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Mass Transfer

Awais Javaid

Mass Transfer Convective Mass Transfer Mass transfer between a moving fluid and a surface or between immiscible moving fluid, separated by a mobile interface (as in gas/liquid or liquid/liquid contactor) is often aided by the dynamic characteristics of the moving fluid. The mode of transfer is called convective mass transfer with the transfer always going from higher concentration to a lower concentration of the species being transfer. Convective mass transfer depends on both the transfer properties and the dynamic behavior of the moving fluid.

Explanation: When a fluid flows pass a solid surface under conditions such that turbulence generally prevails, there is a region immediately adjacent to surface where flow is laminar as shown in figure 1.1.

Figure. 1.1. Boundary layer and turbulence in moving fluid

With increasing distance from the surface the character of the flow gradually changes becoming increasingly turbulent until in the outer most region of the fluid fully turbulent conditions prevail.

Figure 1.2. Velocity of moving fluid over solid surface.

The rate of transfer of a dissolved substance through the fluid will depend on the nature of the fluid motion, prevailing in the various regions.

Errors and omissions are accepted.

Mass Transfer

Awais Javaid

In the turbulent regions particles of fluids no longer flow in the orderly manner found in the laminar sub-layer. Instead relatively large portions of the fluid called eddies move rapidly from one position to the other. The eddies bring with them dissolved material and therefore the eddy motion contribute significantly to the mass transfer process. Since the eddy motion is rapid, mass transfer in the turbulence region is also rapid, much more so then resulting from molecular diffusion in the laminar sub-layer. Because of the rapid eddy motion, the concentration gradients existing in the turbulence region will be smaller than those in the film.

THE RATE EQUATION FOR CONVECTIVE: Mass generalized in a manner analogues to Newton Law of cooling is given as; Rate of mass transfer  concentration difference or concentration driving force If WA is the rate of mass transfer in kmol/sec of the solute, ΔCA is concentration difference between two points and “a” is area of mass transfer. WA  aC A WA  kc aC A

kc = proportionality constant and is called mass transfer coefficient

WA  kc C A a N A  kc C A Where NA is the molar mass flux of specie “A” measured relative to the fix quadrant, ΔCA is concentration difference between the boundary surface concentration and the average concentration of the diffusing specie in the moving stream, kc is the convective mass transfer co-efficient. The reciprocal of the co-efficient,

1 kc

represent the resistance to the transfer

to the moving fluid. In general both the heat and the mass transfer co-efficient are related to properties of the fluid, dynamic characteristics and the system geometry. When the mass transfer in moles of a solute dissolving into a moving fluid, the convective mass transfer is defined as;

N A  kc C A  kc C AS  C A  Where the flux NA represent the moles of solute “A” leaving the interface per unit time and unit interfacial area. The composition of the solute in the fluid at the interface, CAS, is the composition of the fluid if it were in equilibrium with solid solute at temperature and pressure of the system. The quantity CA represent the composition at same point within the fluid phase.

EXAMPLE NO. 1: A pure nitrogen (N2) carrier gas flows parallel to the 0.6 m2 surface of a liquid Acetone in an open tank. The Acetone temperature is maintained at 290K. If average mass

Errors and omissions are accepted.

Mass Transfer

Awais Javaid

transfer coefficient kc for the transfer of Acetone into the N2 stream 0.0324 m/s. Determine the total rate of Acetone release in units of kgmol/sec.

Solution: Total molar rate of Acetone Transfer from the liquid in the gas phase can be evaluated by;

WA  N A  A  kc AC A  kc ACAS  C A 

As N2 is flowing, we can say CA∞ is constant and it would be zero. →

CA∞ = 0

The mass transfer area is sepacified as 0.6 m2. At 290K Acetone exerts an vapor pressure of 161 mmHg (2.148x104 Pa), therefore the concentration of acetone in the gas phase at Acetone surface is;

C AS

C AS

2.148  10 4 Pa Pa.m3 8.314  290 K kgmol.K kgmol  8.91 m3 p  A  RT

And the concentration of Acetone in the N2 carrier gas is zero, because the molar flow rate of the carrier gas is in a large excess relative to acetone transfer therefore WA is; WA  kc AC AS  C A   (0.0324 m / s )  (0.6m 2 )  (8.91kgmol / m3  0kgmol / m3 ) WA  0.1732

kgmol sec

The total rate of Acetone release is 0.1732

kgmol . sec

EXAMPLE NO. 2: Air flows over a solid slab of from CO2 (dry ice) with an exposed cross sectional Area 1.0x10-3 m2. The CO2 sublimes into the 2m/s flowing stream at total release rate 2.29x10-4 mole/s. The air is at 293K and 1.013x105 Pa. determine the value of the mass transfer coefficient of CO2 subliming into the flowing air at conditions of the experiment.

Solution:

N A  kc CAS  CA  Errors and omissions are accepted.

Mass Transfer

Awais Javaid

kc 

NA C AS  C A 

kc 

WA AC AS  C A 

At 293K and 101.3 kPa, pA=4.74x103 Pa C AS

C AS

4.74  103 Pa Pa.m3 8314  293 K mol.K mol  1.946 3 m p  A  RT

If we assume CA∞=0; Then: mol s kc  mol mol   1.0  10  3 m 2 1.946 3  0 3  m m   m kc  0.118 sec 2.29  10 4

The mass transfer coefficient of CO2 subliming into the flowing air is 0.118m/sec at the conditions of the experiment.

TYPES OF MASS TRANSFER CO-EFFICIENT: Convective mass transfer can occur in a gas or a liquid medium. Different types of mass transfer co-efficient has been defined depending upon the following; 1. Whether mass transfer occur in gas phase or in the liquid 2. Choice of driving force 3. Whether it is a case of diffusion of “A” through non-diffusing “B” or case of counter current diffusion. Convective heat transfer is often visualized to occur through a stagnant film adherent to the surface. The transport of heat through film is assumed to occur purely by conduction. In mass transfer this concept is also frequently used.

Diffusion of “A” through non-diffusing “B”: Mass transfer in the gas phase can be represent (on choice of driving force) as;

N A  kG ( p A1  p A2 )  k y ( y A1  y A2 )  kC (C A1  C A2 )

Errors and omissions are accepted.

Mass Transfer

Awais Javaid Mass transfer in the liquid phase can be represent (on choice of driving

force) as; N A  k x x A1  x A2 

 kC C A1  C A2 

Here kG, ky and kC are the gas phase mass transfer coefficients and kx and kC are the liquid phase mass transfer coefficients. The subscript “1” and “2” refers to two positions in the medium or phase. kC  mass transfer co - efficient on the base of concentration gradient as driving force kG  mass transfer co - efficient on the base of partial pressure differnce in gas phase as driving force k y  mass transfer co - efficient on the base of gas composition as driving force k x  mass transfer co - efficient on the base of liquid composition as driving force

Units of mass transfer co-efficient:  Gas composition as driving force; ky 

kmol m .s (y ) 2

Where Δy stands for driving force in mole fraction units.  Liquid composition as driving force;

kx 

kmol m .s(x) 2

Where Δx stands for driving force in mole fraction units.  Partial pressure difference as driving force; kG 

kmol m .s (p ) 2

Where Δp stands for driving force in partial pressure units.  Concentration gradient as driving force; kC 

kmol m .s ( C ) 2

Where ΔC stands for driving force in concentration units.

Errors and omissions are accepted.