Structure, Diffusivity, and Mass Transfer

In this chapter we examine some issues in mass transfer. The reader has already been introduced to some of the key aspects. In Chapter 3 (Section 7), flocculation kinetics of colloidal particles is considered. It shows the importance of diffusivity in the rate process, and in Equation 3.72, the Stokes-Einstein equation, the effect of particle size on diffusivity is observed, leading to the need to study sizes, shapes, and charges on colloidal particles, which is taken up in Chapter 3 (Section 4). Similarly some of the key studies in mass transfe in surfactant systems— dynamic surface tension, smface elasticity, contacting and solubilization kinetics—are considered in Chapter 6 (Sections 6, 7, 10, and 12 with some related issues considered in Sections 11 and 13). These emphasize the roles played by different phases, which are characterized by molecular aggregation of different kinds. In anticipation of this, the microstructures are discussed in detail in Chapter 4 (Sections 2,4, and 7). Section 2 also includes some discussion on micellization-demicellization kinetics. 

In this chaptCT we focus our attention on key optical methods and nuclear magnetic resonance (NMR), which have been indispensable for quantitative descriptions of size and structure, and diffusivity, where size and structure play an important role. Whereas in the previous chapters we have tended to focus on the overall dynamics, we concentrate here at the smallest scale needed to understand what the fundammtal building blocks are in those systems. With the exception of NMR, the other methods are restricted to transparent systems. This can sometimes be a drawback, as in the study of water-in-crude oil emulsions, which are black in color. These are very important systems industrially and require de-emulsification. NMR techniques for measurement of drop size distributions in such emulsions, while beyond the scope of this chapter, have been reviewed by Pena and Hirasaki (2003). 

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Q Size, Shape, Structure, Diffusivity, and Mass Transfer... 

The A, B and C terms are related to flow anisotropy, molecular longitudinal diffusion and mass transfer processes, respectively. The theoretical support for the Knox equation was derived by Horvath [12]. The A term cannot be expressed simply. The theoretical treatment links A to structural parameters of the column packing, porosity, pore volume, pore diameter and tortuosity [12]. A is related to the flow pattern and the general band spreading due to "eddy" diffusion [13]. The B term (longitudinal molecular diffusion) was written as [13] ... 

The inner surface area of solid catalysts is mainly distributed in the pores and channels of crystal-particles, and furthermore the diffusion and mass transfer dm-ing reaction process is directly dependent on the pore structure. Hence, the pore size and pore volume are sometimes more important than the surface area of the pore as structural information. 

The drying of solid food matrices depends heavily on diffusion and mass transfer through the cells and tissue. The presence of intact cell membranes in the food raw material limits mass transfer processes due to their barrier function. Furthermore, the tissue structure and the network of intercellular air spaces affect mass transfer during drying. 

The necessity of forming zeolite powders into larger particles or other structures stems from a combination of pressure drop, reactor/adsorber design and mass transfer considerahons. For an adsorption or catalytic process to be productive, the molecules of interest need to diffuse to adsorption/catalytic sites as quickly as possible, while some trade-off may be necessary in cases of shape- or size-selective reactions. A schematic diagram of the principal resistances to mass transfer in a packed-bed zeolite adsorbent or catalyst system is shown in Figure 3.1 [69]. 

A gas-solid reaction usually involves heat and mass transfer processes and chemical kinetics. One important factor which complicates the analysis of these processes is the variations in the pore structure of the solid during the reaction. Increase or decrease of porosity during the reaction and variations in pore sizes would effect the diffusion resistance and also change the active surface area. These facts indicate that the real mechanism of gas-solid noncatalytic reactions can be understood better by following the variations in pore structure during the reaction. 

With cetyl alcohol, there is the complication that the polarity of the molecule may cause it to reside at the surface of the droplet, imparting additional colloidal stability. Here, the surfactant and costabilizer form an ordered structure at the monomer-water interface, which acts as a barrier to coalescence and mass transfer. Support for this theory lies in the method of preparation of the emulsion as well as experimental interfacial tension measurements [79]. It is well known that preparation of a stable emulsion with fatty alcohol costabilizers requires pre-emulsification of the surfactants within the aqueous phase prior to monomer addition. By mixing the fatty alcohol costabilizer in the water prior to monomer addition, it is believed that an ordered structure forms from the two surfactants. Upon addition of the monomer (oil) phase, the monomer diffuses through the aqueous phase to swell these ordered structures. For long chain alkanes that are strictly oil-soluble, homogenization of the oil phase is required to produce a stable emulsion. Although both costabilizers produce re-... 

Cybulski and Moulijn [27] proposed an experimental method for simultaneous determination of kinetic parameters and mass transfer coefficients in washcoated square channels. The model parameters are estimated by nonlinear regression, where the objective function is calculated by numerical solution of balance equations. However, the method is applicable only if the structure of the mathematical model has been identified (e.g., based on literature data) and the model parameters to be estimated are not too numerous. Otherwise the estimates might have a limited physical meaning. The method was tested for the catalytic oxidation of CO. The estimate of effective diffusivity falls into the range that is typical for the washcoat material (y-alumina) and reacting species. The Sherwood number estimated was in between those theoretically predicted for square and circular ducts, and this clearly indicates the influence of rounding the comers on the external mass transfer. 

Kinetic measurements, infrared investigations and the model calculations give a consistent result, which allows one to understand the factors determining the width of A/F windows on the lean side. These factors are the sorption behavior of carbon monoxide, oxygen and nitrogen oxide as function of temperature and partial pressures and mass transfer influences controlled by the porous structures of the washcoat resp. the boundary layer gas diffusion. 

Work in the area of simultaneous heat and mass transfer has centered on the solution of equations such as 1—18 for cases where the structure and properties of a solid phase must also be considered, as in drying (qv) or adsorption (qv), or where a chemical reaction takes place. Drying simulation (45—47) and drying of foods (48,49) have been particulady active subjects. In the adsorption area the separation of multicomponent fluid mixtures is influenced by comparative rates of diffusion and by interface temperatures (50,51). In the area of reactor studies there has been much interest in monolithic and honeycomb catalytic reactions (52,53) (see Exhaust CONTROL, industrial). For these kinds of applications psychrometric charts for systems other than air—water would be useful. The construction of such has been considered (54). 

Dong, L. L., Cheung, C. S., and Leung, C. W. "Heat Transfer Characteristics of an Impinging Inversion Diffusion Flame Jet. Part I Free Flame Structure." International Journal of Heat and Mass Transfer 50 (2007) 5108-23. 

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