Particle Size Sizing Technique 2: hydrodynamic chromatography sieving microscopy
Lab 5-Particle Sizing
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CHE 565LAB 5: PARTICLE SIZING APPARATUS
ABSTRACT
In many industrial appliati!ns a sin"l# num$#r %ill $# r#&uir#d
t! 'arat#ri(# t'# partil# si(# !) t'# p!%d#r* In many p!%d#r
'andlin" and pr!#ssin" !p#rati!ns+ partil# si(# and si(#
distri$uti!n play a ,#y r!l# in d#t#rminin" t'# $ul, pr!p#rti#s !)
t'# p!%d#r* Si#-in" is pr!$a$ly t'# #asy and #rtainly t'# m!st
p!pular m#t'!d !) si(# analysis* .ry si#-in" usin" %!-#n %ir#
si#-#s is a sampl#+ '#ap m#t'!d !) si(# analysis suita$l# )!r
partil# si(#s "r#at#r t'an /5 0m* Si#-in" "i-#s a mass
distri$uti!n and si(# ,n!%n as t'# si#-# diam#t#r* Sin# t'#
l#n"t' !) t'# partil# d!#s n!t 'ind#r its passa"# t'r!u"' t'#
si#-# ap#rtur#s+ t'# si#-# diam#t#r is d#p#nd#nt !n t'# ma1imum
%idt' and ma1imum t'i,n#ss !) t'# partil#* T'is #1p#rim#nt
d!n# t! d#t#rmin#d t'# distri$uti!n !) partil#s $y usin" si#-in"
m#t'!d* T'# si#-# must $# l#an and dry $#)!r# startin" t'#
#1p#rim#nt* 2#i"'t 344" !) sand and put its !nt! t'# si#-#*
A)t#r 5 minut#s+ t'# s'a,#r st!pp#d t'# sand partil#s l#)t !n
#a' sr##n ar# %#i"'t#d* T'# a-#ra"# sand si#-# an $#
alulat#d t'r!u"' si#-# ap#rtur#s+ dpi !) t'# sand !n #a' tray*
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CHE 565LAB 5: PARTICLE SIZING APPARATUS
1.0 INTRODUCTION
Partil# si(# m#asur#m#nt is an #1tr#m#ly imp!rtant param#t#r ar!ss m!st $ran'#s !)
industry*
T'# sta$ility+ '#mial r#ati-ity+ !paity+ )l!% a$ility and mat#rial str#n"t' !) many
mat#rials ar# a))#t#d $y t'# si(# and 'arat#ristis !) t'# partil#s %it'in t'#m* G#ttin"
t'in"s ri"'t at #-#ry sta"# !) pr!duti!n+ )r!m R 7 . t'r!u"' t! manu)atur# and &uality
!ntr!l !) t'# )inis'#d pr!dut is -ital* 8al-#rn 'as a ran"# !) si(in" s!luti!ns )r!m su$9
nan!m#t#r t! millim#t#rs in si(#*
8al-#rn Instrum#nts is t'# %!rlds l#adin" suppli#r !) partil# si(# m#asur#m#nt
instrum#ntati!n* H!%#-#r+ in t'is #1p#rim#nt sr##nin" m#t'!d is t'# !n# t'at %!uld $#
l!!,#d )!r* Sr##nin" is a m#t'!d !) s#paratin" partil#s a!rdin" t! t'# si(#*
In industrial sr##nin"+ t'# s!lids ar# dr!pp#d !n !r t'r!%n a"ainst a sr##nin" sur)a#* A
sin"l# sr##n an ma,# a sin"l# s#parati!n int! t%! )rati!ns* A mat#rial pass#d t'r!u"' a
s#ri#s !) sr##ns !) di))#r#nt si(#s is s#parat#d int! si(# )rati!ns+ #1ampl# )rati!ns in
%'i' $!t' t'# ma1imum and minimum partil#s si(#s ar# ,n!%n* Sr##nin" is
!asi!nally d!n# %#t $ut mu' m!r# !mm!nly dry* !r -#ry )in# partil#s !t'#r
m#t'!ds !) s#parati!n ar# m!r# #!n!mial* 8any -ari#ti#s and typ#s !) sr##n ar#
a-aila$l# )!r di))#r#nt purp!s#s*
;n t'# !t'#r 'and+ si#-in" is pr!$a$ly t'# #asy and #rtainly t'# m!st p!pular m#t'!d !)
si(# analysis* .ry si#-in" usin" %!-#n %ir# si#-#s is a sampl#+ '#ap m#t'!d !) si(#
analysis suita$l# )!r partil# si(#s "r#at#r t'an /5 0m* Si#-in" "i-#s a mass distri$uti!n
and si(# ,n!%n as t'# si#-# diam#t#r*
8!st la$!rat!ry t#sts us# !nly a small sampl# and t'is 'as t! $# ta,#n )r!m a pr!duti!n
str#am !r )r!m an #1istin"+ st!r#d mat#rial* T'is sampl# 'as t! $# t'# r#pr#s#ntati-# !)
%'!l# mat#rial* By ta,in" many small sampl#s )r!m all parts !) t!tal %'i'+ %'#n
3
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CHE 565LAB 5: PARTICLE SIZING APPARATUS
!m$in#d+ %ill r#pr#s#nt t'# t!tal %it' an a#pta$l# d#"r## !) auray* T'is m#ans t'at
all partil#s in t'# t!tal must 'a-# t'# sam# pr!$a$ility !) $#in" inlud#d in t'# )inal
sampl#*
E-#n t'!u"' %# usually assum# partil#s t! $# sp'#rial in m!st !ur alulati!ns+ t'is is
n!t n##ssarily tru# and may !ntri$ut# #rr!r in !ur #1p#rim#ntati!n and analys#s* T'#
pr#is# s'ap# !) t'# partil#s us#d
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CHE 565LAB 5: PARTICLE SIZING APPARATUS
2.0 OBJECTIVES
T'# !$#ti-# !) t'is #1p#rim#nt is t! study t'# distri$uti!n !) partil#s*
3.0 THEORY
I) t'# p!%d#r mass 8 'as a si(# ran"# !nsistin" !) Npsp'#rial partil#s !) si(# d+ Np3
!) si(# d3+ and s! !n+ t'# sur)a#-!lum# si(#:
( )=
++
++=
dxd
dNdN
dNdNd
sv
pp
pp
sv
C
*****
*****
3
33
3
@
33
@
2'#n si#-in" is us#d d+ d3+Dar# r#pla#d $y a-#ra"#s !) ada#nt si#-# ap#rtur#s+ dpi+
and t'# #&uati!n $#!m#s:
( )=
pii
pidx
dC
T'#r# is n! #ntir#ly satis)at!ry %ay !) !mparin" t'# %idt' !) si(# distri$uti!n !) t%!
p!%d#rs 'a-in" di))#r#nt m#an si(#s+ n!r !) d#)inin" '!% %id# a distri$uti!n is* ;n#
us#)ul %ay is t! sp#i)y t'# r#lati-# spr#ad+ dpm+ and t'# spr#ad is !$tain#d )r!m t'#
umulati-# p#r#nta"# und#rsi(# -s* t'# si(# pl!t*
T'# spr#ad is d#)in# as:
3
F6FG/ dd
=
dpm t'# spr#ad %'#n t'# distri$uti!n is 54F )r!m t'# %'!l# ran"#*
/
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4.0 PROCEDURES
* T'# si#-# trays ar# l#an#d usin" a $rus' and air #t*
3* T'# trays ar# sta,#d t!"#t'#r -#rtially %it' lar"#st ap#rtur# !n t!p and t'#
small#st ap#rtur# !n t'# $!tt!m* Sand is t'#n %#i"'t#d )!r 344 "rams*
@* T'# sand is trans)#rr#d !nt! t'# si#-#*
/* T'# si#-# s'a,#r is #nsur#d t! $# l!s#d*
5* T'# tim#r !) t'# si#-# s'a,#r is s#t )!r 5 minut#s and it is s%it'#d !n*
6* 2'#n t'# s'a,#r st!pp#d+ t'# sand partil#s l#)t !n #a' sr##n inludin" t'#
$!tt!m ar# %#i"'t#d*
* T'# distri$uti!ns !) partil#s ar# n!t#d d!%n*
* T'# si#-# trays ar# l#an#d %'#n )inis'#d*
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5.0 APPARATUS
* Si#-# trays
3* Si#-# s'a,#r ma'in#
@* Brus'
/* Air #t #&uipm#nt
5* Sand
Figure 1 S!"#$e %& 'ie(e ')!*er +)!+ u'i,g &%r +)i' e-#eri"e,+
Si#-#
tr#ys
Si#-#s'a,#r
ma'in#
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.0 RESU/TS
Si#-# ap#rtur#+
JmSi(# dpi+ Jm
2#i"'t Si#-#
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Cu"u$!+i(e 3 U,4er'i5e (er'u' S i5e 4#i
934*44
4*44
34*44
/4*44
64*44
G4*44
44*44
34*44
4*4 54*4 44*4 54*4 344*4 354*4 @44*4 @54*4 /44*4 /54*4 544*4
4#i
2u"u$!+i(e3
d pm H I@ Jm d p G/F H 343dp 6F H G
Figure .1 6r!#) %& Cu"u$!+i(e Pere,+!ge U,er'ie Ver'u' #i
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7eig)+ 3 %& S!,4 89i: (er'u' Si5e 84#i:
/63*5
@@I*5
4*4
@I*5
3*5
65*4
M4*4
335*4
94*444
4*444
4*444
34*444
@4*444
/4*444
54*444
4*4 44*4 344*4 @44*4 /44*4 544*4
4#i
9i
Figure .2 7eig)+ #ere,+!ge i, r!,ge (er'u' #i
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T!$e .2 D!+! &%r H!r"%,i ;e!,
Cumulati-#
P#r#nta"#
Und#r Si(#
Harm!ni
8#an
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>u!4r!+i ;e!, gr!#)
934
4
34
/4
64
G4
44
34
4*44EK44 5*44EK4/ *44EK45 *54EK45 3*44EK45 3*54EK45
>u!4r!+i ;e!, 84#2:
Cu"u$!+i(e3U,4er'i5e
Figure .4 Cu"u$!+i(e Pere,+!ge U,er'ie (er'u' >u!r!+i ;e!,
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Cumulati-#
P#r#nta"#
Und#r Si(#
G#!m#tri
8#an
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T!$e .5 D!+! &%r Ari+)"e+i ;e!,
Cumulati-#
P#r#nta"#
Und#r Si(#
Arit'm#ti
8#an dpi+JmAr#a
44 /63*5 *644EK4
MM*M6 @@*5 M*//EK44MM*M35 335*4 */6EK4@
5M*45 M4*4 *M4/EK4@
/*@5 65*4 3*55@EK43
/6*5 3*5 *35EK4@
3M*55 @*5 5*5EK43
94*4 4*4 4*444EK44
1.24@E?04
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Ari+)"e+i ;e!, 6r!#)
934*44
4*44
34*44
/4*44
64*44
G4*44
44*44
34*44
4*4 44*4 344*4 @44*4 /44*4 544*4
4#i
Cu"u$!+i(e3
Figure . Cu"u$!+i(e #ere,+!ge u,er'ie (er'u' !ri+)"e+i "e!,
Cumulati-#
P#r#nta"#
Und#r Si(#
Cu$i 8#an
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T!$e . D!+! &%r Cui ;e!,
Cui ;e!, 6r!#)
-20
0
20
40
60
80
100
120
93*444EK4I 4*444EK44 3*444EK4I /*444EK4I 6*444EK4I G*444EK4I *444EK4G *344EK4G
Cui ;e!, 84#3:
Cu"u$!+i(e3U4er'i5e
Figure . Cu"u$!+i(e Pere,+!ge U,er'ie (er'u' Cui ;e!,
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.0 SA;P/E OF CA/CU/ATIONS
r!m Ta$l# :
Si(# dpi+Jm m5*/633
/35544=
+
r!m i"ur# 6*+ t'# -alu# !) m#dian+ dpmt'# si(# !rr#sp!ndin" t! t'# 54F -alu# is @
Jm*
T'# r#lati-# spr#ad+pmd
3
F6FG/ dd
=
3
6343 =
m M@=
H#n#+ r#lati-# spr#ad m
m
I@
M@
4*5@6
r!m Ta$l# A in App#ndi1 A+ t'# typ# distri$uti!n !) t'# partil# is %id#*
r!m i"ur# /+ umulati-# p#r#nta"# und#rsi(# Qs arit'm#ti m#an +dpi
44
+
areaTotald ap =
44
M35*3/I5+ =apd
md ap I5*3/+ =
r!m i"ur# 5+ umulati-# p#r#nta"# und#rsi(# Qs 'arm!ni m#an+ dp
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44
+
areaTotald hp =
44
M6II3*4+ =hpd
md hp 44M6G*4+ =
r!m i"ur# 6+ umulati-# p#r#nta"# und#rsi(# Qs "#!m#tri m#an+ L!" dp
44
+
areaTotald gp =
44
64MG6*I6+ =gpd
md gp I66*+ =
r!m i"ur# + umulati-# p#r#nta"# und#rsi(# Qs u$i m#an+ dp@
44+
areaTotald
cp =
44
IM*/55G@5MM+ =cpd
md cp M*/55G@5M+ =
r!m i"ur# + umulati-# p#r#nta"# und#rsi(# Qs &uadrati m#an+ dp3
44+
areaTotald qp =
44
G//*33M5G4+ =qpd
md qp 4*33M5G+ =
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@.0 DISCUSSION
T'#r# ar# many )at!rs t'at d#t#rmin# t'# pr!$a$ility !) a partil# passin" t'r!u"' t'#
si#-# and t'#s# inlud# t'# r#lati!ns'ip !) t'# si(# !) t'# partil# and t'# m#s' !p#nin"+
t'# dir#ti!n !) m!-#m#nt and t'# !ri#ntati!n !) t'# partil# r#lati-# t! t'# )r## si#-in"
sur)a#* T'#r#)!r#+ t'# si#-# m!-#m#nt and si#-in" tim# ar# ritial #l#m#nts t! t'# #1at
and l#ar s#parati!n !) t'# indi-idual si(# )rati!ns*
i"ur# 6* in r#sults s#ti!n a$!-#+ s'!%s t'# Cumulati-# F und#rsi(# -#rsus Si(# dpi
"rap'* T'is "rap' is pl!tt#d $#aus# a pl!t !) umulati-# F und#rsi(# an !n#al
p#uliariti#s !) distri$uti!ns !r in !t'#r %!rds t'# partil# si(# distri$uti!n* Supp!s# t'#
r#sults "i-# a sm!!t' !r"i)* Sin# t'is is an #1p#rim#nt+ t'# ur-# t'at $#in" !$tain#d isn!t sm!!t' #n!u"'* E-#n t'is #1p#rim#nt is #asy t! 'and !n+ t'#r# must $# s!m# #rr!r
!ur durin" m#asurin" t'#s# partil#s* r!m t'# "rap'+ a -alu# !) m#dian+ dpm%'i'
s'!% t'# a-#ra"# si(# partil# an $# !$tain#d* T'# -alu# !) m#dian dpm!rr#sp!ndin" t!
t'# 54 F -alu# !n t'is "rap' is d#t#rmin#d %'i' is @ Jm* r!m t'# sam# "rap'+ t'#
-alu# )!r d/F and d6F ar# $!t' 343 and 6 r#sp#ti-#ly* T'#n+ t'# -alu# is us#d t!
alulat# t'# r#lati-# spr#ad
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m#an !) num$#r distri$uti!n !ns#r-#s t'# num$#r and sur)a# !r !ri"inal p!pulati!n and
is ,n!%n as num$#r sur)a# m#an* r!m i"ur# 6*+ t'# &uadrati m#an "rap' s'!%
-alu# !) ar#a und#r t'# ur-# is us#d t! d#t#rmin# t'# -alu# !) dp+& is 33M5*4 Jm*
T'# ap#rtur#s !) a si#-# may $# r#"ard#d as a s#ri#s !) "au"#s %'i' r##t !r pass
partil#s as t'#y ar# pr#s#nt#d at t'# ap#rtur#* T'# pr!$a$ility t'at a partil# %ill pr#s#nt
its#l) at an ap#rtur# d#p#nds !n t'# )!ll!%in" )at!rs:
a= T'# partil#s si(# distri$uti!n !) t'# p!%d#r
$= T'# num$#r !) partil#s !n t'# si#-#
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10.0 RECO;;ENDATIONS
In !rd#r t! "#t an aurat# r#sult )!r t'is #1p#rim#nt+ '#r# ar# s!m# r#!mm#ndati!ns t'at
an $# us#d*
* B#)!r# startin" t'# #1p#rim#nt+ ma,# sur# t'at t'# si#-# tray is l#an#d $y usin" a
$rus' and air #ts* S! t'at+ an aurat# m#asur#m#nt !) sand )!r #a' si#-# tray
ap#rtur# an $# !$tain#d*
3* in# m#s' t#1til# si#-#s ar# partiularly s#nsiti-# t! m#'anial str#ss and
m#'anial l#anin" %it' a sti)) $rus' %ill dama"# and dist!rt t'# m#s' and
%#a,#n its strutur#*
@* A-!id paralla1 #rr!r durin" %#i"'t t'# 344" sand and durin" %#i"'t #a' tray*/* Ti"'t#n t'# t'um$nuts until t'# #ntir# sta, is s!lidly '#ld t! t'# s'a,#r+ and
#ntr#d %it'in t'# '!ldin" $ra,#ts* T'#r#)!r# t'# s'a,#r ma'in# must $# l!s#d
pr!p#rly in !rd#r t! "#t an aurat# r#sult and t! a-!id n!isy n!is#*
5* 8a,# sur# t'at t'# si#-# s'a,#r st!pp#d $#)!r# ta,# t'# si#-#s tray t! a-!id t'#
aid#nt !urs*
6* It imp!rtant t! #nsur# t'at t'#r# ar# n! sand partil#s l#)t in t'# si#-# pan as t'is
an a))#t t'# r#sult !) #1p#rim#nt*
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REFERENCES
Introduction to Particle Technology, Martin Rhodes, John Wiley and Sons,
reference page 54 !0"
Gas Fluidization Technology# $eldart" %" &ed'# 1(86# John Wiley, )e* +or"
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APPENDI9 A
T!$e A 7i+) %& 'ie i'+riu+i%,' !'e %, re$!+i(e '#re!
)-./er of siees on*hich the .iddle !0
&appro' of the po*der is
fo-nd
3dp. ype of distri/-tion
1 0 ery narro*
2 0"07 )arro*
7 0"1! airly narro*
4 0"25 airly *ide
5 0"77
Wide6 0"41
! 0"48( 0"6 ery *ide
11 0"! ery *ide
917 90"8 :tre.ely *ide