Diffusivities volumetric

Column Si. Size-exclusion chromatography columns are generally the largest column on a process scale. Separation is based strictly on diffusion rates of the molecules inside the gel particles. No proteins or other solutes are adsorbed or otherwise retained owing to adsorption, thus, significant dilution of the sample of volume can occur, particularly for small sample volumes. The volumetric capacity of this type of chromatography is determined by the concentration of the proteins for a given volume of the feed placed on the column. 

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... 

An optimized relationship is obtained between the beU jar, 60° swing-leaf valve, LN trap, baffle for the oil, and the plane of action for the diffusion pump (DP) top jet. The valve open area equals 0.38 of the cross-sectional area of the inside diameter of the furnace. The volumetric speed factor for water vapor is thus 0.38 x 0.9 crr 0.34, where 0.9 is the Clausing factor. 

The Displacement Distance theory suggests that since the stmcture of the flame is only quantitatively correct, the flame height can be obtained through the use of the displacement length or "displacement distance" (35,36) (eq. 12), where h = flame height, m V = volumetric flow rate, m /s and D = diffusion coefficient. 

Consider the case of the simple Bunsen burner. As the tube diameter decreases, at a critical flow velocity and at a Reynolds number of about 2000, flame height no longer depends on the jet diameter and the relationship between flame height and volumetric flow ceases to exist (2). Some of the characteristics of diffusion flames are illustrated in Eigure 5. 

Ertl and DuUien [ibid.] found that Hildebrand s equation could not fit their data with B as a constant. They modified it by applying an empirical exponent n (a constant greater than unity) to the volumetric ratio. The new equation is not generally useful, however, since there is no means for predicting /i. The theory does identify the free volume as an important physical variable, since n > for most hquids implies that diffusion is more stronglv dependent on free volume than is viscosity. 

Volumetric mass transfer coefficient, kLa The proportionality coefficient reflecting both molecular diffusion, turbulent mass transfer, and specific area for mass transfer. 

Manometric and volumetric methods (kinetics) Thermogravimetry (kinetics from very thin films to thick scales stoichiometry) Electrical conductivity of oxides and allied methods (defect structures conduction mechanisms transport numbers) Radioactive tracers and allied methods (kinetics self diffusion markers)... 

In their analysis, however, they neglected the surface tension and the diffusivity. As has already been pointed out, the volumetric mass-transfer coefficient is a function of the interfacial area, which will be strongly affected by the surface tension. The mass-transfer coefficient per unit area will be a function of the diffusivity. The omission of these two important factors, surface tension and diffusivity, even though they were held constant in Pavlu-shenko s work, can result in changes in the values of the exponents in Eq. (48). For example, the omission of the surface tension would eliminate the Weber number, and the omission of the diffusivity eliminates the Schmidt number. Since these numbers include variables that already appear in Eq. (48), the groups in this equation that also contain these same variables could end up with different values for the exponents. 

Baranowski [680] concluded that the decomposition of nickel hydride was rate-limited by a volume diffusion process the first-order equation [eqn. (15)] was obeyed and E = 56 kJ mole-1. Later, Pielaszek [681], using volumetric and X-ray diffraction measurements, concluded from observations of the effect of copper deposited at dislocations that transportation was not restricted to imperfect zones of the crystal but also occurred by diffusion from non-defective regions. The role of nickel hydride in catalytic processes has been reviewed [663]. 

Two ways to reduce the diffusion length in TBRs are 1) use of smaller catalyst particles, or 2) use of an egg-shell catalyst. The first remedy, however, will increase pressure drop until it becomes unacceptable, and the second reduces the catalyst load in the reaction zone, making the loads of the TBR and the MR comparable. For instance, the volumetric catalyst load for a bed of 1 mm spherical particles with a 0.1 mm thick layer of active material is 0.27. The corresponding load for a monolithic catalyst made from a commercial cordierite structure (square cells, 400 cpsi, wall thickness 0.15 mm), also with a 0.1 mm thick layer of active material, is 0.25. 

The convective mass flows in and out are obtained by multiplying the respective concentrations by the volumetric flow rate, which is equal to Ag v. The diffusive mass flows are calculated from the inlet and outlet concentration gradients using the multiplying factor of Ag D. 

For all the essential nutrient ions, the diffusion coefficient, Du is essentially the same with a value of around 10 cm s whereas the water flux at the root surface is typically of the order 10 cm s for soils at around field capacity. The tortuosity factor typically scales with the volumetric moisture content over quite a wide range of moisture content, i.e., / 0. As the soil becomes drier, the water flux will decline much faster than the tortuosity factor due to the typi-... 

The adsorbent—a powder generally, but it could be a metal or oxide film— is placed in a glass tube (the adsorption cell C in Fig. 15) which is connected to the volumetric and vacuum lines. The bottom part of the tube, which contains the adsorbent and is located in the calorimeter cell, is made of thin-walled (0.2-0.3 mm) blown tubing (A in Fig. 18). In order to avoid the slow diffusion of gases through a thick layer of adsorbent (see Section VII.A), the sample is often placed in the annular space between the inner wall of the adsorption cell and the outer wall of a cylinder made of glass,... 

This simplified description of molecular transfer of hydrogen from the gas phase into the bulk of the liquid phase will be used extensively to describe the coupling of mass transfer with the catalytic reaction. Beside the Henry coefficient (which will be described in Section 45.2.2.2 and is a thermodynamic constant independent of the reactor used), the key parameters governing the mass transfer process are the mass transfer coefficient kL and the specific contact area a. Correlations used for the estimation of these parameters or their product (i.e., the volumetric mass transfer coefficient kLo) will be presented in Section 45.3 on industrial reactors and scale-up issues. Note that the reciprocal of the latter coefficient has a dimension of time and is the characteristic time for the diffusion mass transfer process tdifl-GL=l/kLa (s). 

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