8/2/2019 L4_Molecular Diffusion in Liquids

1/9

Molecular diffusion in Liquids

Diffusion coefficient in liquids is slower than ingases (105 times lower).

The flux in liquid is lower around 100 times

than in gases. DABis composition dependent and it is slower

than in the gases.

1

8/2/2019 L4_Molecular Diffusion in Liquids

2/9

Equations for diffusion in liquids

2

A A A AB A BdC C

N D N N dz C

Equimolar counter diffusion (NA = - NB )

1 2

2 1

AB A A

A

D C C N

z z

1 2

2 1

AB avg A A

A

D C x x

N z z

1 21 2

2

M M

avgC

DAB is a function of composition, therefore it

must be calculated based on the average

values between point 1 and 2

8/2/2019 L4_Molecular Diffusion in Liquids

3/9

Equations for diffusion in liquids

3

Diffusion of solute (A) through stagnant solvent (B) (NB

= 0)

1 2

2 1

A B avg A AA

BLM

D C x xN

z z x

2

1

2 1

ln( )BB

B BBLM x

x

x xx

8/2/2019 L4_Molecular Diffusion in Liquids

4/9

Example

An ethanol (A)-water (B) solution in the form ofa stagnant film 2.0 mm thick at 293 K is incontact at one surface with an organic solvent inwhich ethanol is soluble and water is insoluble.

Hence, NB =0. At point 1 the concentration ofenthanol is 16.8 wt% and the solution density is1 = 972.8kg/m

3. At point 2 the concentration ofethanol is 6.8 wt% and

2= 988.1 kg/m3 . The

diffusivity of ethanol is 0.740e-9 m2/s. Calculatethe steady-state flux NA.

4

8/2/2019 L4_Molecular Diffusion in Liquids

5/9

Solution

5

MA

= 46.05, MB

=18

16.846.05

116.8 83.2

46.05 18

0.073Ax

20.0277Ax

xB1 = 0.9268, xB2 = 0.9723

116.8 83.2

46.05 18

10020.07M

218.75M

8/2/2019 L4_Molecular Diffusion in Liquids

6/9

Solution cont.

6

972.8 988.120.07 18.75

50.62

avgC Kg mol/m3

xBLM = 0.949

90.740 10 50.6 0.0732 0.0277

2 / 1000 0.949AN

NA = 8.99e-7 kg mol/s. m2

8/2/2019 L4_Molecular Diffusion in Liquids

7/9

Liquid Diffusivity, DAB

DAB= f(T,P,C).

Effect of pressure is insignificant compared totemperature and concentration.

DAB DBA

Several eqns to estimate the liquid diffusivityare available, however not all of them can give

an accurate prediction. Successful equations are developed for dilute

mixtures.

7

8/2/2019 L4_Molecular Diffusion in Liquids

8/9

Equations for DAB

8

DAB

for dilute solution 1. Wilke and Chang (1955)

1

213

0.6

1.17 10 B BAB

A

M TD

V

ABD Diffusion coefficient in dilute solution, m

2/s

MB = Molecular weight of the solvent

VA = Molar volume of solute at normal boiling point, m3 /kgmol

B = Association factor for solventSolvent

Non-polar 1

Water 2.6

Methanol 1.9

Ethanol 1.5

= viscosity of solution, cP

Error is within 11% when water is

the solvent, and 27% for organic

solvent.

Error can reach up to 200% when

water is the solvent

8/2/2019 L4_Molecular Diffusion in Liquids

9/9

Equations for DAB

9

DAB

for concentrated solution

1. Vignes (1966)

ln

1ln

B Ax x A A B A B BA

A

D D Dx

A = Activity coefficient of solute

2. Leffler and Cullinan (1970)

ln

1

ln

B Ax x A AB mix AB B BA A

A

D D D

x