Overview of mass transfer mechanisms
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The document provides an overview of mass transfer mechanisms, specifically molecular, convective, and interphase mass transfer, outlining their characteristics and calculations. It discusses the definitions and significance of velocities and fluxes in diffusion processes and presents examples of average velocities in gas mixtures. Additionally, it references key literature and instructional videos related to the principles of mass transfer.
![Mass-average and molar-average velocities
• Mass-average velocity v
[v] = m/s
• Molar-average velocity V
• If the molecular weight of
all species are equal, v = V.
• In dilute solutions, the
average velocity becomes
virtually equal to the
velocity of the solvent.
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𝑖=1
𝑛
𝜌𝑖𝑣𝑖
𝑖=1
𝑛
𝜌𝑖
=
𝑖=1
𝑛
𝜌𝑖𝑣𝑖
𝜌
=
1
𝜌
𝑖=1
𝑛
𝜌𝑖𝑣𝑖 =
𝑖=1
𝑛
𝜔𝑖𝑣𝑖
𝑉 =
𝑖=1
𝑛
𝑐𝑖𝑣𝑖
𝑖=1
𝑛
𝑐𝑖
=
𝑖=1
𝑛
𝑐𝑖𝑣𝑖
𝑐
=
1
𝑐
𝑖=1
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𝑐𝑖𝑣𝑖 =
𝑖=1
𝑛
𝑥𝑖𝑣𝑖
𝜌𝑖 = mass concentration of 𝑖
kg
m3
𝜔𝑖 = mass fraction of 𝑖
kg
kg
𝑐𝑖 = molar concentration of 𝑖
mol
m3
𝑥𝑖 = mole fraction of 𝑖
mol
mol](https://image.slidesharecdn.com/2-210203104458/85/Overview-of-mass-transfer-mechanisms-5-320.jpg)
Overview of mass transfer mechanisms
- 1. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 869993. Overview of the mechanisms of mass transfer processes
- 2. Mechanisms of mass transfer processes • Mechanisms of mass transfer are divided into three groups: • Molecular mass transfer • Convective mass transfer • Interphase mass transfer • They often occur simultaneously, but one of them is usually dominant. • Molecular and convective mass transfer consider the diffusion of substances within a single phase. • Calculations of molecular and convective mass transfer are based on the rate of diffusion and total mass transfer. • In interphase mass transfer, two insoluble phases are brought into contact. Calculations are based on equilibrium data.
- 3. Comparison of mechanisms Molecular mass transfer Molecular diffusion Fick’s law Diffusion coefficients Example: dissolving sugar in coffee without stirring Convective mass transfer Mass transfer in bulk motion Mass transfer coefficients Example: dissolving sugar in coffee and stirring at the same time Interphase mass transfer Equilibrium between two phases Equilibrium data Example: distillation of ethanol from water-ethanol mixture
- 4. Velocities and fluxes • Knowledge about velocities and fluxes are needed in diffusion calculations. • SI unit for velocity is m/s and the common symbols are v and u. • In mass transfer operations, velocity can mean both the molecular velocity in microscopic scale and the bulk motion. • Various components of the solution move with different velocities. • The term flux means the amount (mass or molar) of species passing through the unit area in unit time. The unit area is normal to the direction of diffusion. • Flux is a vector quantity. SI unit for mass flux is kg/(m2∙s) and for molar flux mol/(m2∙s). • Common symbols for mass fluxes are ni and ji and for molar fluxes Ni and Ji. • The fluxes can be determined in relative to a stationary observer or to an observer moving with the average velocity.
- 5. Mass-average and molar-average velocities • Mass-average velocity v [v] = m/s • Molar-average velocity V • If the molecular weight of all species are equal, v = V. • In dilute solutions, the average velocity becomes virtually equal to the velocity of the solvent. 𝑣 = 𝑖=1 𝑛 𝜌𝑖𝑣𝑖 𝑖=1 𝑛 𝜌𝑖 = 𝑖=1 𝑛 𝜌𝑖𝑣𝑖 𝜌 = 1 𝜌 𝑖=1 𝑛 𝜌𝑖𝑣𝑖 = 𝑖=1 𝑛 𝜔𝑖𝑣𝑖 𝑉 = 𝑖=1 𝑛 𝑐𝑖𝑣𝑖 𝑖=1 𝑛 𝑐𝑖 = 𝑖=1 𝑛 𝑐𝑖𝑣𝑖 𝑐 = 1 𝑐 𝑖=1 𝑛 𝑐𝑖𝑣𝑖 = 𝑖=1 𝑛 𝑥𝑖𝑣𝑖 𝜌𝑖 = mass concentration of 𝑖 kg m3 𝜔𝑖 = mass fraction of 𝑖 kg kg 𝑐𝑖 = molar concentration of 𝑖 mol m3 𝑥𝑖 = mole fraction of 𝑖 mol mol
- 6. Example: Average velocities • A gas mixture is flowing through a pipe (⌀ 25 mm). Composition of the mixture and velocities of each component are shown in the table. Calculate the mass-average and molar-average velocities of the mixture. Total pressure is 4 atm. Molar-average velocity: 𝑉 = 𝑖=1 𝑛 𝑦𝑖𝑣𝑖 = 0.65 0.03 + 0.08 0.03 + 0.24 0.035 + 0.03 0.02 = 0.0309 m/s % Velocity NH3 65 % 0.03 m/s N2 8 % 0.03 m/s H2 24 % 0.035 m/s Ar 3 % 0.02 m/s For mass-average velocity, you need the molecular weights of each component. The correct answer is 0.029 m/s. Try to solve the exercise by yourself. You can find the explanation from the bonus materials.
- 7. Mass flux and molar flux • Fluxes are commonly used to describe the diffusion rates. • There are three ways to define the flux: 1. With respect to coordinates that are fixed (stationary oserver) 2. With respect to the mass-average velocity (moving observer) 3. With respect to the molar-average velocity (moving observer) Mass fluxes kg/(m2∙s) Molar fluxes mol/(m2∙s) 1. Stationary obsever ni = ρivi Ni = civi 2. Observer moving with mass-average velocity ii = ρi(vi – v) Ii = ci(vi – v) 2. Observer moving with molar-average velocity ji = ρi(vi – V) Ji = ci(vi – V) ρi = mass concentration of i vi = linear velocity of i v = mass-average velocity V = molar-average velocity ci = molar concentration of i
- 8. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 869993. References Benitez, J. 2016. Principles and Modern Applications of Mass Transfer Operations. Wiley, pp. 1-13. Dutta, B. K. 2007. Principles of mass transfer and separation processes. New Delhi: Prentice-Hall, pp. 7-10, 74-76, 102-103. Treybal, R. E. 1980. Mass-transfer operations. 3rd ed. Auckland: McGraw-Hill, pp. 19-22, 104-105. Videos: • Convection versus diffusion: https://youtu.be/EG4ZoVTSA5I • Mass average and molar average velocities: https://youtu.be/w89NSgug5v8 • Convection and diffusion: https://youtu.be/HA3RrWW8uGQ