Mechanical_operations_ppt1_particle characterization

Mechanical_operation - INSTRUCTOR CHETAN M PATEL" $ Particle Characterization& Characterization of solid particles • The characterization

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Unformatted text preview: INSTRUCTOR: CHETAN M. PATEL ! "# $ % Particle Characterization & )% *% ' ' % '' ( '' )% ' % * ' ' Characterization of solid particles • The characterization of powder is quite difficult and offer many complex problems as described by hausner (1960) • Diameter, average diameter • particle shape • specific surface – depends on particle size, size distribution, particle shape and surface conditions • Interparticulate friction - The ratio, tap density over apparent density, is an indicator of interparticulate friction grey & beddow (1968) Particle size measurement +* & + ,( -% * ' *' . , -% * / 4 % *' ! 25 0 # / 4 ' *% ", 12 3 2$3 $ 23 2$ 222 3 $2 62 -% ) 0 * 70 ' %* * 8 ) 4% * 4 * * %* * , 9:; % * ' < * Equivalent Spherical Diameter In, Engineering we wish to perform calculations using diameter, so we need simple Basis to describe irregularly shaped particle,. This is the origin of the concept of equivalent spherical diameter In which some physical properties of particle is related to a sphere that would have same the same property e.g. volume. ,% * * 4 *' -% ) * = 0 * (, * -% ) * * *% , Equivalent diameter $ 6V p >* ' ? )% dv = 3 "@ $ * %' ' π )% ? Sp dS = π 4: % ' -% ) * 9:; @ $ )% %' >* %' ' ? d SV = d sauter = 6 Vp Sp A * ,* % ) * , >* ' ? * , dstokes = 18 µ vt g (ρ − ρ f) ) @B ) , )* -% ) * ? > * ' % * ) % % % % ? ' ' ?$ * ' * (, (A * Description of Populations of Particles C % ,( D ' * ' -% * ( * (, ,* (% %) 0* (% %% ) & %) 0* ? (% '% E The two are related mathematically in that the cumulative distribution is th integral of the frequency distribution; i.e. if the cumulative distribution is denoted as F, then the frequency distribution dF/dx. dF/dx = f(x) 4% E, * '' *%% ) ' -% ,* (% 9 :; /* 0* % % Q ( xi ) = m i =1 )* wi (% ) 0* % % P ( xi ) = 1 i=m )* (% wi =1 − Q (xi ) 4 ( D ? * '%% )* %% (% )* (% %) * ) ,? (% 0 ( (, % ( * (% ' %' )% )% ? * * (% ,* '# D 4# 'D 4 ' 4 D ' -% %% ' -% %% ,* )* ,* )* ,* )* (% (% (% (% (% (% (, % ( (, % ( (, % ' (, % ' (, % ' (, 4 (? * (% 9 :; ' -% %% 4 %' ) * '' % * ' , ( * (% (, 4% %( * #" B ,* 0 (% ? ) %' B % 0G B' # , , (% F % ** #! B/ %, # % %( * % ** * (% (, 0* ' (% ) (, % ( '# D * (, % ' 'D' (% * '' ' * Equivalent diameter of many particles d= F ' m i =1 wi di '$ '$ 0 m i =1 m i =1 m * 0 (dV ) = 3 2 wi di 3 w i di 2 w i di3 w i di 2 (dA) = d 32 = d sv = i =1 m i =1 Particle size is denoted either by x or d Describing the Population by a Single Number, Average size of many particles Table 2. methods of particle size analysis Particle size functions: Theoretical Distribution function # H% ! (% I $ ! (% 4 J# * (% ? * @ 22 3 = K @ :2 ? B B D $B $B =H * ' (% n %% )* $H % * $ % (% * (% A? x Q 3( x) = 1 − exp − xd @/ ' D* @ %* , *D$ 0 03 Fig 7. % Cumulative undersize distribution using Rosin rammler distribution JE 5 % % ) ln − ln 1 − Q 3( x ) 100 = n (ln x − ln x d ) Fig. 8 Types of Particle Size Distributions & !? *L25 M* 25 / # 0* ? ? *% * " ,( * 1 2: @ 2:$ 2 2$ 2$ 222 $2 62 Particle shape measurement & %? 0 ( *) ' % ' * ' %' * * * * A, ( % , % %* % * ? % 0 Fig. 9 Several possible ideal particles shapes ' % Fig 10. Two Different Samples could be Reported as Identical using a Size-Only Distribution [3] Sphericity: %' ' ? ' (, % % *% ' ' -% ) * * π 6 Vp π = Ap 1 3 2 * -% * * , * ,Φ ? Φs = a sphere a particle = 6 Dp S particle / V particle F ! * ' ' )% % M 0 G C @? * M @ $? * M " ' 2 4 ' 4 : % ,' 9; AN A ' ) ,' (? G A ' ' $ ) *' * G Cd ' = 4 ( ρ p − ρ f ) gd v 3 ρ fU t 2 ! '' ψ= dv 2 ds 2 -% ψ= dst 2 dv 2 *' ψ= dv 2 da 2 ' ψ= πdv 2 αsvdv 2 , αsv = SWρ π 6 nidvi 3 nidvi 2 LLJ OP = Q :22 Particle Characterization Measurement of Bulk Properties of Powder % A! ,G • % A* , • • • %! *! /* ( ,G * * (, ** ,G , '% ' ' % *% % <* N ) % )% '? * # Bed Porosity Fraction void volume =Void Volume/ Total volume = VV/VT=1Porosity of a static bed depends upon - Particle shape and surface roughness - Particle size and size distribution -Size of the container relative to the particle diameter - Method of packing B/ s Table 2. Definitions of various types of densities that follow from the volume definitions of . BSI = BritishStandards Institute, ASTM = American Society for Testing and Materials. Fig. 13 Illustration of various volume types. Fig 14 Porosity as a function of sphericity and packing structure. Taken from HANDBOOK of FLUIDIZATION and FLUID-PARTICLE SYSTEMS Edited by Wen-Ching Yang % Hausner ratio = Tapped Density Bulk Density The ratio, tap density over apparent density, is an indicator of interparticulate friction grey & beddow (1968) * Ref: R.P. Zou, A.B. Yu, Powder Technology 88(1996) 71-79 Measurement of Angle of repose Fig 15. D. Geldart ET AL. CHINA PARTICUOLOGY Vol. 4, Nos. 3-4, 104-107, 2006 ' Powder Characteristics Non flowing Cohesive Cohesive Fairly free flowing Free flowing Excellent flowing aerated '' ? ( , % ) *D Hausner Ratio Angle of Repose >1.4 >1.4 1.25-1.4 1-1.25 1-1.25 1-1.25 >60 >60 45-60 30-45 10-30 <10 Effect of particle size on bulk properties and flowability Figure 16 Bulk densities and Hausner ratio against mean particle size. A. Chi-Ying Wong , Chemical Engineering Science 55 (2000) 3855 – 3859 Please refer class notes for more details Figure.17 angle of repose against mean particle size. Figure.18 Hausner ratio vs. angle of repose A. Chi-Ying Wong , Chemical Engineering Science 55 (2000) 3855 - 3859 ...
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This note was uploaded on 11/25/2010 for the course CHEMICAL E CHE 201 taught by Professor N/a during the Spring '09 term at Punjab Engineering College.

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