mass transfer principle

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)


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


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


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



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


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


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


differenceionconcentratarea

transfermassofratek differenceionconcentratarea

transfermassofratek

differenceionconcentratarea

transfermassofratek

s

cm

cmmolcm

smolunit

32

/


But…

area

transfermassofrateJ

AAi

AC CC

JK

Therefore,

…………………..(1)

…………………..(2)


For gas…

AAi

AC CC

JK

RT

Pkkk C

Mcy RT

Pkkk C

Mcy

For liquid…

…………………..(3)

…………………..(4)


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

mass transfer principle

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