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# Tutorial - PowerPoint PPT Presentation

Tutorial #7 WWWR# 24.1, 24.12, 24.13, 24.15(d), 24.22. To be discussed on March 11, 2014. By either volunteer or class list. Tutorial/HW Week #7 WWWR Chapters 24-25 ID Chapter 14. Molecular Mass Transfer. Molecular diffusion Mass transfer law components: Molecular concentration:

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WWWR# 24.1, 24.12, 24.13, 24.15(d), 24.22.

To be discussed on March 11, 2014.

By either volunteer or class list.

Tutorial/HW Week #7WWWR Chapters 24-25ID Chapter 14

• Molecular diffusion

• Mass transfer law components:

• Molecular concentration:

• Mole fraction:

(liquids,solids) , (gases)

• Velocity:

mass average velocity,

molar average velocity,

velocity of a particular species relative to mass/molar average is

the diffusion velocity.

• Flux:

A vector quantity denoting amount of a particular species that passes per given time through a unit area normal to the vector,

given by Fick’s First Law, for basic molecular diffusion

or, in the z-direction,

For a general relation in a non-isothermal, isobaric system,

• Fick’s law proportionality/constant

• Similar to kinematic viscosity, n, and thermal diffusivity, a

• Gas mass diffusivity

• Based on Kinetic Gas Theory

• l = mean free path length, u = mean speed

• Hirschfelder’s equation:

• Lennard-Jones parameters s and e from tables, or from empirical relations

• for binary systems, (non-polar,non-reacting)

• Extrapolation of diffusivity up to 25 atmospheres

• With no reliable s or e, we can use the Fuller correlation,

• For binary gas with polar compounds, we calculate W by

• For gas mixtures with several components,

• with

• Liquid mass diffusivity

• No rigorous theories

• Diffusion as molecules or ions

• Eyring theory

• Hydrodynamic theory

• Stokes-Einstein equation

• Equating both theories, we get Wilke-Chang eq.

• Pore diffusivity simplified to Hayduk-Laudie eq.

• Diffusion of molecules within pores of porous solids

• Knudsen diffusion for gases in cylindrical pores

• Pore diameter smaller than mean free path, and density of gas is low

• Knudsen number

• From Kinetic Theory of Gases,

• But if Kn >1, then simplified to Hayduk-Laudie eq.

• If both Knudsen and molecular diffusion exist, then

• with

• For non-cylindrical pores, we estimate

Example 6 simplified to Hayduk-Laudie eq.

• F solids2 is the hydrodynamic hindrance factor, one equation is by Renkin,

Example 7 solids

Convective Mass Transfer solids

• Mass transfer between moving fluid with surface or another fluid

• Forced convection

• Free/natural convection

• Rate equation analogy to Newton’s cooling equation

Example 8 solids

Differential Equations solids

• Conservation of mass in a control volume:

• Or,

in – out + accumulation – reaction = 0

• For reaction at rate solidsrA,

• Summing the terms and divide by DxDyDz,

• with control volume approaching 0,

• In molar terms, general form:

• For the mixture,

• And for stoichiometric reaction,