DEFINITION OF MASS FLUXES

Let vi = velocity of the ith species relative to stationary coordinate axis

Local Mass Average Velocity

Local Molar Average Velocity

Local Volume Average Velocity

partial molar volume of component iMi molecular weight of component i

Forms of FICK’s First Law

flux relative to the volume average velocity

flux relative to the molar average velocity

flux relative to the mass average velocity

flux relative to stationary coordinate

Relationship between N and J

(5-182 ChE HB)

DIFFUSION IN BINARY SYSTEMS

STEADY-STATE DIFFUSION

(5-191 ChE HB)

Limiting cases: (1) unimolecular diffusion; (2) equimolar counterdiffusion

1. UNIMOLECULAR DIFFUSION (UMD)- diffusion of A through a stagnant, non-diffusing B

NB = 0

(5.189 ChE HB)

2. EQUIMOLAR COUNTERDIFFUSION (EMD)- the molar fluxes of A and B are equal but opposite in direction - NA = -NB

N = NA + NB = 0

(5-190 ChE HB)

Important!

For EMD: DAB = DBA

For UMD: There is no such thing as DBA!

I. DIFFUSION IN GASES

Case 1 UMD

B

A

1

2

Eq. 5-189 ChE HB

Case 2 EMD

Diffusivity or Diffusion Coefficient Of Solute A In Gases (B)

1. Experimental data

Table 2-371 pp. 2-328 to 2-329 ChE HBDiffusion of pairs of gases and vapors (1atm)

Table 6.2-1 p. 395 GeankoplisDiffusion coefficients of Gases at 1 atm pressure

2. Prediction using correlations

Table 5-14 ChE HB

Error

Chapman-Enskog 7.3%Wilke-Lee 7.0%Fuller-Schettler-Giddings 5.4%

A,C

Eq. 5-190 ChE HB

Correction of DAB:

Fuller-Schettler-Giddings Correlation

(5-196 ChE HB / 6.2-45 Geankoplis)

V atomic diffusion volumes (Table 5-16 ChE HB / Table 6.2-2 Geankoplis )

MAB = MA-1 + MB

-1

T absolute temperatureP pressure in atmosphereDAB diffusivity (cm2/s in ChE HB; m3/s in Geankoplis)

II. DIFFUSION IN LIQUIDS

Case 1 UMD (diffusion of A through nondiffusing B)

Case 2 EMD

Diffusivity of solute A in liquids

For liquids

1. Experimental data

Table 2-372 ChE HB Diffusivities at 25oC (cm2/s)

Table 6.3-1 p. 401 Geankoplis

2. Correlation

Wilke-Chang

(5-208 ChE HB /

6.3-9 Geankoplis)

MB molecular weight of solvent BB association parameter of the solvent (p. 5-50 ChE HB)T temperature in kelvinsB viscosity of solvent B, cPVA molar volume of solute at the boiling point, cm3/gmol

Table 6.3-2 Geankoplis (m3/kgmol)