Chapter 3. Particle Size Analysis

Size: px

Start display at page:

Download "Chapter 3. Particle Size Analysis"

Evan Chapman
5 years ago
Views:

1 Chapter 3. Particle Size Analysis 3. Introduction Particle size/particle size distribution: a key role in determining the bulk properties of the powder... Size Ranges of Particles - Coarse particles : > μm - Fine particles : ~ μm - Ultrafine(nano) particles : <. μm (nm) 3.2 Describing the Size of a Single Particle Description of regular-shaped particles: Table 3.

2 Figure 3. - Equivalent circle diameter - Martin's diameter - Feret diameter Equivalent (sphere) diameters Figure Equivalent volume (sphere) diameters: the diameter of the hypothetical sphere having the same volume d p, v = ( 6V π ) /3 - Equivalent surface diameter: the diameter of the hypothetical sphere having the same surface area d p, s = ( S π ) /2 - Surface-volume diameter: the diameter of the hypothetical sphere having the same surface-to-volume ratio d p, sv = 6V S - Stokes diameter: the diameter of the hypothetical sphere having the same terminal settling velocity - Aerodynamic diameter: the diameter of the hypothetical unit-density sphere having the same terminal settling velocity "Which diameter we use depends on the end use of the information."

3 3.2 Description of Population of Particles ) Introduction to Size Distribution of Particles Particle size ~ diameter, d p ( μm) Data on particle size measurement Size Range d p, i ~d p, i +, μm -4 Count 4 Cumulative Fraction, F i.4 Fraction, F i + - F i.4 F i +- F i d p, i + - d p, i > 5.. Count(number) size distribution: or frequency distribution by number * F i +- F i d p, i + - d p, i vs. d p : discrete size distribution * Lim Δd p F i + -F i = df N ) d p, i + -d p, i dd p f N ) vs. d p - continuous size distribution : where f N ),( fraction/ μm): count(number) size distribution function f N )dd p : fraction of particle counts(numbers) with diameters between d p and d p +dd p -Cumulative count size distribution : F N (a)= cf. f N )= df N ) dd p a f N )dd p, (fraction)

4 .8.6 f N ) Particle size distribution curve..8.6 F N ) Cumulative distribution curve Mass(or volume) size distribution function f M ),( mass fraction/ μm) : mass size distribution function f M )dd p : fraction of particle mass with diameters between d p and d p +dd p f M )dd p = π ρ p 6 d 3 pf )dd p d 3 pf )dd p = π ρ p 6 d 3 = f V ) pf )dd p d 3 pf )dd p

5 Volume or mass size distribution function.8 Count Mass.6 f N ) or f M ) Count and mass size distribution curves Surface-area size distribution function f S )dd p = π d 2 pf )dd p = d 2 pf )dd p πd 2 pf )dd p d 2 pf )dd p Figure 3.4 Table Describing the Population by a Single Number: ) Averages Averages Based on count size distribution: - Arithmetic Mean: d p = d p f )dd p = d p df ).8 μm - Median : d p at F(dp )=.5 9. μm - Mode : most-frequent size 6. μm The differences in averages come from skewed distribution with

6 long tail. Other Arithmetic Means Mass mean diameter d p, mm = d p f M )dd p = or d p df M d p, mm = Surface-area mean diameter d p d 3 pf N )dd p = d 3 pf N )dd p d 4 pdf N d 3 pdf N d p, sm = d p f S )dd p = d p df S Count Mass.8.6 f N ) or f M ) Various average diameters for skewed distribution with long tail Moment average First moment average: arithmetic count mean d p = [ d p df ] Second moment average: diameter of average surface area or

7 quadratic mean d p, s = [ d 2 /2 pdf ] Third moment average: diameter of average mass or cubic mean /3 d p, m = [ d 3 pdf ] 위의 surface-mean, mass(volume)-mean 직경및 second, third moment 평균 직경은모두직경의지수배 ( 보다큰 ) 의 weight 가주어지므로산술평균 직경보다당연히커진다. Figure 3.6 Geometric mean Harmonic mean logd p = [ logd pdf ] = d p, h [ df d p ] 2) Standard deviation σ = [ - d p ) 2 /2 df ) ] = [ - d p ) 2 f )dd p ] /2 Degree of dispersion 입도의분산 ( 흩어짐 ) 을수치화한값 Next section 3.7 Common Methods of Displaying Size Distribution: Standard Size Distribution Functions ) Arithmetic Normal(Gaussian) distribution:

8 f )dd p = σ 2π [ exp - - d p ) 2 2σ ] 2 dd p and σ = d p,84% - d p,5% = d p,5% - d p,6% =.5,84% - d p,6% ) - Hardly applicable to particle size distribution Particles : no negative diameter/distribution with long tail 2) Lognormal distribution : 위의정규분포함수에서 d p 를 lnd p 로 σ 를 ln σ g 로바꾸면얻어진다. f(lnd p )dlnd p = (lnσ g ) 2π [ exp - (lnd p- lnd p ) 2(lnσ g ) 2 2 ] d lnd p where ln d p = - lnd p df )= - lnd p df(lnd p )= - lnd p f(lnd p )dln d p =lnd p, g d p, g : geometric mean(median) diameter /2 ln σ g = [ - d p ) 2 df ) ] = [ (lnd p -lnd p, g ) 2 f(lnd p )d ln d p ] /2 - σ g : geometric standard deviation σ g = d p, 84% d p,5% = d p, 5% d p,6% = [ d p,84% d p, 6% ] /2 From the Table above our sample data can be plotted as follows: 위의그림에서우리데이터는대수정규분포함수에가까움을확인할 수있다.

9 f ) or f(ln d p ) Count-mean diameter Mass mean diameter Count Mass -. Particle diameter μm Expression of data as a logarithmic size distribution function * Log-probability diagram For cumulative size distribution F(lna)= ln a f(lnd p )dlnd p F vs. a probability scale logarithmic scale

10 Count Mass Cumulative % 위그림에서보듯대수정규분포함수에가까움을재확인할수있고, 두 직선이나란하므로두분포함수에서표준편차의값은같음을알수있다. * Dispersity criterion Count Mass E Cumulative % Representation of cumulative % of the data on log-probability graph - Monodisperse : σ = or σ g =., in actual σ g <.4 (.2)

11 - Polydisperse 여기서굳이.4로정한것은이값이모든입자시스템을자연스레오랜시간방치하면도달하는입도분포의값이기때문이다..2는이에비해단분산의기준을좀더엄격히정한값이다. 3.8 Methods of Particle Size Measurement ) Sieving 2) Microscopy 3) Sedimentation 4) Permeametry 5) Electrozone Sensing 6) Laser Diffraction 3.9 Sampling Avoiding segregation... - The poeder should be in motion when sampled - The whole of the moving stream should be taken for many short time increments...

Chapter 1. Particle Size Analysis

Chapter 1. Particle Size Analysis 1.1 Introduction Particle size/particle size distribution: a key role in determining the bulk properties of the powder... μ μ μ Size ranges of particles (x) - Coarse particles