Tutorial hw week 7 wwwr chapters 24 25 id chapter 14
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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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Tutorial hw week 7 wwwr chapters 24 25 id chapter 14

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 #7WWWR Chapters 24-25ID Chapter 14


Molecular mass transfer
Molecular Mass Transfer

  • Molecular diffusion

  • Mass transfer law components:

    • Molecular concentration:

    • Mole fraction:

      (liquids,solids) , (gases)


For 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,






Diffusion coefficient
Diffusion Coefficient

  • 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



and

  • For gas mixtures with several components,

  • with


2


  • 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
Example 6 simplified to Hayduk-Laudie eq.




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


Example 7
Example 7 solids


Convective mass transfer
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
Example 8 solids


Differential equations
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,


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