Transport Phenomena: Mass Transfer

Transport Phenomena: Mass Transfer (CAB 3033) Instructor Date

:Dr. Nurul Hasan :06/03/09

Universiti Teknologi PETRONAS

What we learn today? •Fick’s Law of Binary Diffusion •Non-dimensional number for diffusion •T and P dependence: Diffusion •Diffusion Theory: at low density •Diffusion Theory: binary liquid •Shell Balance: Mass Transfer

Continue…. Fick’s law of diffusion for binary mixtures The basic equation for Fick’s law for an isobaric and isothermal is :

J A = − ρD AB

dw A dy

Which is diffusive molar flux along the y-dir.

Continue…. Fick’s law of diffusion for binary mixtures The basic equation for Fick’s law for an isobaric and isothermal is :

J A = − ρD AB ∇w A Which is diffusive molar flux along the all three direction

Continue…. Fick’s law of diffusion for binary mixtures The basic equation for Fick’s law for an isobaric and isothermal is :

J B = − ρDBA ∇wB Which is diffusive molar flux along the all three direction

Non-dimensional Number •Prandle number

υ Cˆ p µ Pr = = α k

•Schimdt number

υ µ Sc = = D AB ρD AB

•Lewis number

Le =

α k = D AB ρCˆ p D AB

T & P Dependence: Diffusion •Liquid: increases with T •Gas: Increases with T, •Gas: decreases with P •Liquid: P does not have any effect

Diffusivity: Theory •Example 17.3-1: At low density •Example 17.4-1: Binary liquid •Section 17.5: colloidal suspensions

Shell Balance: M Transfer  Rate of   Rate of   rate of mass    −   +    mass in   mass out   production  = ( Accumalation )

Shell Balance: M Transfer •Take a shell (volume) •Divide by some parameters •Take Limit PDE •Fick’s Law •Integrate and apply Boundary conditions •Concentration of species