Transfer lumped film

The transport dispersive model (TDM) is an extension of the transport model and summarizes the internal and external mass transfer resistance in one lumped film (= effective) transfer coefficient, keii (compare Eq. 6.30) ... 

Lujuid-Pha.se Transfer. It is difficult to measure transfer coefficients separately from the effective interfacial area thus data is usually correlated in a lumped form, eg, as k a or as These parameters are measured for the Hquid film by absorption or desorption of sparingly soluble gases such as O2 or CO2 in water. The Hquid film resistance is completely controlling in such cases, and kjji may be estimated as since x (Fig. 4). This... 

If the degree of superheat is large, it will be necessary to divide the temperature profile into sections and determine the mean temperature difference and heat-transfer coefficient separately for each section. If the tube wall temperature is below the dew point of the vapour, liquid will condense directly from the vapour on to the tubes. In these circumstances it has been found that the heat-transfer coefficient in the superheating section is close to the value for condensation and can be taken as the same. So, where the amount of superheating is not too excessive, say less than 25 per cent of the latent heat load, and the outlet coolant temperature is well below the vapour dew point, the sensible heat load for desuperheating can be lumped with the latent heat load. The total heat-transfer area required can then be calculated using a mean temperature difference based on the saturation temperature (not the superheat temperature) and the estimated condensate film heat-transfer coefficient. 

To prepare thin, uniform smears, place a drop of saline on a glass slide (1 by 3 in. [ca. 2.5 by 7.5 cm]). With an applicator stick, transfer a small, representative portion of the specimen to the drop of saline, and mix the two. Spread the solution into a film by rolling the applicator stick along the surface. Remove any lumps. 

Ma et al. [104] attributed a decrease in diffusivity with an increase in initial concentration to pore diffusion effects. Because zeolites are bi-dispersed sorbents, both surface and pore diffusions may dominate different regions. In micropores, surface diffusion may be dominant, while pore diffusion may be dominant in macropores. This, therefore, supports the use of a lumped parameter (De). To explore further the relative importance of external mass transfer vis-a-vis internal diffusion, Biot number (NBl — kf r0/De) was considered. Table 9 summarizes the NBi values for the four initial concentrations. The NBi values are significantly larger than 100 indicating that film diffusion resistance was negligible. 

In this report, a kinetic model based on the solid film linear driving force assumption is used. Unlike the equilibrium-dispersive model, which lumps all transfer and kinetic effects into an effective dispersion term, the kinetic model is effective when the column efficiency is low and the effects of column kinetics are significant. 

The other subgroup of the lumped rate approach consists of the reaction dispersive model where the adsorption kinetic is the rate-limiting step. It is an extension of the reaction model (Section 6.2.4.3). Like the mass transfer coefficient in the transport dispersive model, the adsorption and desorption rate constants are considered as effective lumped parameters, kads,eff and kdes.eff- Since no film transfer resistance exists (Cpi = q), the model can be described by Eq. 6.79 ... 

In this second lumped kinetic model and in contrast to the first one, we assume that the kinetics of adsorption-desorption is infinitely fast but that the mass transfer kinetics is not. More specifically, the mass transfer kinetics of the solute to the surface of the adsorbent is given by either the liquid film linear driving force model or the solid film linear driving force model. In the former case, instead of Eq. 6.41, we have for the kinetic equation ... 

According to Glueckauf [27,28], the lumped mass transfer coefficient, km, is related to the film mass transfer coefficient and to the pore diffusion by the equation ... 

In these kinetic models of chromatography, all the sources of mass transfer resistance are lumped into a single equation. In the case of the solid film linear driving force model, we have for each component i... 

Henry s law (i.e., c = po/H) relates the equilibrium oxygen solubility in the liquid (c ) to oxygen partial pressure in the gas (po) by the corresponding Henry s law constant (H). Because the liquid film mass transfer coefficient, l, is difficult to measure independently, kj a (i.e., times a) is used. It is a lumped parameter known as the volumetric mass transfer coefficient to characterize the overall mass transfer rate. 

The result obtained from the film theory is that the mass transfer coefficient is directly proportional to the diffusion coefficient. However, the experimental mass transfer data available in the literature [6], for gas-liquid interfaces, indicate that the mass transfer coefficient should rather be proportional with the square root of the diffusion coefficient. Therefore, in many situations the film theory doesn t give a sufficient picture of the mass transfer processes at the interfaces. Furthermore, the mass transfer coefficient dependencies upon variables like fluid viscosity and velocity are not well understood. These dependencies are thus often lumped into the correlations for the film thickness, 1. The film theory is inaccurate for most physical systems, but it is still a simple and useful method that is widely used calculating the interfacial mass transfer fluxes. It is also very useful for analysis of mass transfer with chemical reaction, as the physical mechanisms involved are very complex and the more sophisticated theories do not provide significantly better estimates of the fluxes. Even for the description of many multicomponent systems, the simplicity of the model can be an important advantage. 

We are now going to apply this algorithm to one of the most important cases, diffusion through a boundaiy layer. Here we consider the boundary layer to be a hypothetical "stagnant film" in which all the re.sistance to mass transfer is lumped. 

In this stagnant film model, we consider all the resistance to mass transfer to be lumped into the thickness 5. The reciprocal of the mass transfer coefficient can be thought of as this resistance... 

The adhesive transfer of organic plastics has some special features of it own. Makinson and Tabor [24] observed that polytetrafluoroethylene sliding on glass left transferred material on the counter surface in the form of lumps, ribbons, sheets or very thin films, depending on the rubbing conditions. Pooley and Tabor [25], who studied the transfer process more intensively, also reported the behavior of other polymers such as fluorocarbon copolymers, polyethylene, polypropylene, polystyrene, polymethylmethacrylate and polyvinyl chloride. Descriptions of transfer in relation to wear were reported for PTFE by Tanaka tt ai. [20] and for polyethylene by Miller a.1. [21]... 

Gonsequently, the two remaining groups considering columns with a low number of stages are the lumped and the general rate models. Under the simplification mentioned above, general rate models take into account the individual mass transfer resistance in the liquid film/boundary layer (Equation 6.80) and inside the pore... 

If the overall mass transfer resistance is lumped in the fluid film surrounding the particle or in the thin skin at the particle surface, a simple, lumped parameter, film resistance model can be used ... 

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