Organization, Introduction, Brownian Diffusion. Davide Dr. Yoon Dr. Güntner Pascal Jan Nicolay Sebastian

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1 Chapter 1 Organization, Introduction, Brownian Diffusion Max Eggersdorfer Mass Transfer Dr. Wegner Dr. Büchel Davide Dr. Yoon Dr. Güntner Pascal Jan Nicolay Sebastian Two mandatory tests (30%) Mass Transfer Introduction, Brownian Diffusion 1-1

2 Literature: E.L. Cussler, Diffusion, Mass Transfer in Fluid Systems 2 nd edition, 1997, Cambridge University Press 3 rd edition, 2009, Cambridge University Press 2 TESTS of 45 min. October 24 November 28 (2009) (1997) Mass Transfer Introduction, Brownian Diffusion 1-2

3 1. Introduction What is mass transfer? Oxford Dictionary: Why does one substance move through or into another? How large is the driving force? How fast does it move? How far does it move? How much of a substance moves? Why do we care? Mass Transfer Introduction, Brownian Diffusion 1-3

4 1. Introduction The driving force for mass transfer is a difference in chemical potential. A substance moves from high to low chemical potential, for example: Tea from a tea bag in hot water travels from high concentration to low concentration. The mass transfer process is a slow, rate limiting step that: Limits efficiency of commercial distillations. Limits rate of industrial reactions with catalysts. Influences corrosion of metals and marbles. Controls the growth of microorganisms. Mass Transfer Introduction, Brownian Diffusion 1-4

5 Combustion a reaction-diffusion process Cylindrical flame from above: The temperature of the flame is lower in the dark regions. Oxygen and fuel (hydrocarbon) diffuse with different speeds Increasing gas feed rate forms increasingly complex patterns Photos: El-Hamdi, Michael Gorman, University of Houston, Texas (1994) Mass Transfer Introduction, Brownian Diffusion 1-5

6 Examples from nature with diffusion limitations Mineral dendrites of manganese in limestone Computer simulations of diffusion-limited agglomeration Recommended reading: Philip Ball «Shapes: Nature s Patterns» Mass Transfer Introduction, Brownian Diffusion 1-6

7 Crystallization Pharmaceuticals Paracetamol Naillon, Joseph, Prat, J. Crystal Growth (2017) Mass Transfer Introduction, Brownian Diffusion 1-7

8 Spray-drying Particle diffusion > evaporation Particle diffusion < evaporation Vehring, Foss, Lechuga-Ballesteros, J. Aerosol Sci. (2007) Mass Transfer Introduction, Brownian Diffusion 1-8

9 Types of Mass Transfer: 1. Molecular diffusion (or just diffusion). Mass is transferred by the random motion of molecules across a concentration gradient. Sometimes, but not always, this is similar to heat transfer by conduction. 2. Eddy diffusion (mixing or dispersion or agitation). Mass is transferred by finite parcels of fluids as in momentum and heat transfer. Approximate rates of diffusion in: Gases: 10 cm/min (a lady with a nice perfume). Liquids: 0.05 cm/min (stir cream into the coffee). Solids: cm/min (takes long to rust an iron axe) Mass Transfer Introduction, Brownian Diffusion 1-9

10 Relationship with Momentum and Heat Transfer Mass transfer is similar to momentum and heat transfer but there is nothing equivalent to radiation heat transfer. Molecular diffusion easily gives rise to convection something that was not so with conduction heat transfer. This is distinguished by talking about diffusion at low and high concentrations. Mass Transfer Introduction, Brownian Diffusion 1-10

11 Description of Mass Transfer 1. Molecular model (Fick s laws and diffusivity). This is an elegant model based on first principles that everyone dreams of having to work with especially in physics, physical chemistry and biology. 2. Mass transfer coefficient model (Mass Transfer correlations) This is a model typically employed by chemical and process engineers when the complexity of the process leaves little space for elegance. The choice between models is a compromise between ambition and resources. Mass Transfer Introduction, Brownian Diffusion 1-11

12 Example for Models Imagine two large bulbs with equal volume connected by a long thin capillary at constant temperature. 2 N 2 Measure now the CO 2 concentration inside the bulb containing nitrogen. 1 CO 2 area Goal: To determine physical properties that determine the amount of mass transferred. Mass Transfer Introduction, Brownian Diffusion 1-12

13 amount of gas from 1 to 2 Define the flux: CO 2 flux time area This removes the influence of a particular apparatus. area 2 N 2 Model 2: Recognize that the CO 2 flux is proportional to CO 2 concentration difference between 1 and 2. CO flux k (CO concentration difference) 2 2 k is a mass transfer coefficient and this is the mass transfer coefficient model. CO 2 1 Model 1: Recognize that increasing the length of the capillary will decrease the flux. concentration difference CO 2 flux D capillary length D is the diffusion coefficient and this is the other model or Fick s first law. Mass Transfer Introduction, Brownian Diffusion 1-13

14 This is similar to electric circuits, Ohm s law: current voltage 1 or = or resistance area flux of electrons potential difference Thus the mass transfer coefficient k is analogous to the reciprocal of the resistance. An alternative form to Ohm s law is: current density 1 potential difference or = resistivity length flux of electrons The diffusion coefficient D is analogous to the reciprocal of resistivity. Mass Transfer Introduction, Brownian Diffusion 1-14

15 In heat transfer k is analogous to the heat transfer coefficient h, while D is analogous to thermal conductivity l. Neither the k-model nor the D-model are always successful as they depend heavily on assumptions made in their development. For example: The flux CO 2 concentration difference if the capillary is too thin or if the gases react. Similarly Ohm s law is not always valid at very high voltages. However, both Fick s and Ohm s law work well in most practical uses. Resistance or resistivity give a clue about the choice of the 2 models: Using the resistance is good for practical applications & rough measurements. In contrast, resistivity is a fundamental material property. We start with the fundamental description of the diffusion coefficient, the D-model, following with the description of the k-model later on. Mass Transfer Introduction, Brownian Diffusion 1-15

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