L 1 - Principles of Mass Transfer 567777777788888888.pdf

Mass transfer

1. ChE 3201: Mass Transfer II
Principles of Mass Transfer
Diffusion
Safat Anam
Lecturer
Dept. of ChE, RUET
1

2. Ref. Book:
Transport Processes & Unit Operations (3
rd
ed)
Christie J. Geankoplis
Chapter 6
2
Safat Anam, Lecturer, Dept. of ChE, RUET

3. Variousunitoperationscouldbeclassifiedintothreefundamentaltransfer
(or"transport")processes:
Momentumtransfer:Fluidflow,mixing,.sedimentation,and
filtration.
Heattransfer:Conductiveandconvectivetransferofheat,
evaporation,distillation,anddrying.
Masstransfer:Distillation,absorption,drying,extraction,adsorption,
membraneprocessetc.
Whenmassisbeingtransferredfromonedistinctphasetoanotheror
throughasinglephase,thebasicmechanismsarethesamewhetherthephase
isagas,liquid,orsolid.
All three of the molecular transport processesof momentum, heat, and
mass are characterized by the same general type of equation
3
Safat Anam, Lecturer, Dept. of ChE, RUET

4. Fick's Law for Molecular Diffusion
Moleculardiffusionormoleculartransportcanbedefinedasthetransferor
movementofindividualmoleculesthroughafluidbymeansoftherandom,
individualmovementsofthemolecules.
4
Safat Anam, Lecturer, Dept. of ChE, RUET

5. Fick’s1
st
lawstatesthat,“Themovementofparticles(diffusionflux)froma
highconcentrationregiontoalowconcentrationregionortherateofmass
flowperunitareaisdirectlyproportionaltotheconcentrationgradient”.
5
Safat Anam, Lecturer, Dept. of ChE, RUET

6. EXAMPLE6.1-1.MolecularDiffusionofHeliuminNitrogenAmixtureof
HeandN
2gasiscontainedinapipeat298Kand1atmtotalpressurewhich
isconstantthroughout.Atoneendofthepipeatpoint1thepartialpressure
P
AlofHeis0.60atmandattheotherend0.2m,P
A2=0.20atm.Calculatethe
fluxofHeatsteadystateifD
ABoftheHe-N
2mixtureis0.687x10
-4
m
2
/s.
Convective Mass-Transfer Coefficient
Whenafluidisflowingoutsideasolidsurfaceinforcedconvectionmotion,
therateofconvectivemasstransferfromthesurfacetothefluid:
N
A= k
C(C
L1–C
L2)
Where, k
C= mass-transfer coefficient in m/s,
C
Ll= bulk fluid concentration in kg mol A/m
3
C
L2= concentration in the fluid next to the surface of the solid.
6
Safat Anam, Lecturer, Dept. of ChE, RUET

7. MOLECULAR DIFFUSION IN GASES
Equimolar Counter diffusion in Gases:
TwogasesAandBatconstant
totalpressurePintwolarge
chambersconnectedbyatube
wheremoleculardiffusionat
steadystateisoccuring.
Stirringineachchamberkeeps
theconcentrationsineach
chamberuniform.Thepartial
pressureP
A1>P
A2andP
B2>P
B1.
MoleculesofAdiffusetothe
rightandBtotheleft.
SincethetotalpressurePis
constant,thenetmolesofA
diffusingtotherightmustequal
thenetmolesofBtotheleft.
7
Safat Anam, Lecturer, Dept. of ChE, RUET

8. ForabinarygasmixtureofAandBthediffusivitycoefficientD
ABforA
diffusinginBisthesameasD
BAforBdiffusingintoA.
EX –6.2-1
8
Safat Anam, Lecturer, Dept. of ChE, RUET

9. General Case for Diffusion and Convection
9
Safat Anam, Lecturer, Dept. of ChE, RUET

10. SpecialCaseforADiffusingThroughStagnantNondiffusingB:
Evaporationofapureliquid
suchasbenzene(A)atthe
bottomofanarrowtube,
wherealargeamountofinert
ornondiffusingair(B)is
passedoverthetop.The
benzenevapor(A)diffuses
throughtheair(B)inthetube.
Theboundaryattheliquidsurfaceatpoint1isimpermeabletoair,sinceairis
insolubleinbenzeneliquid.Hence,air(B)cannotdiffuseintoorawayfrom
thesurface.Atpoint2thepartialpressureP
A2=0,sincealargevolumeofair
ispassingby.
10
Safat Anam, Lecturer, Dept. of ChE, RUET

11. 11
Safat Anam, Lecturer, Dept. of ChE, RUET

12. Time of diffusion:
12
Safat Anam, Lecturer, Dept. of ChE, RUET

13. Ex6.2-2:Waterinthebottomofanarrowmetaltubeisheldataconstant
temperatureof293K.Thetotalpressureofair(assumeddry)is1.01325x
10
5
Pa(1.0atm)andthetemperatureis293K(20°C).Waterevaporatesand
diffusesthroughtheairinthetubeandthediffusionpathZ
2-Z
Iis0.1524m
(0.5ft)long.Calculatetherateofevaporationatsteadystatekgmol/s·m
2
.
Thediifusivityofwatervaporat293Kand1atmpressureis0.250x10
-4
m
2
/s.Assumethatthesystemisisothermal.
DiffusionThroughaVaryingCross-SectionalArea
13
Safat Anam, Lecturer, Dept. of ChE, RUET

14. Diffusion from a Sphere:
Evaporationofadropofliquid,theevaporationofaballofnaphthalene.
Considerasphereoffixedradiusr
1minan
infinitegasmedium.Component(A)at
partialpressureP
Alatthesurfaceis
diffusingintothesurroundingstagnant
medium(B),whereP
A2=0.Assume
Steady-statediffusion.
14
Safat Anam, Lecturer, Dept. of ChE, RUET

15. If P
A1is small compared to P (a dilute gas phase),
(For both gas
& liquid)
Time for diffusion: (derive by
yourself in the
previous way)
Ex6.2-4:Asphereofnaphthalenehavingaradiusof2.0mmissuspendedin
alargevolumeofstillairat318Kand1.01325x10
5
Pa(1atm).Thesurface
temperatureofthenaphthalenecanbeassumedtobeat318Kanditsvapor
pressureat318Kis0.555mmHg.TheD
ABofnaphthaleneinairat318Kis
6.92x10
-6
m
2
/s.Calculatetherateofevaporationofnaphthalenefromthe
surface.
15
Safat Anam, Lecturer, Dept. of ChE, RUET

16. Diffusion Coefficients for Gases
Experimental determination of diffusion coefficients:
Two-bulbmethod:Theapparatus
consistsoftwoglassbulbswith
volumesV
1andV
2m
3
connectedby
acapillaryofcross-sectionalareaA
m
2
andlengthLwhosevolumeis
smallcomparedtoV
1andV
2.Pure
gasAisaddedtoV
1andpureBto
V
2atthesamepressures.
Thevalveisopened,diffusionproceedsforagiventime,andthenthevalveis
closedandthemixedcontentsofeachchamberareanalyzed.
Assumeeachbulbisalwaysofauniformconcentrationandquasi-steady-
statediffusioninthecapillary.
16
Safat Anam, Lecturer, Dept. of ChE, RUET

17. 17
Safat Anam, Lecturer, Dept. of ChE, RUET

18. Prediction of diffusivity for gases:
(i).Thediffusivityofabinarygasmixtureinthedilutegasregion,i.e.,atlow
pressuresnearatmospheric,canbepredictedusingthekinetictheoryofgases:
D
AB= 1/3ūλ
Where,ūistheaveragevelocityofthemoleculeandλisthemeanfreepath.
(ii)Boltz-manequation:averagecollisiondiameterandcollisionintegral(8%
errorupto1000K):
Thisequationconsidertheintermolecularforcesofattraction&repulsion
betweenmoleculesandalsothedifferentsizeofthemoleculesAandB.This
equationpredictsdiffusivitywithanaveragedeviationofabout8%upto
1000K.
18
Safat Anam, Lecturer, Dept. of ChE, RUET

19. (iii)Theaboveequationiscomplicatedtouse&oftensomeoftheconstants
suchasσ
ABarenotavailable.Thusamoreconvenientequationisusedto
predictthediffusivityobtainedbycorrelatingmanyrecentdataanduses
atomicvolumes.Thisequationcanbeusedformixtureofnon-polargasesor
forapolar-nonpolarmixture.Itsaccuracyisnotquiteasgoodasprevious.
Schmidtnumberofgases:TheSchmidtnumberofagasmixtureofdiluteA
inBisdimensionlessandisdefinedas
TheSchmidtnumberisthedimensionlessratioofthemolecularmomentum
diffusivityμ/ρtothemolecularmassdiffusivityD
AB.ValuesoftheSchmidt
numberforgasesrangefromabout0.5to2.ForliquidsSchmidtnumbers
rangefromabout100toover10000forviscousliquids.
19
Safat Anam, Lecturer, Dept. of ChE, RUET

20. MOLECULAR DIFFUSION IN LIQUIDS
Diffusionofsolutesinliquids,forexampleliquid-liquidextractionor
solventextraction,gasabsorption,anddistillation.
Therateofmoleculardiffusioninliquidsisslowerthaningases.
Themoleculesinaliquidareveryclosetogethercomparedtoagas.
ThemoleculesofthediffusingsoluteAwillcollidewithmoleculesof
liquidBmoreoftenanddiffusemoreslowlythaningases.
Thediffusioncoefficientinagaswillbeoftheorderofmagnitudeof
about10
5
timesgreaterthaninaliquid.
Themoleculesinaliquidarepackedtogethermuchmorecloselythanin
gases,thedensityandtheresistancetodiffusioninaliquidaremuchgreater.
20
Safat Anam, Lecturer, Dept. of ChE, RUET

21. Equimolar counter diffusion in Liquids:
21
Safat Anam, Lecturer, Dept. of ChE, RUET

22. Diffusion of A through nondiffusing B:
Where solute A is diffusing and solvent B is stagnant or nondiffusing.
22
Safat Anam, Lecturer, Dept. of ChE, RUET

23. Ex.6.3-1:Anethanol(A)-water(B)solutionintheformofastagnantfilm
2.0mmthickat293Kisincontactatonesurfacewithanorganicsolventin
whichethanolissolubleandwaterisinsoluble.Hence,N
B=0.Atpoint1the
concentrationofethanolis16.8wt%andthesolutiondensityisρ
1=972.8
kg/m
3
.Atpoint2theconcentrationofethanolis6.8wt%andρ
2=988.1
kg/m
3
.Thediffusivityofethanolis0.740x10
-9
m
2
/s.Calculatethesteady-
statefluxN
A.
Experimental measurement of diffusivity in liquids:
23
Safat Anam, Lecturer, Dept. of ChE, RUET

24. 24
Safat Anam, Lecturer, Dept. of ChE, RUET

25. 25
Safat Anam, Lecturer, Dept. of ChE, RUET

26. Suppose,fortheliquiddiffusioncoefficientmeasuringapparatus,
Volumeofwater,V=1.1L
Lengthofcapillaries,x=0.5cm
Diameterofcapillaries,d=0.1cm
Numberofcapillaries,N=97
Electricalconductivitychangeperunitmolarconcentrationchange,
C
M=4.1×105μS/(mol/L) 26

27. 27
Safat Anam, Lecturer, Dept. of ChE, RUET

28. Prediction of Diffusivities in Liquids:
1.Stoke-Einsteinequation:
2.Wilke-Changequation:Forsmallersolutemolarvolumes/smaller
molecules:
28

29. Molecular Diffusion in Solids
Leachingoffoods,suchassoybeans,andofmetalores;
Dryingoftimber,salts,andfoods;
Diffusionandcatalyticreactioninsolidcatalysts;
Separationoffluidsbymembranes;
Diffusionofgasesthroughpolymerfilmsusedinpackaging;
Treatingofmetalsathightemperaturesbygases.
29
Safat Anam, Lecturer, Dept. of ChE, RUET

30. Diffusion in Solids Following Fick's Law
30
Safat Anam, Lecturer, Dept. of ChE, RUET

31. Ex.6.5-1:Thegashydrogenat17°Cand0.010atmpartialpressureis
diffusingthroughamembraneofvulcanizedneoprenerubber0.5mmthick.
ThepressureofH
2ontheothersideoftheneopreneiszero.Calculatethe
steady-stateflux,assumingthattheonlyresistancetodiffusionisinthe
membrane.ThesolubilitySofH
2gasinneopreneat17°Cis0.051m
3
(atSTP
of0
o
Cand1atm)/m
3
solid.atmandthediffusivityD
ABis1.03x10
-10
m
2
/sat
17°C.
31
Safat Anam, Lecturer, Dept. of ChE, RUET

32. 32
Safat Anam, Lecturer, Dept. of ChE, RUET

33. 33

34. Ex.6.5-2:Apolyethylenefilm0.00015m(0.l5mm)thickisbeing
consideredforuseinpackagingapharmaceuticalproductat30°C.Ifthe
partialpressureofO
2outsideis0.21atmandinsidethepackageitis0.01
atm,calculatethediffusionfluxofO
2atsteadystate.Usepermeabilitydata
fromTable6.5-1.Assumethattheresistancestodiffusionoutsidethefilm
andinsidearenegligiblecomparedtotheresistanceofthefilm.
Diffusion of liquids in porous solids:
Ex 6.5 –3 (self)
34
Safat Anam, Lecturer, Dept. of ChE, RUET

35. Diffusion of gases in porous solids:
Assignment & Self Practice:
Exercise Problem (C. J. Geankoplis/3
rd
ed/ chapter 6)
6.1 –1, 2.
6.2 –1, 2, 3, 4, 5, 8, 9.
6.3 –1, 2.
6.5 –1, 2, 3, 4, 6, 7, 8.
35
Safat Anam, Lecturer, Dept. of ChE, RUET