Chapter 1.0Principles of Diffusion and
Mass Transfer
By: In. Nurul Hasyimah Mohd Amin
Objectives
• At the end of this chapter, student should be able to
1) Define mass transfer2) Define diffusion3) Derive Fick’s Law4) Derive mass transfer coefficient
Background of mass transfer
La,xa
Va,ya
Vb,yb Lb,xb
- How do we know the amount of mass exchanged by two phases?
- What is the new composition of the phases?
1.1 Introduction
• Basis behind Mass transfer…
Movement of something that has mass Just refers to the movement of all things Tendency to move from an area of high
concentration to low concentration Example:
- sprayed perfume in one corner of the room - pour bubble bath into a tub of running
water
1.1 Introduction
• Mass transfer…
… the term used to denote the transference of a component in a mixture from high concentration to low concentration .
1.1 Introduction
• Principles of Mass transfer
Mass transfer by ordinary molecular diffusion occurs because of a concentration difference
The mass transfer rate is proportional to the area normal to the direction of mass transfer. Not to the volume. So, the rate expressed as a flux
Mass transfer stops when the concentration is uniform
1.1 Introduction
• Diffusion…
… the movement under the influence of a physical stimulus of an individual component through a mixture.
What is the cause of diffusion
concentration gradient tends to move the component in such a direction as to equalize concentrations and destroy the gradient
In all the operations, diffusion occurs in at least one phase @ both phases
Role of diffusion in mass transfer
Gas Gas absorptionabsorption
Solute diffuses through the gas phase to the interface between the phases
DistillationDistillation -Low boiler diffuses through the liquid phase to the interface- away from interface to the vapor
ExtractionExtraction Solute diffuses through the raffinate phase to interface and then into the extract phase
Gas Gas absorptionabsorption
Solute diffuses through the gas phase to the interface between the phases
DistillationDistillation -Low boiler diffuses through the liquid phase to the interface- away from interface to the vapor
ExtractionExtraction Solute diffuses through the raffinate phase to interface and then into the extract phase
5 interrelated concepts are used in diffusion theory
Theory of diffusion
Velocity, uVelocity, u Length/time
Flux across a plane, NFlux across a plane, N Moles/(area) (time)
Flux relative to a plane zero Flux relative to a plane zero velocity, Jvelocity, J
Moles/(area) (time)
Concentration, cConcentration, c
Molar density, Molar density, MM
Moles/volume
Concentration gradient, dc/dbConcentration gradient, dc/db b = length of the path perpendicular to the area which diffusion is occuring
Total molal flux (moles/time-area)
Total molal fluxes for components A and B
Molar flux of component A through this reference plane
Theory of diffusion
Diffusion flux
Flux due to flow
Flux of A for a stationary plane
Fick’s first law of diffusion
Theory of diffusion
Component A
concentrationgradient
diffusivity
check your understanding
Consider a local concentration of 106 units per cm3 which drops by 10% over a distance of 1 cm. Then the gradient is -105 units cm-4. Assume the diffusivity is 103 cm2/s, calculate the value of flux, J.
Theory of diffusion
6.1-1-Geankoplis(413)
check your understanding
Think of the last time that you washed the dishes. You placed the first greasy plate into the water and the dishwater got a thin film of oil on the top of it. Find the flux, J of oil droplets through the water to the top surface. The sink is 18 cm deep, and the concentration of oil on the plate is 0.1 mol/cm3. Assume the diffusivity is 7x10-7 cm2/s.
Theory of diffusion
6.1-1-Geankoplis(413)
Theory of diffusion
Equimolal diffusion
for binary mixture A and B, component A and B diffuses at the same molar but at against direction
hence, convective term, uo=0
0
Theory of diffusion
Equimolal diffusion
for diffusion that pass through film thickness/plane BT and at the constant flux rate
yAi = ratio of mole A outside the plane
yA = ratio of mole A inner the plane
yAi
yA
db0 BT
Theory of diffusion
Equimolal diffusion
Ay
AiydbAdy
mDAJ
pls integrate
ACAiC
TBvD
AJ
ACAiC
TBvD
AJ
check your understanding
A mixture of He and N2 gas is contained in a pipe at 298 K and 1 atm total pressure which is constant throughout. At one end of the pipe at point 1 the partial pressure pA1 of He is 0.60 atm and at the other end 0.2 m pA2 =0.20 atm. Calculate the flux of He at steady state if DAB of He-N2 mixture is 0.687 x 10-4 m2/s.
Theory of diffusion
6.1-1-Geankoplis(413)
check your understanding
Ammonia gas (A) diffusing through a uniform tube 0.10 m long containing N2 gas (B) at 1.0132x105 Pa pressure and 298 K. At point 1, pA1=1.013x104 Pa and point pA2= 0.507x104 Pa. Calculate the flux of JA at steady state if DAB is 0.230 x 10-4 m2/s.
Repeat the calculation for component B, JB.
Theory of diffusion
6.1-1-Geankoplis(413)
Theory of diffusion
One component diffusion
when only component A is being transferred, the molal flux to/away from the interface, the equation becomes
Theory of diffusion
One component diffusion
after simplify and rearrangement, the equation becomes
AiyAy
TBMvD
AN
1
1ln
check your understanding
For the diffusion of solute A through a layer of gas to an absorbing liquid, with yA=0.10 and yAi=0.2, calculate;
1) the transfer rate for one way diffusion
2) the transfer rate for equimolal diffusion
3) what is the value of yA halfway through the layer for one way diffusion
Theory of diffusion
21.1-mccabe (654)
most mass transfer operations turbulent flow is desired to increase the rate of transfer per unit area Create more interfacial area
NA and JA can be used to predict the molar flux in diffusion for steady state mass transfer through stagnant layer
transfer is treated using same type equation which feature ‘k’ (mass transfer coefficient)
1.2 Mass transfer coefficient and film theory
Mass transfer coefficient,k
1.2 Mass transfer coefficient and film theory
differenceionconcentratarea
transfermassofratek differenceionconcentratarea
transfermassofratek
differenceionconcentratarea
transfermassofratek
s
cm
cmmolcm
smolunit
32
/
1.2 Mass transfer coefficient and film theory
But…
area
transfermassofrateJ
AAi
AC CC
JK
Therefore,
…………………..(1)
…………………..(2)
1.2 Mass transfer coefficient and film theory
For gas…
AAi
AC CC
JK
RT
Pkkk C
Mcy RT
Pkkk C
Mcy
For liquid…
…………………..(3)
…………………..(4)
1.2 Mass transfer coefficient and film theory
For steady state equimolal diffusion…
AAi
AC CC
JK
RT
Pkkk C
Mcy RT
Pkkk C
Mcy
substitute (5) into (1)…
…………………..(5)
► In order to illustrate the concept of interphase mass transfer let’s consider the process of
transport of a volatile chemical across the air/water interphase.
Pa - partial pressure of solute in the gas phase, atm Ca - concentration of solute in the gas phase, g/m3 Cw - concentration of solute in the water phase, g/m3
1.3 Interphase mass transfer
► The equilibrium partition between the air and water phases can be described as shown in the attached figure
1.3 Interphase mass transfer