Cussler diffusion pdf free download

Electrolytes D. Reacting Systems E. Conclusions Chapter 7. Membranes without Mobile Carriers A. General Flux Equations B. The Onsager Relations across Membranes D. Conclusions Chapter 8. Carrier-Containing Membranes A. Facilitated Diffusion B. Counter-Transport D. Co-Transport E. Conclusions Chapter 9. Multicomponent Mass Transfer A. Concentration Profiles B. Multicomponent Mass-Transfer Coefficients C. Examples of Multicomponent Mass Transfer D. Conclusions Nomenclature References Subject Index.

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Support Center. Free Shipping Free global shipping No minimum order. Powered by. You are connected as. Connect with:. Thank you for posting a review! We value your input. Substituting for N1 from Eq. This system is academically ubiquitous, showing up again and again in problems of mass transfer. Indeed, if you read the literature, you can get the impres- sion that it is a system where mass transfer is very important, which is not true. Why is it used so much? Benzoic acid is studied thoroughly for three distinct reasons.

First, its concentration is relatively easily measured, for the amount present can be determined by titration with base, by ultraviolet spectrophotometry of the benzene ring, or by radioactively tagging either the carbon or the hydrogen. This is not true of all dissolutions. For example, the dissolution of aspirin is essentially independent of events in solution. Experiments with benzoic acid dissolving in water can be compared directly with heat transfer experiments.

These three reasons make this chemical system popular. Its concentration is about half saturated in 3 minutes. This particular problem is similar to the calculation of a half-life for radioactive decay. After 7 min, the bubble is 0. It is a rate constant for an interfacial physical reaction, most similar to the rate constant of an interfacial chemical reaction. This is not true for the other processes in this table. Four of the more common of these are shown in Table 8.

This variety is largely an experimental artifact, arising because the concentration can be measured in so many different units, including partial pressure, mole and mass fractions, and molarity. This is especially true for gas adsorption, distillation, and extraction described in Chapters 10— There, we will frequently use kx, the third form in Table 8.

In the membrane separations in Chapter 18, we will mention forms like kx but will carry out our discussion in terms of forms equivalent to k. To explore the ambi- guity more carefully, consider the packed tower shown schematically in Fig. Water trickles down through the column and absorbs the ammonia: ammonia is scrubbed out of the gas mixture with water.

Water nearly Ammonia scrubbing. In this example, ammonia is separated by washing a gas mixture with water. The ambiguities occur because the concentration difference causing the mass transfer changes and because the interfacial area between gas and liquid is unknown. The con- centration difference between interface and bulk is not constant but can vary along the height of the column. Which value of concentration difference should we use? In this book, we always choose to use the local concentration difference at a particular position in the column.

As an example, we again consider the packed tower in Fig. This may seem like cheating, but it works like a charm. This complication does not exist in dilute solution, just as it does not exist for the dilute diffusion described in Chapter 2. The consequence of this convection, which is like the concentrated diffusion problems in Section 3.

Fortunately, many transfer-in processes like distillation often approximate equimolar counterdiffusion, so there is little diffusion-induced convection. Also fortunately, many other solutions are dilute, so diffusion induced convection is minor. We will discuss the few cases where it is not minor in Section 9.

To spur this thought, try solving the examples that follow. The manufacturer expressed both pressures in mm Hg. Solution From Table 8. We want to correlate our results not in terms of this local value but in terms of a total experimental time t0.

The bed is fed with pure water, and the benzoic acid concentration at the sphere surfaces is at saturation; that is, it equals c1 sat. Solution By integrating a mass balance on a differential length of bed, we showed in Example 8. After all, these critics assert, you implicitly repeat this derivation every time you make a mass balance.

Why bother? Why not use klog and be done with it? This argument has merit, but it makes me uneasy. Thus we have a method for analyzing the results of mass transfer experiments. This method can be more convenient than diffusion when the experiments involve mass transfer across interfaces. Experiments of this sort include liquid—liquid extraction, gas absorption, and distillation. However, we often want to predict how one of these complex situations will behave.

We do not want to correlate experiments; we want to avoid experiments if possible. These numbers are often named, and they are major weapons that engineers use to confuse scientists. The characteristics of the common dimensionless groups frequently used in mass transfer correlations are given in Table 8.

In the same way, a Sherwood number of 2 means different things for a membrane and for a dissolving sphere. The accuracy of these correlations is typically of the order of thirty percent, but larger errors are not uncommon.

Raw data can look more like the result of a shotgun blast than any sort of coherent experiment because the data include wide ranges of chemical and physical properties. For example, the Reynolds number, that characteristic parameter of forced convection, can vary 10, times. Over a more moderate range, the correlations can be more reliable.

Many of the correlations in Table 8. This Sherwood number varies with Schmidt number, a charac- teristic of diffusion. These variations are surprisingly uniform. These correlations are rarely important in common separation processes like absorption and extraction. They can be important in leaching, in membrane separations, and in adsorption. However, the chief reason that these correlations are quoted in undergraduate and graduate courses is that they are close analogues to heat transfer.

Heat transfer is an older subject, with a strong theoretical basis and more familiar nuances. Often k varies with the square root of v0. Gas scrubbing in a wetted-wall column.

The problem is to calculate the length of the column necessary to reach a liquid concentration equal to ten percent saturation. How fast will it dissolve in a large volume of water?

How fast will it dissolve in a large volume of air? The solubility of benzoic acid in water is 0. Solution Before starting this problem, try to guess the answer. Will the mass transfer be higher in water or in air? Did you guess this? An experimental apparatus for the study of aeration. Oxygen bubbles from the sparger at the bottom of the tower partially dissolve in the aqueous solution.

How can we do this? Mass transfer correlations are developed using a method called dimensional analysis. Before embarking on this description, I want to emphasize that most people go through three mental states concerning this method. We now turn to the examples. This is especially true for deep-bed fermentors and for sewage treatment, where the rising bubbles can be the chief means of stirring.

We want to study this process using the equipment shown schematically in Fig. We plan to inject pure oxygen into a variety of aqueous solutions and measure the oxygen concentration in the bulk solution with oxygen selective electrodes. We measure the steady-state oxygen concentration as a function of position in the bed. This equation, a close parallel to the many mass balances in Section 8.

Now the dimensions or units on the left-hand side of this equation must equal the dimensions or units on the right-hand side. We cannot have centimeters per second on the left-hand side equal to grams on the right. We can solve these equations in terms of the two key exponents and thus simplify Eq. We choose the two key exponents arbitrarily. This analysis suggests how we should plan our experiments.

We want to cover the widest possible range of independent variables. Our resulting correlation will be a convenient and compact way of presenting our results, and everyone will live happily ever after. Unfortunately, it is not always that simple for a variety of reasons. First, we had to assume that the bulk liquid was well mixed, and it may not be. This can happen if the oxygen transferred is consumed in some sort of chemical reaction, which is true in aeration.

Third, we do not know which independent variables are important. We might suspect that ka varies with tank diameter, or sparger shape, or surface tension, or the phases of the moon. Such variations can be included in our analysis, but they make it complex.

Still, this strategy has produced a simple method of correlating our results. The foregoing objections are important only if they are shown to be so by experiment. Until then, we should use this easy strategy. Tablets of drug are placed in the basket. Samples are drawn from the water and analyzed. If the amount of drug dissolved is reproduceable, these tablets may be acceptable for marketing.

We want a dimensional analysis suitable for organizing our results. Thus we want to guess an answer which implies neglecting less important factors. We then try to guess the answer. Right away, we can see two possibilities. First, dissolution may be limited by mass transfer from the tablets to the edge of the basket. This says the basket radius R will be important. Second, dissolution may be limited by mass transfer from the basket to the surrounding solution.

Then the basket rotation will be important. This correlation will be successful only if we have guessed the right key variables. It may work if the tablets remain intact. Still, they are an easy way to correlate experi- mental results or to make estimates using the published relations summarized in Tables 8.

This case occurs more frequently than does transfer from an interface into one bulk phase; indeed, I had trouble dreaming up the examples earlier in this chapter. But what is Dc1? To illustrate this, consider the three examples shown in Fig. Equal temperature is the criterion for equilibrium, and the amount of energy transferred per time turns out to be proportional to the temperature difference between the liquids.

Everything seems secure. As a second example, shown in Fig. Driving forces across interfaces. In heat transfer, the amount of heat transferred depends on the temperature difference between the two liquids, as shown in a.

Two cases are shown.