Table Of ContentAerosol Filtration
Series Editor
Laurent Falk
Aerosol Filtration
Dominique Thomas
Augustin Charvet
Nathalie Bardin-Monnier
Jean-Christophe Appert-Collin
"Lecteur, ne perdez point votre temps
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Où vous ne puissiez reprendre,
Il n’en est pas de si mal fait
En qui vous ne puissiez apprendre."
"Reader, do not waste your time
Hunting out mistakes in a book,
There is no book so perfect
That you can never find a mistake within,
Nor yet one so hopeless
That you may not still learn from it."
Jean de La Rivière (1721)
First published 2017 in Great Britain and the United States by ISTE Press Ltd and Elsevier Ltd
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ISBN 978-1-78548-215-1
Printed and bound in the UK and US
Notation
−12 −1
ε0 Vacuumpermittivity(8.8410 F.m )
−19
e Elementarycharge(1.60210 C)
−34
h Planck’sconstant(6.62610 J.s)
P
−23 −1
kB Boltzmannconstant(1.38110 J.K )
α Packingdensity(−)
α Liquidpackingdensity(−)
l
α Packingdensityofthedeposit(−)
d
α Maximumliquidpackingdensity(−)
film
α Packingdensityofthefiltermedium(−)
f
α Inter-agglomerateor-aggregatepackingdensity(−)
Inter
α Intra-agglomerateor-aggregatepackingdensity(−)
Intra
α Packingdensityofawettedfiltermedia(−)
m
α Packingdensityoftheparticles(−)
p
β Inhomogeneitycoefficient(−)
χ Dynamicshapefactor(−)
ΔP Pressuredropacrossthefilter(Pa)
x AerosolFiltration
ΔP Pressuredropacrossthecake(Pa)
G
ΔP Pressuredropacrossavirginfilter(Pa)
M
ΔP Finalpressuredropacrossthefilter(Pa)
f
ΔP Pressuredropacrossapleatedfilter(Pa)
MF
ΔP Pressuredropacrossaflatfiltermedia(Pa)
MP
ΔP Initialpressuredropacrossthefilter(Pa)
o
ΔP Pressuredropacrosssingularities(Pa)
S
η Singlefibercollectionefficiency(−)
η Single fiber collection efficiency for collection through electrostatic
elec
effects(−)
η Single fiber collection efficiency related to the interaction between
DR
diffusionandinterception(−)
η Singlefiberdiffusionefficiency(−)
D
η Single fiber collection efficiency through impaction and interception
IR
(−)
η Singlefiberimpactionefficiency(−)
I
η Minimumsinglefibercollectionefficiency(−)
min
η Singlefiberinterceptionefficiency(−)
R
−1
γ Surfacetensionoftheliquid(N.m )
l
3 −1
κ Forchheimer’spermeability(s .kg )
f
2
κ Permeabilityofthefiltermedia(m )
−1
λ Linearchargeofthefibers(C.m )
c
λ Meanfreepathofthegas(m)
g
λ Meanfreepathoftheparticle(m)
p
μ Dynamicviscosityofthegas(Pa.s)
Notation xi
2
Ω Filtrationarea(m )
−3
ρ Effectivedensity(kg.m )
e
−3
ρ Densityofthefluid(kg.m )
f
−3
ρ Densityoftheliquid(kg.m )
l
−3
ρ Referencedensity(1,000kg.m )
o
−3
ρ Densityoftheparticle(kg.m )
p
−3
ρ Densityoffibers(kg.m )
Fi
−3
ρ Densityofthematerial(kg.m )
m
σ Geometricstandarddeviation(−)
G
τ Relaxationtimeoftheparticle(s)
Θ Liquid/fibercontactangle
E
ε Dielectricconstantforafiber(−)
f
ε Dielectricconstantforaparticle(−)
p
ε Porosityofthedeposit(−)
d
ε Inter-agglomerateor-aggregateporosity(−)
Inter
ε Intra-agglomerateor-aggregateporosity(−)
Intra
ζ Pressuredropcoefficient(−)
z¯ Averagedistancetravelledbyaparticle(m)
D Diffusioncoefficientfortheparticle(m2.s−1)
F Force(N)
2
A Projectedareaofthefibers(m )
−1
a Specificareaofthefibers(m )
f
2
A Projectedareaoftheparticle(m )
p
xii AerosolFiltration
a Specific surface area of the particles (= 6/d for spherical particles)
p p
−1
(m )
−1
B Mechanicalmobility(s.kg )
B Bondnumber(Equation6.2)(−)
o
−3
C Concentration(#.m )
C Theoreticaldragcoefficientforthefibers(−)
T
−3 −3
C Concentrationofparticlesupstreamofthefilter(#.m orkg.m )
amont
−3
C Concentration of particles downstream of the filter (#.m or
aval
−3
kg.m )
C Realdragcoefficientforthefibers(−)
Treal
C (Z,t) Dragcoefficientforafiberloadedwithparticles(−)
Tm
C Dragcoefficientforafiber(−)
T
Ca Capillarynumber(Equation6.3)(−)
Co Overlapcoefficient(Equation5.39)(−)
Ct Dragcoefficientoftheparticle(−)
Cu Cunningham’scoefficient(Equation1.10)(−)
d Diameterofthefibers(m)
f
(cid:2)
d DiameterofthefiberscalculatedusingtheDaviesequation(m)
f
d Diameteroftheparticles(m)
p
d Aerodynamicdiameter(m)
ae
d Porediameter(m)
eq
d Diameterofthewettedfiber(m)
fm
D Fractaldimension(−)
frac
d Gyrationdiameter(m)
G
Notation xiii
D Hydraulicdiameter(m)
H
d Electricalmobilitydiameter(m)
me
d Massequivalentdiameter(m)
M
d Mostpenetratingparticlesize(MPPS)(m)
pmin
d Diameteroftheprimaryparticles(m)
pp
d Stokesdiameter(m)
St
d Geometricvolumeequivalentdiameter(m)
VG
d Meanvolumeequivalentdiameterforprimaryparticles(m)
Vpp
d Volumeequivalentdiameter(m)
V
(cid:2)
df EffectivediameterofthefibersaccordingtoDavies(m)
(cid:2)
df EffectivediameterofthefibersaccordingtoDavies(m)
df (Z,t) Diameterofthefiberloadedwithparticles(m)
m
Dr Drainagerate(−)
E Efficiencyofafilter(−)
E Minimumenergyofattractionbetweentheparticles(J)
M
−1
E Electricfield(V.m )
ce
E Fractionalcollectionefficiencyofafilter(−)
di
F Totalforcerelatedtothepresenceofwater(N)
C
f Fractionofthesurfaceareaoccupiedbytheperforation(−)
h
f Fractionofelectriccharges(−)
n
F Correctionfactor(Equation5.38)(−)
Co
F Laplaceforceorcapillarypressure(N)
La
F Forceproducedbycapillarytension(N)
LV
xiv AerosolFiltration
f Fractionofthetotalareaofthemedium(−)
S
f Fractionofthetotalvolumeoffibers(−)
Vf
Fe Electricforce(N)
Fp Weightoftheparticle(N)
Ft Dragforce(N)
−2
G Grammage(g.m )
h Distancebetweentwomolecules(m)
h Pleatheight(m)
H Hamakerconstant(J)
A
H Hydrodynamicfactorforthe“fan”model(Equation4.25)(−)
Fan
H HydrodynamicfactoraccordingtoHappel(Table4.2)(−)
Ha
H HydrodynamicfactoraccordingtoKuwabara(Table4.2)(−)
Ku
h Kozeny’sconstant(−)
k
H HydrodynamicfactoraccordingtoLamb(Table4.2)(−)
La
H HydrodynamicfactoraccordingtoPich(Table4.2)(−)
Pi
H HydrodynamicfactoraccordingtoYehandLiu(Table4.2)(−)
Ye
k Penetrationfactor(−)
k Fractalprefactor(−)
f
Kn Knudsennumber(−)
Kn Knudsennumberforfibers(Equation4.24)(−)
f
L Pleatlength(m)
L Totallengthofthefibers(m)
(cid:2) −2
L Totallengthofthefibersperunitvolume(m )
f
