IN THE NAME OF ALLAH THE MOST GRACIOUS EVER MERCIFUL.

Topic of presentation

• The Two film theory, its Applications and practical Examples.

Group members

Waqar Ahmed Naseer2009-CH-224Waqas Hameed 2009-CH-250Sabeeh Ahmed 2009-CH-255Aiman Shabir 2009-CH-217Fahad Hanif 2009-CH-223

Hafiz Usama Mushtak Khan 2009-CH-218

Contents

• Introduction • Mechanism of mass transfer along the films• Calculating mass transfer coefficients and its significance• The Henry's law and its role in Two film theory• Applications• In the process of fermentation• The distillation column• The absorption column• Draw backs

Waqar ahmad naseerIntroduction &

Mechanism of mass transfer along the films

Introduction• The two film theory or the double-resistance, theory,

was first proposed by Whitman in 1923.• The two-film model starts by assuming that the gas

and liquid phases are in turbulent contact with each other, separated by an interface area where they meet.

• This assumption may be correct, but no mathematical expressions adequately describe the transport of a molecule through both phases in turbulent motion.

Cont….• Therefore, the model proposes that a mass-transfer

zone exists to include a small portion (film) of the gas and liquid phases on either side of the interface.

• The mass-transfer zone is comprised of two films, a gas film and a liquid film on their respective sides of the interface. These films are assumed to flow in a laminar, or streamline, motion.

• In laminar flow, molecular motion occurs by diffusion, and can be categorized by mathematical expressions. This concept of the two-film theory is illustrated in Figure 11-3.

Visualization of two-film theory

• Liquid phase

• Liquid film

• Gas phase• pAb

• CAi

• CAb

• pAi

• Gas film

• Mass transport

double-resistance theory

• The theory assumes that complete mixing takes place in both gas and liquid bulk phases and that the interface is at equilibrium with respect to pollutant molecules transferring in or out of the interface.

• This implies that all resistance to movement occurs when the molecule is diffusing through the gas and liquid films to get to the interface area, hence the name double-resistance theory.

Steps of mass transfer

• Migrate from the bulk-gas phase to the gas film• Diffuse through the gas film• Diffuse across the interface• Diffuse through the liquid film• Mix into the bulk liquid.

Applications and practical examples

Aiman Shabir

In Fermentation

Film theory

15

The two film theory is a useful model for mass transfer between phase. Mass transfer of solute from one phase to another involves transport from bulk of one phase to the interface, and then from the interface to the bulk of the second phase. This theory is based on idea that a fluid film or mass transfer boundary layer forms whenever there is contact between two phases. According to film theory, mass transfer through the film is solely by molecular diffusion and is the major resistance.

CA1i CA1 Bulk fluid 1

Bulk fluid 2

CA2i

CA2 Film 2 Film 1

Convective mass transfer

AGiAGGAG

ALALiLAL

CCakN

CCakN

AiAoA CCkaN

16

It refers to mass transfer occurring in the presence of bulk fluid motion

k: mass transfer coefficient [m/s]

a: area available for mass transfer [m2/m3]

CAo: concentration of A at bulk fluid

CAi: concentration of A at interface

For gas-liquid system, A from gas to liquid:

Overall mass transfer coefficient

ALALLA

LGG

CCaKN

ak

m

akaK

*

'11

17

Oxygen transport to fermentation broth can be modeled as diffusion of A through stagnant or non-diffusing B.

If A is poorly soluble in the liquid, e.g. oxygen in aqueous solution, the liquid-phase mass transfer resistance dominates and kGa is much larger than kLa. Hence, KLa ≈ kLa.

Oxygen transfer from gas bubble to cell

Eight steps involved:i. Transfer from the interior of the bubble to the gas-liquid interface

ii. Movement across the gas-liquid interface

iii. Diffusion through the relatively stagnant liquid film surrounding the bubble

iv. Transport through the bulk liquid

v. Diffusion through the relatively stagnant liquid film surrounding the cells

vi. Movement across the liquid-cell interface

vii. If the cells are in floc, clump or solid particle, diffusion through the solid of the individual cell

viii. Transport through the cytoplasm to the site of reaction.

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Analyzes for most bioreactors in each step involved

i. Transfer through the bulk phase in the bubble is relatively fastii. The gas-liquid interface itself contributes negligible resistanceiii. The liquid film around the bubble is a major resistance to

oxygen transferiv. In a well mixed fermenter, concentration gradients in the bulk

liquid are minimized and mass transfer resistance in this region is small, except for viscous liquid.

v. The size of single cell <<< gas bubble, thus the liquid film around cell is thinner than that around the bubble. The mass transfer resistance is negligible, except the cells form large clumps.

vi. Resistance at the cell-liquid interface is generally neglectedvii. The mass transfer resistance is small, except the cells form

large clumps or flocs.viii. Intracellular oxygen transfer resistance is negligible because of

the small distance involved19

Waqas Hameed2009-CH-250

In absorption column

Absorption column

Gas absorption is a process in which a gaseous mixture is brought into contact with a liquid and during this contact a component is transferred between the gas stream and the liquid stream.

The gas may be bubbled through the liquid or The feed is a gas introduced at the bottom of the column,

and the solvent is feed to the top, as a liquid; the absorbed gas and the solvent leave at the bottom of the column, and the unabsorbed components leave as gas from the top.

Mechanism of Absorption column

The most useful concept of the process of absorption is given by the two-film theory given by WHITMAN.

According to this theory,1. material is transferred in the bulk of the

phases by convection currents, and2. rates of mass transfer in gas absorption are controlled by the extent of the departure of the system from the equilibrium concentrations.

Sabeeh Ahmed2009-CH-255

Diffusion through a gas phase

The process of absorption may be regarded as the diffusion of a soluble gas A into a liquid. The molecules of A have to diffuse through a gas film and then through a liquid film before entering the main bulk of liquid. To the absorption of a gas consisting of a soluble component A and an insoluble component B Stefan’s law applies:

The final relation is:

Diffusion through liquid phaseThe basic equation is taken as similar to that for gases, and for dilute concentrations:

On integration

Where CA, CB are the molar concentrations of A and B, zL is the thickness of liquid film through which diffusion occurs, DL is the diffusivity in the liquid phase.

Rate of absorption

In a steady-state process of absorption, the rate of transfer of material through the gas film will be the same as that through the liquid film, and the general equation for mass transfer of a component A may be written as:

Where PAG is the partial pressure in the bulk of the gas, CAL

is the concentration in the bulk of the liquid, and PAi and CAi

are the values of concentration at the interface where equilibrium conditions are assumed to exist. Therefore:

Graph: driving forces in the gas and liquid phases

Point A (CAe, PAG) represents a concentration of CAe in the liquid in equilibrium with PAG in the gas.

Point B (CAi , PAi) represents the concentration of CAi in the liquid in equilibrium with PAi in the gas, and gives conditions at the interface. Point F (CAL, PAe) represents a partial pressure PAe in the gas phase in equilibrium with CAL in the liquid.

Overall coefficients

In order to obtain a direct measurement of the values of kL and kG the measurement of the concentration at the interface would be necessary. It is of considerable value to use two overall coefficients KG and KL defined by:Overall mass transfer coefficient with respect to gas stream is:

Overall mass transfer coefficient with respect to liquid stream is

Relation between film and overall coefficients

With respect to gas stream:

(1)

With respect to liquid stream:

(2)

FAHAD HANIF2009-CH-223

Henry’s lawIt relates the partial pressure and the mole fraction linearly it states as:

“In the presence of a phase boundary the partial pressure of any component in gaseous phase is directly proportional to the mole fraction of that component in liquid phase”

Mathematically is written as:

Here “Pa” is the partial pressure in gaseous “Xa” is concentration (mole fraction) in liquid phase and is the “H” Henry's constant

Here H relates the concentration of A in bulk gas to the concentration of A in liquid, which is the same as ‘m’ relates so H and m are replaced by each other.

So in Equation (1) and (2) m is replaced by H.

and

Significance of Henry's constant

If H is very small (which means the gas is very soluble in the liquid), then

and absorption is said to be gas-film controlled. The major resistance to mass transfer is in the gas phase.

If H is very large, and Equation reduces to

The mass-transfer rate is liquid-film controlled and the major resistance to mass transfer is in liquid phase.

And if H has the moderate value then both films offer an appreciable resistance.

Uses of absorption

Acetone can be recovered from an acetone–air mixture by passing the gas stream into water in which the acetone dissolves while the air passes out. Similarly, ammonia may be removed from an ammonia–air mixture by absorption in water. Gas absorption is in the carbonation of beverages. Carbon dioxide under pressure is dissolved in the liquid beverage, so that when the pressure is subsequently released on opening the container, effervescence occurs.

Usama Mushtaq2009-CH-218

In Distillation Columns

The separation of liquid mixtures into their various components is one of the major operations in the process industries, and distillation, the most widely used method of achieving this end.

The concept of two film theory is also applicable in the case of Distillation.

Draw backs…

• Assumptions• Steady-state: concentrations at any position in

the tower do not change with time.• Interface between the gas phase and the liquid

phase is a sharp boundary.• Laminar film exist at the interface on both sides

of the interface

Cont…

• Theoretically predicted values of the individual mass-transfer coefficients (kg and kl) based on the two-film theory, do not correlate well with observed values.

• Overall mass-transfer coefficients are more easily determined fro m experimental or operational data.

Questions?????