MASS TRANSFER CLASS NOTES FOR ENGINEERING

 

MASS TRANSFER  CLASS

NOTES FOR ENGINEERING

Before discussing convective mass

transfer, it is necessary to compare

convective heat transfer and convective

mass transfer since there is a similarity

between these two. In heat transfer,

there is convective heat transfer

coefficient ‘ h’. Similarly there is mass

transfer coefficient in mass transfer.

Prandtl number (Pr = ν / α) is replaced

by Schmidt number (Sc = ν / DAB) and

the Nusselt number (Nu = hL/kf) is

replaced by Sherwood number

(Sh = kc L / DAB) and Tf is mean film

temperature. Mass transfer may occur in a gas mixture.

Further mass transfer may occur in a liquid

solution. Also, mass transfer may occur in a

solid. The basic mechanisms of mass

transfer are the same whether the phase is

a gas, or a liquid, or a solid. Driving force

for mass transfer is concentration gradient

of species. Mass transfer due to

concentration gradient is diffusion which is

very analogous to heat transfer by

conduction.

Table: Mass transfer coefficients in Forced Convection Mass Transfer

Sr. 

No.

Empirical

equation

Object

Type of

flow

local or

average 

temp

Range of

dimensionless number

1.
Shx= 0.332 Rex1/2 Sc 1/3
Flat plate
Laminar
Local
0.6≤Sc ≤50
2.
Shav= 0.664 Rex1/2 Sc 1/3
Flat plate
Laminar
Average
0.6 ≤Sc ≤50
3.
Sh= 0.0296 Rex4/5 Sc 1/3
Flat plate
Turbulent
local
Rex≤105, 0.6 ≤Sc ≤50
4.
Sh= (0.037 Rex4/5 −871) Sc 1/3
Flat plate
Transition
Local
5×105< Rex ≤107, 0.6≤Sc ≤50
5.
Sh = 0.3+ [0.62ReD1/2Sc1/3 ×[1 + (0.4/Sc)2/3]-1/4] ×[1 + (ReD/282,000)5/8]4/5
Cylinder
Cross flow
Average
ReD Sc > 0.2
6.
Sh= 2 + (0.4 ReD1/2+ 0.060 ReD2/3) Sc0.4 ×(μ/μs)1/2
Sphere
Cross flow
Average
3.5 < ReD< 7.6×104,
0.71 < Sc < 380 and 1.0 < (μ/μs) < 3.2
For an ideal gas
pAV =nA RT
CA=nA / V Normally in gases, there is equimolar counter diffusion which gives J*AZ = — DAB dCA/dz = — J*BZ = –(–) DBA dCB/dz = DBA dCB/dz DAB = DBA For a binary gas mixture of A and B, the diffusivity coefficient DAB=DBA in counter molar diffusion of gases. Other parameters of equimolar counter diffusion are J*AZ = — J*BZ or J* is constant in a steady state dcA = –dCB C= CA + CB DAB = DBA

Mass transfer Coefficients

These empirical correlations are valid for low mass transfer rate (or equi-molar mass transfer) where the mole fraction of species ‘A’ is less than about 0.05. For higher mass transfer rate, corrected mass transfer coefficients, using the log mean concentration difference, must be used. Hence kc is replaced by kc/(1 − yA)lm
Where lm is logarithmic mean and is given by
(1 − yA)lm = [(1–yA) –(1–yAi)] /[ ln((1–yA) / (1–yAi))] yA is gas mole fraction of species A = pA / pt yAi is gas mole fraction of species A at the interface = pAi / pt pA is the partial pressure of species A pAi is the partial pressure of species A at the interface

Mass transfer coefficients at Macro level

When a fluid flowing outside a solid surface in forced convection motion, rate of convective molar flux is given by:
NA = kc (cL1— cLi)
NA=molar flux of species A = kmol/s m2 kc = mass transfer coefficient (m/s) cL1 = bulk fluid concentration, kmol/m3 cLi = concentration of fluid near the solid surface, k mol/m3 kc depends on the following factors: 1. System geometry—pipe or flat plate or channel 2. Flow velocity—laminar, transition or turbulent flow 3. Fluid properties—density, viscosity, specific heat etc. From the empirical equation of Sherwood number applicable, first mass transfer coefficient is calculated. Only then, mass flux can be known. These calculations are very similar to convective heat transfer calculations i.e.
Convective heat flux = h Δt
Where h is the convective heat transfer coefficient
Δt is the temperature difference

MASS TRANSFER

Four terms frequently used in mass transfer 

  1. Molar concentration or Mole concentration or 3.5 < ReD< 7.6×104,

          0.71 < Sc < 380

          1.0 < (μ/μs) < 3.2

or volume concentration,  ’ CA

ii. Mass concentration, ‘ ρA’

iii. Mole fraction ‘ xA’

iv. Mass fraction ‘mA*’

Definition of Mole concentration’ CA’ of Species A in a mixture

Number of molecules of species A present per unit volume of the mixture (atoms/m3 or molecules/m3 or moles/m3 or kmol/m3)

Definition of mass concentration, ‘ρA, of Species A in a mixture

Mass concentration of species A = Mass of species A per unit volume of the mixture ( kg of species A / m3 mixture)

Definition of Mole fraction’ xA’ of Species A in a mixture

It is a ratio of molar concentration of A to the total molar concentration

xA  = CA/C = CA/(CA + CB)

It has no units.

Definition of mass fraction ‘mA*’ of Species A in a mixture

It is a ratio of mass concentration of A to the total mass concentration

mA* = ρA/( ρA+ ρB)

It has no unit.

Diffusion

It is the movement of particles in a medium from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance.

Diffusion in gases >> diffusion in liquids>>diffusion in solids.

Types of Diffusion

(a) Concentration diffusion: Concentration diffusion is due to concentration gradient. Fick’s law gives a linear relation between the rate of diffusion of chemical species and the concentration gradient of that species. (b) Thermal diffusion: Diffusion due to a temperature gradient. Usually negligible unless the temperature gradient is very large. (c) Pressure diffusion: Diffusion due to a pressure gradient. Usually negligible unless the pressure gradient is very large.

Diffusion in solids Knudsen diffusion: Diffusion phenomena in porous solids is called Knudsen diffusion.

Cause Of Diffusion Concentration difference—Whenever there is concentration difference in a medium, there is mass transfer by natural flow from the high concentration to the low concentration region.

Practical Examples Of Mass Transfer (Diffusion)

1. There is a tank which is divided into two equal parts by a partition. Initially, the left half of the tank contains oxygen O2 gas while the right half contains N2 gas at the same temperature and pressure. As soon as the partition is removed, the O2 molecules will start diffusing into the N2 while the N2 molecules will diffuse into O2. Over the passage of time, there will have a homogeneous mixture of N2 and O2 in the tank. It is mass transfer due to concentration gradients either way.

2. A drop of red liquid dye when added to a cup of water, the dye molecules will diffuse slowly by molecular diffusion in all directions in the remaining water till a homogeneous color is established. 3. Water evaporates from an open pan into air because of the difference in concentration of water vapor at the water surface and the surrounding air. 4. Evaporation of water from an open tray 5. Mass transfer is there in any open thermodynamic system i.e. suction, compression and discharge by a compressor is mass transfer.

6. Mass transfer in extraction

7. Mass transfer in distillation

8. Mass transfer in absorption

9. Mass transfer in separation

10. Mass transfer in purification