Ball mill
instrute INSTRUCTION
BALL MILL Introduction: Reduction of particle size is an important operation in many chemical and other industries. The important reasons for size reduction are
!asy handlin" Increase in surface area per unit #olume Separation of entrapped components The operation is hi"hly ener"y intensi#e$ hence a #ariety of specialized e%uipment is a#aila&le for speci'c applications. The e%uipment may utilize one or more of the follo(in" physical mechanisms for size reduction )i* Compression+ )ii* Impact+ )iii* Attrition+ )i#* Cuttin". !stimation of ener"y for the operation is important and is usually done &y empirical e%uations. !normous %uantities of ener"y are consumed in size reduction operations. Size reduction is the most ine,cient unit operations in terms of ener"y+ as -- of the ener"y supplied "oes to operatin" the e%uipment and producin" undesira&le heat and noise+ (hile less than / "oes in creatin" ne( interfacial area. Reduction to #ery 'ne sizes is much more costly in terms of ener"y as compared to relati#ely coarse products. Sie#in" refers to the separation of a mi0ture of particles of di1erent sizes usin" sie#es each (ith a uniform sized openin". Standard sie#es of speci'ed openin" sizes are used. Sie#es are stac2ed (ith the sie#e (ith the lar"est openin" on the top and the material is separated into fractions &y sha2in". The material &et(een t(o sie#es is smaller than the upper sie#e openin" &ut lar"er than the smaller sie#e openin".
Objectives: /. To "rind the "i#en material to a smaller size usin" a &all mill and to o&tain the size distri&ution of the initial and 'nal mi0ture &y sie#in".
3. To estimate the ener"y re%uired for the "rindin" operation. 4. To analyze the results usin" a#aila&le theories.
Theory and Analysis: The minimum ener"y re%uired for crushin" is the ener"y re%uired for creatin" fresh surface. In addition+ ener"y is a&sor&ed &y the particulate material due to deformation+ friction+ etc.+ (hich results in an increase of the material temperature. 5e'nin" the crushin" e,ciency as
A (¿ ¿ wb − A wa ) ( 1) W n Surface energy created ɳ C = = es ¿ Energy absorbed by material
6here
es
is the surface ener"y per unit area and
a&sor&ed. 6e can e0perimentally 'n 7.78 9 /.77. If
ɳ m
d ɳ C
W n is the ener"y
. The ran"e of
ɳ C
is &et(een
is the mechanical e,ciency+ the ener"y input is
A
(¿ ¿ wb − A wa ) ɳ C ɳ m
(SINCE W n= ɳ m w )( 2) W = e s ¿
:inally+ the "rindin" ener"y used per unit mass is
(
)
6 es 1 1 W = − (3 ) ´ sb ϕa D ´ sa m η c ηm ρ p ϕ b D
(here m is mass of material &ein" "round. In the a&o#e e%uation ; is the sphericity+
´ s is the surface #olume diameter and the su&scripts a and b D
refer to the initial and 'nal states+ respecti#ely.
!0periments sho( that the 'rst term in !%. )4* is not independent of
´s + D
and as a result the a&o#e e%uation is di,cult to use for analysis. Instead a num&er of empirical la(s ha#e &een proposed for calculation the ener"y re%uirements for crushin". The la(s can &e uni'ed in a di1erential form as follo(s
d
( ) W m
=−k
dD s
´s D n
( 4)
The di1erent la(s for the di1erent #alues of the e0ponent are
´ sa D W ( n =1: = K K ln Kic k slaw ) ( 5 ) ´ sb m D
( )
n =2:
n=
3 2
(
)
W 1 1 = K ! ´ − ´ ( !ittnge r s "aw ) ( 6 ) m D sb D sa
:
(
)
W 1 1 ( #ond s "aw ) (7 ) = K # − m √ D 80 b √ D 80 a
Note that the de'nition of particle size in
?article size such that =7 &y (ei"ht of the sample is smaller than it.
W m
= 10 W
i
(
1
´ 80 b √ D
−
1
´ 80a √ D
)
(8 )
6here the (or2 inde0 is de'ned as the ener"y re%uired per unit mass in 26h@ton to reduce an in'nitely lar"e particles to
´ 80=100 $m . In the a&o#e D
´ 80 is m+ of 6 is 26h and of m is ton. Balues of the (or2 e%uation+ unit of D inde0 o&tained from e0periments for di1erent materials are "i#en in the ta&le &elo(.
Material
6i )26h@ton*
37./ D4.= //.8 /4.E 4.7= /.4
Procedure: /. 6ei"h the "i#en sample and o&tain the initial size distri&ution &y sie#in". 3. Frind the sample in the &all mill for 47 minutes notin" the ener"y consumed durin" "rindin". 4. Measure the size distri&ution &y sie#in". . Note the R?M of &all mill. E. Note readin"s and dra( size distri&ution cur#es for a. Cumulati#e size distri&ution. &. :re%uency size distri&ution. c. Initial distri&ution and distri&utions o&tained after sie#in". d. Calculate the surface #olume diameter in each case.
´ 80 for all three distri&utions. e. O&tain the diameter D f. O&tain the coe,cients of 22 2R and the (or2 inde0 6i for all runs. ". Assumin" reasona&le #alues of G c and G c estimate es.
