Molar diffusion resistance

The general definition of the effectiveness factor states that the factor describes the ratio between the real molar flux (A)) and the molar flux (AT) that would be obtained if the reaction proceeded in the absence of diffusion resistance. This ratio is equal to the ratio of observed rate and the rate if the diffusion resistance does not have an influence on reaction rate. 

Diffusion resistance R can be generally expressed as a function of a slope of the coulometric titration curve dV/dx of the host material with molar share X of diffusing ions [34] ... 

A simple rectifying column consists of a tube arranged vertically and supplied at the bottom with a mixture of benzene and toluene as vapour. At the top a condenser returns some of the product as a reflux which flows in a thin film down the inner wall of the tube. The tube is insulated and heat losses can be neglected. At one point in the column the vapour contains 70 mol% benzene and the adjacent liquid reflux contains 59 moi% benzene. The temperature at this point is 365 K. Assuming the diffusional resistance to vaponr transfer to be equivalent to the diffusional resistance of a stagnant vapour layer 0.2 mm thick, calculate the rate of interchange of benzene and toluene between vapour and liquid. The molar latent heats of the two materials can be taken as equal. The vapour pressure of toluene at 365 K is 54.0 kN/nt2 and the diffusivity of the vapours is 0.051 cm2/s... 

At a particular location in a distillation column, where the temperature is 350 K and the pressure 500 m Hg, the tnol fraction of the more volatile component in the vapour is 0.7 at the interface with the liquid and 0.5 in the bulk of the vapour. The molar latent heat of the more volatile component is 1.5 times that of the less volatile. Calculate the mass transferrates (kmol m s-11 of the two components. The resistance to mass transfer in the vapour may be considered to lie in a stagnant film of thickness 0.5 mm at the interface. The diffusivity in the vapour mixture is 2 x )() ° mV. ... 

We will now describe the application of the two principal methods for considering mass transport, namely mass-transfer models and diffusion models, to PET polycondensation. Mass-transfer models group the mass-transfer resistances into one mass-transfer coefficient ktj, with a linear concentration term being added to the material balance of the volatile species. Diffusion models employ Fick s concept for molecular diffusion, i.e. J = — D,v ()c,/rdx, with J being the molar flux and D, j being the mutual diffusion coefficient. In this case, the second derivative of the concentration to x, DiFETd2Ci/dx2, is added to the material balance of the volatile species. 

Reid, Sherwood and Prausnitz [11] provide a wide variety of models for calculation of molecular diffusion. Dr is the Knudsen diffusion coefficient. It has been given in several articles as 9700r(T/MW). Once we have both diffusion coefficients we can obtain an expression for the macro-pore diffusion coefficient 1/D = 1/Dk -i-1/Dm- We next obtain the pore diffusivity by inclusion of the tortuosity Dp = D/t, and finally the local molar flux J in the macro-pores is described by the famiUar relationship J = —e D dcjdz. Thus flux in the macro-pores of the adsorbent product is related to the term CpD/r. This last quantity may be thought of as the effective macro-pore diffusivity. The resistance to mass transfer that develops due to macropore diffusion has a length dependence of R]. 

Pharmaceutical scientists assess and express drug permeation across membrane barriers in terms of flux. Flux measures the molar unit of a drug that permeates a resistant barrier (e.g., skin or gastrointestinal epithelial cells) per unit time and surface area (Box 13.1). Permeation enhancers, such as alcohols and surfactants, increase flux by modulating resistance factors that counteract drug diffusion across barriers at the site of administration. 

We can think of the air and liquid films as being resistances in series. In this respect, they are similar to thermal resistances. If we designate the acetone by subscript A (i.e., the diffusing species) and the air by subscript B (i.e., the inert or insoluble species), we can write an expression for the concentration of each species in terms of their individual molar densities ... 

Point efficiency is usually discussed in terms of the two-film theory. The theory postulates resistances to mass transfer in both the vapor and liquid films near a vapor-liquid ihterface (Fig. 7.2a). The molar rate of diffusion, N (moles/s), is given by... 

The driving force for the transport is provided by a concentration gradient as the reactant moves further towards the center of the pellet its concentration is decreased by reaction. The resistance to the transport mainly originates from collisions of the molecules, either with each other or with the pore walls. The latter dominate when the mean free path of the molecules is larger than the pore diameter. Usually both type of collisions are totally random, which amounts to saying that the transport mechanism is of the diffusion type. Hence the rate of transport, expressed as a molar flux in mol mp2 s-1, in the case of equimolar counterdiffusion can be written as ... 

The efficiency concept is based on two-resistance theory and is usually expressed in terms of the molar rate of diffusion ... 

A detailed investigation of the effect of micellar solubilization on the transport of lipids has been made by Westergaard and Dietschy [59]. They studied in vitro uptake of lipids into rabbit intestinal disks by varying the proportions of lipid and bile salts in mixed micelles in 3 different ways. Either lipid concentration was increased with bile salts kept at a constant level, lipid concentration was unchanged while bile salt concentration was varied, or both lipid and bile salt concentration was increased with the molar ratio kept constant. Theoretical calculations of how the mass of the lipid probe was distributed between the aqueous and the micellar compartment showed that there was a good correlation between calculated aqueous monomer concentration and experimentally obtained values for lipid uptake. The rate of uptake is thus proportional to the aqueous monomer concentration of a particular lipid. The conclusion drawn was that diffusion of the lipid molecules in monomeric form through the aqueous phase is an obligatory step before uptake into the plasma membrane, and that the role of bile salt is therefore to overcome the resistance of the unstirred water layer by micellar solubilization. 

Consider the situation shown in Figure 3.5. Since the equilibrium-distribution curve for the system is unique at fixed temperature and pressure, then yA, in equilibrium with xA L, is as good a measure of xA L as xA[ itself, and moreover, it is on the same thermodynamic basis as yA G. The entire two-phase mass-transfer effect can then be measured in terms of an overall mass-transfer coefficient, Ky, which includes the resistance to diffusion in both phases in terms of a gas-phase molar fraction driving force,... 

In its applicability to self diffusion and to gaseous systems, the tendency of the resistivities to be constant was first observed by Ljunggren. In condensed systems in general, the conditions are more complicated, as shown for example by the usefulness of Stokes law for molar frictions. 

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