Mass, effective dispersion

Colorant containing annatto and Ca caseinate as carrier mixed with water to be added directly to cheese milk yielding uniform colored cheese mass Water-dispersible beadlet of p-carotene is mixed with oil to attein composition that remains stable even in presence of polyphosphates and with antioxidant action even in absence of ascorbic acid Blending carotenoid pigment and soybean fiber (wifii tomato juice) as effective ingredient for dispersion stability... 

Solve the tanker truck spill problem of Example 2.2 using explicit, central differences to predict concentrations over time in the groundwater table. Compare these with those of the analytical solution. The mass spilled is 3,000 kg of ammonia over 100 nf, and the effective dispersion coefficient through the groundwater matrix is 10 m2/s. 

Note Since the model is linear for the special case considered, the same equation is also satisfied by the other three variables.) The following observations may be made from Eq. (98) that expresses the dimensionless dispersion coefficient A (i) The first term describes dispersion effects due to velocity gradients when adsorption equilibrium exists at the interface. We note that this expression was first derived by Golay (1958) for capillary chromatography with a retentive layer, (ii) The second term corresponds to dispersion effects due to finite rate of adsorption (since this term vanishes if we assume that adsorption and desorption are very fast so that equilibrium exists at the interface), (iii) The effective dispersion coefficient reduces to the Taylor limit when the adsorption rate constant or the adsorption capacity is zero, (iv) As is well known (Rhee et al., 1986), the effective solute velocity is reduced by a factor (1 + y). (v) For the case of irreversible adsorption (y — oo and Da —> oo), the dispersion coefficient is equal to 11 times the Taylor value. It is also equal to the reciprocal of the asymptotic Sherwood number for mass transfer in a circular... 

Mass spectrometry has been an established analytical technique in organic chemistry for many years. Until recently, however, the very low volatility of proteins made mass spectrometry useless for the investigation of these molecules. This difficulty has been circumvented by the introduction of techniques for effectively dispersing proteins and other macromolecules into the gas phase. These methods are called matrix-assisted laser desorption-ionization (MALDI) and electrospray spectrometry. We will focus on... 

Unlike the tablet dosage form, dmg particles in a capsule are not subjected to high compression forces, which tend to compact the powder or granules and reduce the effective surface area. Hence, upon disruption of the shell, the encapsulated powder mass should disperse rapidly to expose a large surface area to the G1 fluid. This rate of dispersion, in turn, influences the rate of dissolution and, therefore, bioavailability. It is, therefore, important to have suitable diluents and/or other excipients in a capsule dosage form, particularly when the drug is hydrophobic (Fig. 9.3). 

Ultrasound also presents the capacity to emulsify a mixture of immiscible liquids due to cavitational processes occurring at the liquid/liquid phase boundary effectively dispersing the biphasic system. This sonoemulsification allows product extraction from the aqueous phase, but at the same time may also prevent electrode passivation whilst keeping very fast rates of mass transport. The reduction of MG in the presence of a sonoemulsion of toluene (see Sect. 2.10.3.4) is one fine example of this. Another example of successful electroorganic process in a sonoemulsi-fied mixture is the oxidation of carboxylic acids, known as Kolbe processes (see Sect. 2.10.3.5). 

To suppress the effect of certain molecular characteristic on sample retention volume so that the resulting chromatogram reflects mainly or even exclnsively other molecular characteristic(s) of sample. In practice, it is usually attempted to partially or fully suppress the influence of polymer molar mass. In this instance, the coupling of LC retention mechanisms may allow assessment of chemical structure or physical architecture of a complex polymer irrespective of its molar mass average and dispersity. Under favorable conditions, also the constituents of a complex polymer system with similar molar masses can be discriminated and molar mass of one constituent determined. For example, in the case of a two-component polymer system, the molar mass effect can be suppressed selectively for one constituent so that it elutes in a completely different retention volume compared with the retention volume pertaining to SEC. In some cases, the... 

The two equations for the mass and heat balance, Eqs. (4.10.125) and (4.10.126) or the dimensionless forms represented by Eqs. (4.10.127), (4.10.128) and (4.10.130), consider that the flow in a packed bed deviates from the ideal pattern because of radial variations in velocity and mixing effects due to the presence of the packing. To avoid the difficulties involved in a rigorous and complicated hydrodynamic treatment, these mixing effects as well as the (in most cases negligible contributions of) molecular diffusion and heat conduction in the solid and fluid phase are combined by effective dispersion coefficients for mass and heat transport in the radial and axial direction (D x, Drad. rad. and X x)- Thus, the fluxes are expressed by formulas analogous to Pick s law for mass transfer by diffusion and Fourier s law for heat transfer by conduction, and Eqs. (4.10.125) and (4.10.126) superimpose these fluxes upon those resulting from convection. These different dispersion processes can be described as follows (see also the Sections 4.10.6.4 and 4.10.7.3) ... 

The effective dispersion coefficients of heat and mass (Xax, Dax) te calculated by the Pedet numbers [Pem,ax= Wsdp/(eDax), P h.ax = WsCpPmoidp/kax]- Both numbers are approximately 2 (Section 4.10.6.4). Correlations that also consider the static contribution are (VDI, 2002) ... 

The influence of the axial dispersion coefficient of mass Dax on the spread of the reaction zone is even smaller, as shown in Figure 6.9.18 [see also Kem (2003)]. Even modeling with an unrealistically high value of the effective dispersion coefficient [lOOOx higher than the correct value as calculated by Eq. (6.9.33)] does not lead to a significant enlargement of the reaction zone. [Remark if the axial dispersion of mass is completely neglected in the model D = 0), the width of the reaction zone... 

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