Matrix rate factors

Matrix of dimensionless mass transfer rate factors with the elements defined as... 

Step 5 Calculate the elements of the matrix of mass transfer rate factors [O] from Eqs. (6.67) and (6.68). Step 6 Calculate the elements of the matrix of correction factors PE] using Eq. (6.76), which may be obtained from the Sylvester expansion... 

We may also write the elements of the rate factor matrix [[Pg.166]

The rate factor matrix [O] also is diagonal with all diagonal elements equal... 

The method of successive substitution can be a very effective way of computing the from Eqs. 8.3.24 when the mole fractions at both ends of the diffusion path y-g and y g, are known. In practice, we start from an initial guess of the fluxes and compute the rate factor matrix [< >]. The correction factor matrix [a] may be calculated from an application of Sylvester s expansion formula (Eq. A.5.20)... 

The parameter 3 in this expression accounts for the nonlinearity of the composition profiles it is, in fact, a high flux correction factor as is [3] in the matrix methods described above. Equation 8.5.18 involves no iteration because the rate factor <1> and the correction factor 3 can be calculated from Eqs. 8.5.15 all we need to know are the boundary conditions y Q and y Q. 

It is the eigenvalues (literally characteristic values ) of [0] that characterize the correction factor matrix [S]. Thus, the scalar rate factor 0 and correction factor S when multiplied by identity matrices frequently are quite good models for the behavior of the complete matrices [0] (or [ ]) and [H] in the exact and linearized methods. 

The binary K j may be calculated as a function of the appropriate Maxwell-Stefan diffusion coefficient from a suitable correlation or physical model (e.g., the surface renewal models of Chapter 10). These binary must also be used directly in the calculation of the rate factor matrix [ ] (cf. Eqs. 8.3.28 and 8.3.29). 

Taking the upper limit of this integral to be, the reduced distance from the wall at which the bulk compositions (ft,) are attained, we define a matrix of rate factors [O] by... 

The eigenvalues of the rate factor matrix are given by Eq. 10.4.34 with numerical values... 

The elements of the matrix of mass transfer rate factors are computed next using Eqs. 8.3.32... 

Matrix of mass transfer rate factors in linearized film model (Eq. 8.4.4) [ - ] Matrix of mass transfer rate factors in turbulent diffusion model (Eq. 10.3.9) [-]... 

Material produced from spray-drying processes are generally spherical and hollow due to process in which the solution of dissolved drug and polymer are sprayed as fine droplets and then rapidly dried in an inert stream of warm air. Spray-dried dispersions are oftentimes porous and fragile due to the escape of solvent through the solid matrix. Processing factors that influence the particle properties of the spray-dried dispersion (drying temperature, spray rate, droplet size, air flow, etc.) will influence the dissolution rate. 

The model should produce statistical statements on the lifetime in terms of the overall applied stress field, the overall volume of material, and boundary effects. Important input parameters are fiber packing geometry, fiber strength, matrix and interface creep exponents, rate factors in the stress-corrosion chemistry, and the applied stress level. 

Elution volume, exclusion chromatography Flow rate, column Gas/liquid volume ratio Inner column volume Interstitial (outer) volume Kovats retention indices Matrix volume Net retention volume Obstruction factor Packing uniformity factor Particle diameter Partition coefficient Partition ratio Peak asymmetry factor Peak resolution Plate height Plate number Porosity, column Pressure, column inlet Presure, column outlet Pressure drop... 

Removing an analyte from a matrix using supercritical fluid extraction (SEE) requires knowledge about the solubiUty of the solute, the rate of transfer of the solute from the soHd to the solvent phase, and interaction of the solvent phase with the matrix (36). These factors collectively control the effectiveness of the SEE process, if not of the extraction process in general. The range of samples for which SEE has been appHed continues to broaden. Apphcations have been in the environment, food, and polymers (37). 

In the inner-loop calculation sequence, component flow rates are computed from the MESH equations by the tridiagonal matrix method. The resulting bottoms-product flow rate deviates somewhat from the specified value of 50 lb mol/h. However, by modifying the component stripping factors with a base stripping factor, S, in (13-109) of 1,1863, the error in the bottoms flow rate is reduced to 0,73 percent. 

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