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Diffusion mass transfer in fluid systems: Mass Transfer in Fluid Systems

Why not use klog and be done with it? In the leaching of metal by pouring acid over ore, we assume that the acid is homogeneous, except in a thin layer next to the solid ore particles.

William Murphy
Saturday, January 27, 2018
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  • General questions and heterogeneous chemical reactions:

  • General Questions and Heterogeneous Chemical Reactions.

  • Diffusion : Mass Transfer in Fluid Systems. Calderbank and M.

  • Now the dimensions or units on the left-hand side of this equation must equal the dimensions or units on the right-hand side. Find the dissolution rate of a cholesterol gallstone 1 cm in diameter immersed in a solution of bile salts.

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Diffusion : Mass Transfer in Fluid Systems. Publication date ISBN hc pb hc pb. Personalised recommendations.

Jasmone is about times more soluble in toluene than in the suspension. Indeed, explaining this repeatedly is a large part of my consulting practice. These examples are important. How can we do this? You are evaluating a new mixed solvent for dewaxing that has physical processes like those of catechol.

  • We use practically the same procedure in this situation as we did previously; we develop a differential equation, and a solution containing arbitrary constants evolves. Bibliographic information.

  • The foregoing objections are important only if they are shown to be so by experiment.

  • Mass Transfer in Fluid Systems. Homogeneous Chemical Reactions.

  • Cite chapter How to cite?

Fundamentals of mass transfer-- 9. Multicomponent diffusion-- Part III. Skip to search Skip to main content. Diffusion of Interacting Species. ThesisUniversity of Illinois,

Its concentration is about half saturated in 3 minutes. If you have a system with the same solute concentration everywhere, will mass transfer occur? For example, one such process uses a mixture of propane and cresylic acid. Retaining the trademark enthusiastic style, the broad coverage now extends to biology and medicine. Answer: 0. Also fortunately, many other solutions are dilute, so diffusion induced convection is minor.

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Absorption-- Calderbank, Trans. This service is more advanced with JavaScript available. Diffusion : Mass Transfer in Fluid Systems. Free Convection.

  • Higbie, Trans.

  • 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. It can be reproduced by almost everyone who studies the subject.

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  • These numbers are often named, and they are major weapons that engineers use to confuse scientists.

  • Free Convection. After all, these critics assert, you implicitly repeat this derivation every time you make a mass balance.

Mass Transfer: 8. Diffusion is a key part of the undergraduate chemical engineering curriculum and at the core of understanding chemical purification and reaction engineering. Taylor, L. Multicomponent Diffusion. Full view. Lewis and W.

Mills, A. In this case, gas on the left yransfer being transferred into the liquid on the right. It is often in equilibrium with the concentration across the interface in a second, adjacent phase; we will defer discussion of transport across this interface until Section 8. Solution From Table 8. Problems 1. Estimate Ky in the units given.

The new edition offers increased coverage of unit operations, with chapters on absorption, distillation, extraction and adsorption. Problem URL. Minowa, Trans.

Multicomponent Diffusion. It retains diffsion features that won praise for the first edition - informal style, emphasis on physical insight and basic concepts, and lots of simple examples. Buy options. Unable to display preview. New chapters on membranes and drug release broaden the book's scope. The entire text is extensively illustrated, and many new worked examples and homework problems have been added.

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These three reasons make this chemical system popular. We can do this in two ways. This case occurs more frequently than does diffusion mass transfer in fluid systems from an interface into one bulk phase; indeed, I had trouble dreaming up the examples earlier in this chapter. A disk of radioactively tagged benzoic acid 1 cm in diameter is spinning at 20 rpm in 94 cm3 of initially pure water. We measure the steady-state oxygen concentration as a function of position in the bed. Fundamentals of Diffusion. Also fortunately, many other solutions are dilute, so diffusion induced convection is minor.

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  • Still, this strategy has produced a simple method of correlating our results. Taylor Dispersion.

  • Download preview PDF. It retains the features that won praise for the first edition - informal style, emphasis on physical insight and basic concepts, and lots of simple examples.

  • It can be reproduced by almost everyone who studies the subject. His research, which centers on membrane separations, has led to over papers and four books.

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Problem URL. Multicomponent Diffusion. Steele and C. SAL3 off-campus storage.

Mass Transfer. Skip to search Skip to main content. Edition 2nd ed. Simultaneous Heat and Mass Transfer.

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It transfer a spontaneous mixing process basic to such diverse phenomena as transport in living cells, the efficiency of distillation, and the dispersal of pollutants. Still, this strategy has produced a simple method of correlating our results. Of course, this reversal of the concentration in the liquid might be expressed in moles per liter and that in gas as a partial pressure in atmospheres, so it is not surprising that strange things happen. Before introducing these complexities, we shall go over some easy examples.

ThesisUniversity of Illinois, Librarian view Catkey: Adsorption-- Taylor Dispersion.

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Diffusion in Concentrated Solutions. Skip to main content. Fundamentals of Diffusion. Taylor Dispersion. DevinnyMarc A. For another discussion of the various models of mass transfer refer to E.

Minowa, Tetsu-to-Hagane 53 Jensen, Chem. D47 C Personalised recommendations. Mass Transfer in Biology and Medicine. Mass Transfer. Absorption--

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Mass Transfer. This can happen if the oxygen transferred is consumed in some sort of chemical reaction, which is true in aeration. Mass transfer across a gas—liquid interface. Often k varies with the square root of v0.

  • Adsorption-- Diffusion : Mass Transfer in Fluid Systems.

  • This correlation will be successful only if we have guessed the right key variables. When will a bulk concentration equal an interfacial concentration?

  • Danckwerts, Ind. It retains the features that won praise for the first edition - informal style, emphasis on physical insight and basic concepts, and lots of simple examples.

  • The spheres have 23 cm2 surface per 1 cm3 of bed.

Bibliography Includes bibliographical references and indexes. CrossRef Google Scholar. Multicomponent Diffusion. Distillation-- Skip to search Skip to main content. Bibliographic information.

In awe assume that the air is at constant humidity, except near the air—water interface. Thus we want to guess an answer which implies neglecting less important factors. Estimate Ky in the units given. Diffusion Coupled With Other Processes.

New chapters on membranes and drug release broaden the book's scope. AIChEJ 31 Jensen, Chem. Transport Phenomena in Materials Processing pp Cite as. Fundamentals of Mass Transfer.

Models for diffusion-- Part I. Homogeneous Chemical Reactions. In this chapter, diffusuon consider how to formulate and describe elementary diffusion and mass transfer problems in fluid systems. Problem URL. We use practically the same procedure in this situation as we did previously; we develop a differential equation, and a solution containing arbitrary constants evolves. Taylor, L. Multicomponent Diffusion.

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Values of Diffusion Coefficients. The values for these two gases may be similar because methane and ammonia have similar molecular weights. Example 8. Right away, we can see two possibilities. Mills, A. Enter the email address you signed up with and we'll email you a reset link. Download pdf.

Japan Iron and Steel Inst. This second edition of a highly acclaimed text provides a clear and complete description of diffusion in fluids. Diffusion Coupled With Other Processes. Diffusion in Concentrated Solutions.

The entire text is extensively illustrated, and many new worked examples and homework problems have been added. D47 C Available. CusslerEdward Lansing Cussler. For reviews, see P.

However, the chief reason that these correlations are systens in undergraduate and graduate courses is that they are close analogues to heat transfer. We want to study this process using the equipment shown schematically in Fig. McCabe, W. This complication does not exist in dilute solution, just as it does not exist for the dilute diffusion described in Chapter 2. Values of Diffusion Coefficients.

Mills, A. Our resulting correlation will be a convenient and compact way of presenting our results, and everyone will live happily ever after. As an example, we again consider the packed tower in Fig. CH A PT E R 8 Fundamentals of Mass Transfer Diffusion is the process by which molecules, ions, or other small particles spontaneously mix, moving from regions of relatively high concentration into regions of lower concentration. We do not want to correlate experiments; we want to avoid experiments if possible. Four of the more common of these are shown in Table 8.

How long will it take to reach ninety percent jn In c and dwe assume that the liquid solution, which is the continuous phase, is at constant composition, except near the droplet or bubble surfaces. The model is most useful for mass transfer across phase boundaries. We choose the two key exponents arbitrarily.

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. For example, the Reynolds number, that characteristic parameter of forced convection, can vary 10, times. Solution This is essentially a problem in unit conversion. Substituting for N1 from Eq. The new edition offers increased coverage of unit operations, with chapters on absorption, distillation, extraction, and adsorption. In the same way, a Sherwood number of 2 means different things for a membrane and for a dissolving sphere. Water trickles down through the column and absorbs the ammonia: ammonia is scrubbed out of the gas mixture with water.

Japan Iron and Steel Inst. In this chapter, we consider how to formulate and describe elementary diffusion and mass transfef problems in fluid systems. Edition 2nd ed. In Chapters 2 and 7, we demonstrated the development of differential equations pertinent to momentum and energy transport in simple fluid systems. New chapters on membranes and drug release broaden the book's scope.

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. Gas absorption is commonly controlled by mass transfer in the liquid and is one reason that reactive liquids are effective. Diffusion Coupled With Other Processes. We cannot have centimeters per second on the left-hand side equal to grams on the right.

  • Adsorption-- Homogeneous chemical reactions--

  • Values of Diffusion Coefficients.

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Your name. Multicomponent Diffusion. Simultaneous Heat and Mass Transfer. ThesisUniversity of Illinois,

Physical description xviii, p. Minowa, Trans. Steele and C. Advertisement Hide.

The new edition offers increased coverage of unit operations, with chapters on absorption, distillation, extraction, and adsorption. CusslerEdward Lansing Cussler. Jelinek, and C.

They can be important in leaching, in membrane separations, and in adsorption. New York: McGraw-Hill. Over a more moderate range, the correlations can be more reliable. Solution For convenience, we designate all concentrations in the toluene phase with a prime and all those in the water without a prime. Diffusion in Concentrated Solutions. Solution By integrating a mass balance on a differential length of bed, we showed in Example 8.

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Fundamentals of mass transfer-- 9. Contents 1. Controlled Release and Related Phenomena. Mass Transfer in Fluid Systems. Kosaka and S. Garner and R. Process Design and Development 6 ,

The entire text is extensively illustrated, and many new worked examples and homework problems have been added. Diffusion in Concentrated Solutions. Geiger, Metall. Find it at other libraries via WorldCat Limited preview.

Danckwerts, Ind. Publication date ISBN hc pb hc pb. Authors Authors and affiliations D.

Its concentration is about half saturated in 3 minutes. Englewood Cliffs: Prentice Hall. In the same way, a Sherwood number of 2 means different things for a membrane diffusion mass transfer in fluid systems for a dissolving sphere. New chapters on membranes and drug release broaden the book's scope. As you think about this more carefully, you will realize that the units of pressure or concentration cloud a deeper truth: Mass transfer should be described in terms of the more fundamental chemical potentials. How much is the previous answer changed if the benzoic acid solution in the tube is in benzene, not water? This may seem like cheating, but it works like a charm.

Taylor, L. Mass Transfer in Biology and Medicine. Diffusion of Interacting Species. Kosaka and S.

Free convection-- Part IV. Name of resource. Find it at other libraries via WorldCat Limited preview. Simultaneous heat and mass transfer. Responsibility E.

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  • Diffusion in Dilute Solutions.

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General Questions and Heterogeneous Chemical Reactions. Nanda and G. Vanek, R. Physical description xviii, p. Simultaneous Heat and Mass Transfer.

Benzoic acid is studied thoroughly for three distinct reasons. Englewood Cliffs: Prentice Hall. We then try to guess the answer. Of course, this reversal of the concentration in the liquid might be expressed in moles per liter and that in gas as a partial pressure in atmospheres, so it is not surprising that strange things happen.

Unable to display preview. Fundamentals of mass transfer-- 9. Diffusion Coefficients. Google Scholar. Process Design and Development 6 ,

The solubility of cholesterol in this solution is about 3. Gas scrubbing in a wetted-wall column. Over a more moderate range, the correlations can be more reliable. This second edition of a highly acclaimed text provides a clear and complete description of diffusion in fluids.

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Geankoplis, I. Fundamentals of Diffusion: 2. Fundamentals of mass transfer-- 9. Jelinek, and C. Fundamentals of Mass Transfer.

This is especially true for deep-bed fermentors and for sewage treatment, where the rising bubbles can be the chief means of diffusion mass transfer in fluid systems. Subject Index. In the leaching of metal by pouring acid over ore, we assume that the acid is homogeneous, except in a thin layer next to the solid ore particles. Two cases are shown. 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. Diffusion Coefficients.

How fast will it dissolve in a large volume of water? First, the result is a complete parallel to Eq. It is basic stuff for chemical engineers, but it is an unexplored method for many others.

In the same way, a Sherwood number of 2 means different things for a diffusion mass transfer in fluid systems and for a dissolving sphere. It may work if the tablets remain intact. However, the chief reason that these correlations are quoted in undergraduate and graduate courses is that they are close analogues to heat transfer. Water nearly Solution By integrating a mass balance on a differential length of bed, we showed in Example 8. Diffusion is as central to our daily lives as it is to the chemical industry.

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This is a preview of subscription content, log in to check access. Retaining the trademark enthusiastic style, the broad coverage now extends to biology and medicine. Subjects Diffusion. Fundamentals of mass transfer-- 9. SAL3 off-campus storage.

D47 C Available. Diffusion : Mass Transfer in Fluid Systems. Fundamentals of Diffusion: 2. Kosaka and S.

  • Help Need help? Buy options.

  • Diffusion of Interacting Species. A disk of radioactively tagged benzoic acid 1 cm in diameter is spinning at 20 rpm in 94 cm3 of initially pure water.

  • Unable to display preview.

  • This exceptionally clear and inviting text on diffusion will be used by students of engineering, chemistry, and life science. Geiger, Metall.

We now want to write Eq. Unfortunately, it is not always that simple for a variety of reasons. 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. Second, dissolution may be limited by mass transfer from the basket to the surrounding solution. The foregoing objections are important only if they are shown to be so by experiment. Mass transfer correlations are developed using a method called dimensional analysis.

Right away, we can see two possibilities. The values for these two gases may be similar because methane and ammonia have similar molecular weights. Example 8. We then try to guess the answer. Substituting for N1 from Eq.

Available online. Multicomponent Diffusion. Theories of Mass Transfer. Cite chapter How to cite?

Such a description is called a lumped-parameter model. We do not want to correlate experiments; we systmes to avoid experiments if possible. Models for Diffusion. This analysis suggests how we should plan our experiments. How much is the previous answer changed if the benzoic acid solution in the tube is in benzene, not water?

The entire text is extensively illustrated, and many new worked examples and homework problems have been added. Homogeneous chemical reactions-- Bird, W. New chapters on membranes and drug release broaden the book's scope. It retains the features that won praise for the first edition - informal style, emphasis on physical insight and basic concepts, and lots of simple examples.

They can be important in leaching, in membrane separations, and in adsorption. You trnsfer studying mass transfer of a solute from a gas across a gas—liquid interface into a reactive liquid. This overview of diffusion and separation processes brings unsurpassed, engaging clarity to this complex topic. Diffusion is as central to our daily lives as it is to the chemical industry.

CrossRef Google Scholar. Homogeneous Chemical Reactions. This process is experimental and the keywords may be updated as the learning algorithm improves. Taylor Dispersion.

I have this trouble too. The con- centration diffusion mass transfer in fluid systems between interface and bulk is not constant but can vary along the height of the column. We might suspect that ka varies with tank diameter, or sparger shape, or surface tension, or the phases of the moon. Two points about this problem deserve mention. Diffusion is a key part of the undergraduate chemical engineering curriculum and at the core of understanding chemical purification and reaction engineering.

Models for diffusion-- Part I. Freuhanand, L. For students, Diffusion goes from the basics of mass transfer and diffusion itself, with strong support through worked examples and a range of student questions. SAL3 off-campus storage. It retains the features that won praise for the first edition - informal style, emphasis on physical insight and basic concepts, and lots of simple examples. Yoo-Young, Chem.

The largest liquid—liquid extraction process is probably the dewaxing of lubricants. Heat Transfer. Experiments with benzoic acid dissolving in water can be compared directly with heat transfer experiments.

It is a spontaneous mixing process basic to such diverse phenomena as diffusiln in living cells, the efficiency of distillation, and the dispersal of pollutants. Multicomponent diffusion-- Part III. Poirier G. Again, we demonstrate the principles involved by considering specific examples, but first let us reconsider the general situation. Homogeneous chemical reactions-- Sherwood, Ind.

  • These constants are evaluated by applying boundary conditions that specify the concentration or the mass flux at the bounding surfaces.

  • This is especially true for deep-bed fermentors and for sewage treatment, where the rising bubbles can be the chief means of stirring. Finally, in Section 8.

  • New chapters on membranes and drug release broaden the book's scope.

  • Unfortunately, this simple scheme conceals a variety of approximations and ambi- guities. They are not useful in studies of the solid state, where concentrations vary with both position and time, and lumped-parameter models do not help much.

  • Taylor, L.

  • Download Free PDF. A wet t-shirt hung on a hanger has a total surface area of about 0.

New chapters on membranes and drug release broaden the book's scope. Higbie, Trans. These constants are evaluated by applying boundary conditions that specify the concentration or the mass flux at the bounding surfaces. Values of diffusion coefficients-- 6. Controlled release--

Skip to search Skip to main content. This spontaneous mixing process is also central to our daily lives, with importance in phenomena as diverse as the dispersal of pollutants to digestion in the small intestine. Values of diffusion coefficients-- 6. Unable to display preview.

Controlled Release and Related Phenomena. Vanek, R. It is a spontaneous mixing process basic to such diverse phenomena as transport in living cells, the efficiency of distillation, and the dispersal of pollutants.

  • General Questions and Heterogeneous Chemical Reactions. Gill, R.

  • How much is the previous answer changed if the benzoic acid solution in the tube is in benzene, not water? Four easy examples.

  • Diffusion in concentrated solutions-- 4. It retains the features that won praise for the first edition - informal style, emphasis on physical insight and basic concepts, and lots of simple examples.

  • Professor Cussler teaches chemical engineering at the University of Minnesota.

  • This Sherwood number varies with Schmidt number, a charac- teristic of diffusion.

  • Diffusion Coefficients: 5. Diffusion : Mass Transfer in Fluid Systems.

For example, the Reynolds number, that characteristic parameter of forced convection, can vary 10, times. Finally, in Section 8. It may work if the tablets syste,s intact. Of course, this reversal of the concentration in the liquid might be expressed in moles per liter and that in gas as a partial pressure in atmospheres, so it is not surprising that strange things happen. It repays careful study. A large value of k implies fast mass transfer, and a small one means slow mass transfer. To explore the ambi- guity more carefully, consider the packed tower shown schematically in Fig.

However, the chief reason that these correlations are quoted in undergraduate and graduate courses is that they are close analogues to heat transfer. We now turn to a variety of examples illustrating mass transfer across an interface. We might suspect that ka varies with tank diameter, or sparger shape, or surface tension, or the phases of the moon. You are using a model lubricant with properties characteristic of hydrocarbons. Taylor Dispersion. Homogeneous Chemical Reactions.

This second edition of a highly acclaimed text provides a clear and complete description of diffusion in fluids. Homogeneous Chemical Reactions. Fundamentals of Mass Transfer.

Jelinek, and C. New chapters on membranes and drug release broaden the book's scope. The entire text is extensively illustrated, and many new worked examples and homework problems have been added. His research, which centers on membrane separations, has led to over papers and four books.

  • It retains the features that won praise for the first edition - informal style, emphasis on physical insight and basic concepts, and lots of simple examples.

  • Fundamentals of Diffusion.

  • Controlled Release and Related Phenomena. Diffusion : Mass Transfer in Fluid Systems.

  • Skip to main content.

Mass transfer correlations are developed using a method called dimensional analysis. Also fortunately, many other solutions are dilute, so diffusion induced convection is minor. Unfortunately, it is not always that simple for a variety of reasons. You are studying mass transfer of a solute from a gas across a gas—liquid interface into a reactive liquid.

Example 8. In the same way, a Sherwood number of 2 means different diffusion mass transfer in fluid systems for a membrane and un a dissolving sphere. In the leaching of metal by pouring acid over ore, we assume that the acid is homogeneous, except in a thin layer next to the solid ore particles. In this example, ammonia is separated by washing a gas mixture with water. Its concentration is about half saturated in 3 minutes. This second edition of a highly acclaimed text provides a clear and complete description of diffusion in fluids. Combining Eqs.

Heat transfer-- Heat Transfer. CusslerEdward Lansing Cussler. Personalised recommendations. Poirier G.

CusslerEdward Lansing Cussler. Find it at other libraries via WorldCat Limited preview. This second transsfer of a highly acclaimed text provides a clear and complete description of diffusion in fluids. These constants are evaluated by applying boundary conditions that specify the concentration or the mass flux at the bounding surfaces.

We do not want to correlate experiments; we diffusino to avoid experiments if possible. We can solve these equations in terms of the two key exponents and thus simplify Eq. First, we had to assume that the bulk liquid was well mixed, and it may not be. Diffusion in Concentrated Solutions.

ENW EndNote. Professor Cussler teaches chemical engineering at the University of Minnesota. Calderbank, Trans. Diffusion in Dilute Solutions. Diffusion Coupled With Other Processes.

This is a preview of subscription content, log in to check access. Diffusion of Interacting Species. It retains the features diffusion mass transfer in fluid systems won praise fluir the first edition - informal style, emphasis on physical insight and basic concepts, and lots of simple examples. Diffusion in dilute solutions-- 3. This service is more advanced with JavaScript available. Subject Index. In this chapter, we consider how to formulate and describe elementary diffusion and mass transfer problems in fluid systems.

  • Your name.

  • General Questions and Heterogeneous Chemical Reactions. Mass transfer correlations are developed using a method called dimensional analysis.

  • Describe the connection issue. Simultaneous Heat and Mass Transfer.

  • Sherwood, Ind.

Freuhanand, L. Fundamentals 4 Diffusion Coupled with Other Processes: Higbie, Trans. CusslerEdward Lansing Cussler. Physical description xviii, p. Yoo-Young, Chem.

Simultaneous Heat and Difusion Transfer. The entire text diffusion mass transfer in fluid systems extensively illustrated, and many new worked examples and homework problems have been added. It retains the features that won praise for the first edition - informal style, emphasis on physical insight and basic concepts, and lots of simple examples. SAL3 off-campus storage. Diffusion is a key part of the undergraduate chemical engineering curriculum and at the core of understanding chemical purification and reaction engineering. Diffusion Coupled With Other Processes.

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