant, = molecular diffusivity of reactant, and k- = mass-transfer coefficient. Reaction... 

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, usiag software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Ke. To faciUtate these calculations, the foUowiag data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sb, is defined as Sh = 0.04 S c , where Sc is the Schmidt... 

The net transport of component A in the +2 direction in the centrifuge is equal to the sum of the convective transport and the axial diffusive transport. At the steady state the net transport of component A toward the product withdrawal point must be equal to the rate at which component A is being withdrawn from the top of the centrifuge. Thus, the transport of component is given by equation 72 ... 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

These values are as much as one hundred times larger than those typically observed in conventional liquids. The improved transport rates in SCFs versus liquid solvents are important in practical appheations including supercritical extraction. Furthermore, carbon dioxide diffuses through condensed-hquid phases (e.g., adsorbents and polymers) faster than do typical solvents which have larger molecular sizes. 

FIG. 25-6 Lapse-rate characteristics of atmospheric-diffusion transport of stack emissions. 

The experimental value for Agl is 1.97 FT cirT1 [16, 3], which indicates that the silver ions in Agl are mobile with nearly a thermal velocity. Considerably higher ionic transport rates are even possible in electrodes, by chemical diffusion under the influence of internal electric fields. For Ag2S at 200 °C, a chemical diffusion coefficient of 0.4cm2s, which is as high as in gases, has been measured... 

Rabt Ratio of transport rate by thermal diffusion to that by Pick s law ... 

The above methods measure ion transport rates as ionic conductivities. By varying the parameters of the experiment, it is often possible to indirectly identify the mobile ion(s),173 and in some cases to estimate individual ion mobilities or diffusion coefficients.144 Because of the uncertainty in identifying and quantifying mobile ions in this way, EQCM studies that provide the (net) mass change accompanying an electrochemical process36 have played an important complementary role. 

Laminar flame speed is one of the fundamental properties characterizing the global combustion rate of a fuel/ oxidizer mixture. Therefore, it frequently serves as the reference quantity in the study of the phenomena involving premixed flames, such as flammability limits, flame stabilization, blowoff, blowout, extinction, and turbulent combustion. Furthermore, it contains the information on the reaction mechanism in the high-temperature regime, in the presence of diffusive transport. Hence, at the global level, laminar flame-speed data have been widely used to validate a proposed chemical reaction mechanism. 

In Og (Figure 8.1.5b), xmlike in the Ig case, the fuel jet momentum dispersed and the centerline velocity decayed rapidly owing to the lack of buoyancy. As a result, the fuel molecules diffused in every direction and formed a quasi-spherical flame. The slow diffusion processes (1) limited the transport rates of the fuel and oxygen into the flame zone and (2) decreased... 

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