Minia University Faculty of Engineering Chemical Engineering Department

Minia University Faculty of Engineering Chemical Engineering Department Course Title: Mass Transfer Course Code: CHE 313 Third Year Course Coordinator: P r o f. D r. M o h a m m a d S h a w k y Lecture No. 8 DIFFUSIVITY for LIQUIDS

Contents n What is Diffusivity? n Determination of Diffusivity of Liquids : By Diaphragm Cell Method n Prediction of Diffusivity : 1. Stokes – Einstein Correlation (1905) 2. Wilke-Chang Correlation (1955) 3. Hayduk – Laudie Correlation (1974) 4. Hayduk – Minhas Correlation (1982) n Effect of Some Variables on Diffusivity of Liquids

What is Diffusivity? n The proportionality factor of Fick’s law is called diffusivity or diffusion coefficient which can be defined as the ratio of the flux to its concentration gradient out-of-plane. n Dimensions: L 2 / θ n Units (SI): m 2 / s

Determination of Diffusivity in Liquids n Here, a certain value of diffusivity is obtained by, 1 - Practical Methods (Experimental – Literature) 2 - Prediction Methods n In a prediction method, we use correlations or empirical correlations which have no mathematical derivation.

Determination of Diffusivity There are few methods of determination of liquid-phase diffusivities. The most commonly used method is Diaphragm Cell Method • Diaphragm cell contains two compartments as shown in the figure. These are separated by diaphragm. • Let the area of the diaphragm is ‘a’ and porosity is ‘ε’. • Effective area for diffusion = a ε Diaphragm cell

(1) (2) and (3)

Boundary conditions Therefore,

Prediction of Diffusivity in Liquids 1. Stokes – Einstein Correlation (1905) Restrictions: Ø (Mwt) A (solute) ≥ 1000 kg/kmol Ø (Mwt)B (solvent) small Ø VA ≥ 0. 5 m 3 / kmol

2. a) Wilke-Chang Correlation (SI System) (1955) Restrictions: Ø (Mwt) A (solute) < 1000 kg/kmol Ø (Mwt)B (solvent) is small Ø VA ≥ 0. 5 m 3/kmol

Types of Solvents Associated Solvents Unassociated Solvents (1)Water ØW=2. 6 or 2. 26 (2)Methanol (CH 3 OH) ØM=1. 9 q Examples: Ether Heptane Benzene (3) Ethanol (CH 3 CH 2 OH) ØE= 1. 5 q Ø=1. 0 Hydrocarbons (all of them) q Acetone=0. 5

2. b) Wilke - Chang Correlation (Cgs System) (1955)

3. Hayduk – Laudie Correlation (1974)

4. Hayduk – Minhas Correlation (SI) (1982) Restrictions: 1. Solute (A) If the solute is an organic acid and the solvent isn't water , methanol or butanol we should double parachor value (P) 2. Not Valid if Viscous Solvent B

Effect of Some Variables on Diffusivity of Liquids 1) Dynamic Viscosity 2) Temperature 3) Molar Volume (Composition)

4) Associated Parameter (∅) 5) Molecular Weight 6) Parachor (Hayduke-Minhas)

T h a n k Y o u