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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)

slide3
For gases,
  • Velocity:

mass average velocity,

molar average velocity,

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

the diffusion velocity.

slide7
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,

slide8
Since mass is transferred by two means:
    • concentration differences
    • and convection differences from density differences
    • For binary system with constant Vz,
    • Thus,
    • Rearranging to
slide9
As the total velocity,
  • Or
  • Which substituted, becomes
slide12
Related molecular mass transfer
    • Defined in terms of chemical potential:
    • Nernst-Einstein relation
diffusion coefficient
Diffusion Coefficient
  • Fick’s law proportionality/constant
  • Similar to kinematic viscosity, n, and thermal diffusivity, a
slide14
Gas mass diffusivity
    • Based on Kinetic Gas Theory
    • l = mean free path length, u = mean speed
    • Hirschfelder’s equation:
slide15
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
slide19
With no reliable s or e, we can use the Fuller correlation,
  • For binary gas with polar compounds, we calculate W by
slide21
and
  • For gas mixtures with several components,
  • with
slide23
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.
slide26
For infinite dilution of non-electrolytes in water, W-C is simplified to Hayduk-Laudie eq.
  • Scheibel’s equation eliminates FB,
slide27
As diffusivity changes with temperature, extrapolation of DAB is by
  • For diffusion of univalent salt in dilute solution, we use the Nernst equation
slide28
Pore diffusivity
    • 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,
slide29
But if Kn >1, then
  • If both Knudsen and molecular diffusion exist, then
  • with
  • For non-cylindrical pores, we estimate
slide35
Hindered diffusion for solute in solvent-filled pores
    • A general model is
    • F1 and F2 are correction factors, function of pore diameter,
    • F1 is the stearic partition coefficient
convective mass transfer
Convective Mass Transfer
  • Mass transfer between moving fluid with surface or another fluid
  • Forced convection
  • Free/natural convection
  • Rate equation analogy to Newton’s cooling equation
differential equations
Differential Equations
  • Conservation of mass in a control volume:
  • Or,

in – out + accumulation – reaction = 0

slide45
For in – out,
    • in x-dir,
    • in y-dir,
    • in z-dir,
  • For accumulation,
slide46
For reaction at rate rA,
  • Summing the terms and divide by DxDyDz,
    • with control volume approaching 0,
slide48
So by conservation of mass,
  • Written as substantial derivative,
    • For species A,
slide49
In molar terms,
    • For the mixture,
    • And for stoichiometric reaction,
ad