Diffusional interaction methods

Vogelpohl (193) and Medina et al. (203) applied the diffusional interaction method for predicting ternary distillation composition profiles using binary data. They achieved this by eliminating the first two steps and assuming that all the mass transfer resistance is in the vapor. This procedure was shown to give excellent agreement with experimental data for dissimilar components. Biddulph and Kalbassi (194), however, report some discrepancies between prediction and experiment due to this assumption. 

Diffusional interaction methods have also been applied successfully to packed columns. Gorak (204) found that the Krishna-Standart model (205) is relatively simple and sufficiently accurate to predict multicomponent composition profiles. Gorak s own variation of the diffusional interaction method was also reported to predict experimental data well, while use of HETP was reported to give poor data predictions. 

Diffuslonal interaction methods. These calculate component efficiencies, but account for diffusional interactions. The calculation procedure is based on the Maxwell-Stefan diffusion equations, as developed by Krishna et al. (200,201). The equations are complex and are presented in the original reference. Lockett (12) has an excellent summary. For a ternary system, the steps below are followed (12) ... 

Additional data of Arnold and Toor are compared to the predictions of the linearized equations and of the effective diffusivity models in the triangular diagram in Figure 6.4. Clearly, the agreement with the data is very bad indeed. Thus, we have our second demonstration of the inability of the effective diffusivity method to model systems that exhibit strong diffusional interactions. ... 

Using an entirely different approach to the modeling of multicomponent mass transfer in distillation (an approach that we describe in Chapter 14), Krishnamurthy and Taylor (1985c) found significant differences in design calculations involving nonideal systems. For an almost ideal system (a hydrocarbon mixture), pseudobinary methods were found to be essentially equivalent to a more rigorous model that accounted for diffusional interaction effects. 

In any event, we hope it is now well understood that mass transfer in multicomponent systems is described better by the full set of Maxwell-Stefan or generalized Fick s law equations than by a pseudobinary method. A pseudobinary method cannot be capable of superior predictions of efficiency. For a simpler method to provide consistently better predictions of efficiency than a more rigorous method could mean that an inappropriate model of point or tray efficiency is being employed. In addition, uncertainties in the estimation of the necessary transport and thermodynamic properties could easily mask more subtle diffusional interaction effects in the estimation of multicomponent tray efficiencies. It should also be borne in mind that a pseudobinary approach to the prediction of efficiency requires the a priori selection of the pair of components that are representative of the... 

A comparison of the film models that ignore diffusional interaction effects (the effective diffusivity methods) with the film models that take multicomponent interaction effects into account (Krishna-Standart (1976), Toor-Stewart-Prober (1964), Krishna, (1979b, c) and Taylor-Smith, 1982). 

We see from these figures that the mass transfer models that take diffusional interactions into account are quite a lot better than the effective diffusivity model, which underpredicts the rate of condensation of 2-propanol in every case. However, the effective diffusivity methods give good predictions of the overall temperature drops (Fig. 15.19) although there is little to distinguish any of the models here on this basis. 

The number of theoretical plates is proportional to the column length and inversely proportional to the particle size. The advantage of using small particles is that they distribute flow more uniformly and, as a result, reduce the eddy diffusion, term A in the Van Deemter equation. However, the smaller particles increase the diffusional resistance of the solvent as well as the pressure drop (for a given flow rate). Choosing the flow rate is a critical parameter in developing an HPLC method. Low flow rates allow the analyte sufficient time to interact with the stationary phase and will affect both the B and C terms of the Van Deemter equation. 

It is well known that water interacts intermolecularly with proteins in aqueous solution and sometimes forms hydrogen bonds. This leads to significant biochemical activity of proteins. A lot of work on intermolecular interactions between water and proteins from various dimensions as studied from the point of view of their diffusional behavior using the field-gradient NMR method have appeared recently [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. 

Penetration of a substance is measured by the permeability coefficient, P, which could be converted to a measurable diffusional coefficient, D, if Pick s law applied strictly. In the more complex situation of a membrane barrier, Kedem and Katchalsky (1958, 1961) have shown that under rigidly controlled conditions there exist at least three parameters which must be considered when characterizing the behavior of a membrane toward a particular solute (1) the interaction between membrane and solvent (2) the interaction between solute and membrane and (3) the interaction between solute and solvent. The reflection coefficient, (T, measures relative rates of solute and solvent permeabilities in the system (Staverman, 1952) and is therefore a measure of semipermeability. Lp is the mechanical coefficient of filtration or pressure filtration coefficient, and co is the solute mobility or solute diffusional coefficient. In the case of living membranes, conditions such as volume flow, osmotic gradients, and cell volume can be manipulated in order to measure the phenomenological coefficients cr, o>, and Lp. Detailed discussions of the theories, methods, and problems involved in such... 

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