1 Millimeter. 1 Micron. 1 Nanometer. 1 Angstrom ELECTRON SEPARATION PROCESS COMMON MATERIALS PARTICLE SIZE LOG SCALE MAGNETIC RANGE SPECTRUM

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1 HANDOUT 3. Millimeter Micron Nanometer Angstrom 00 APPROX. MOLEC. WT Radio waves Infrared Ultraviolet Visible X-rays MACRO MICRO MOLECULAR IONIC MOLECULE MACRO 200k 20k VISIBLE TO EYE OPTICAL MICROSCOPE ELECTRON MICROSCOPE COAL DUST BEACH SAND MILLED FLOUR GRAVEL TOBACCO SMOKE COLLOIDAL SILICA VIRUS SUGARS ATOMS POLYMER POWDERS -LUCITE -GEON -ETC. METAL IONS YEAST CELLS PYROGEN BACTERIA PAINT PIGMENT CARBON BLACK AQUEOUS SALTS HUMAN HAIR POLLEN RED BLOOD CELLS TALC CLAY ALBUMIN PROTEIN PARTICLE FILTRATION MICROFILTRATION ULTRAFILTRATION REVERSE OSMOSIS PARTICLE SIZE LOG SCALE ELECTRO- PARTICLE MAGNETIC RANGE SPECTRUM COMMON MATERIALS SEPARATION PROCESS

2 HANDOUT 3.2 STANDARD MESH SIZE Tyler US mm Inches

3 HANDOUT 3.3 Taken from Tables 2., 2.2, 2.3, and 2.7 in L. Svarovsky, Solid-Liquid Separation, 3 rd Ed., Butterworths, London, 990. DEFINITIONS OF EQUIVALENT AND STATISTICAL DIAMETERS. Symbol Name Definition DEFINITIONS OF EQUIVALENT SPHERE DIAMETERS x v Volume diameter Diameter of sphere with the same volume as the particle. x s Surface diameter Diameter of sphere with the same surface area as the particle. x d Drag diameter Diameter of sphere that has the same resistance to motions at the same velocity as the particle. x f Free-falling diameter Diameter of sphere of same density as the particle with the same free-falling speed in the same liquid. x St Stoke s diameter Same as x f but for when Stoke s Law applies (Re < 0.2) x A Sieve diameter Largest diameter sphere that can pass through the square aperture of the sieve screen. x SV Surface to Volume Ratio Diameter of sphere that has the same surface area to volume ratio as the particle. DEFINITIONS OF EQUIVALENT CIRCLE DIAMETERS x z Projected area diameter Projected area if the particle is resting in a stable position. x p Projected area diameter Projected area if the particle is randomly oriented. x c Perimeter diameter Diameter of a sphere with the same projected perimeter as the perimeter of the projected outline of the particle. DEFINITIONS OF STATISTICAL DIAMETERS x F Feret s diameter Distance between two tangents on opposite sides of the particle. x M Martin s diameter Length of the line which bisects the projected image of the particle (the two halves of the image have equal areas). x SH Shear diameter Particle width obtained with an image shearing eyepiece. x CH Maximum chord diameter Maximum length of a line limited by the contour of the projected image of the particle.

4 HANDOUT 3.4 LABORATORY METHODS OF PARTICLE SIZE MEASUREMENTS METHOD APPROX SIZE, µm SIZE TYPE Sieving (wet or dry) Woven wire Electro formed x A TYPE OF SIZE DISTRIBUTION By mass Microscopy By number Optical Electron x z, x F, x M x SH, x CH Gravity sedimentation 2-00 x St, x f By mass Centrifugal sedimentation x St, x f By mass Flow Classification Gravity elutriation (dry) Centrifugal elutriation (dry) Impactors (dry) Cyclonic (wet or dry) x St, x f By mass By mass By mass or by number By mass Coulter principle (elect. resist.) x v By number Field flow fractionation x d Depends upon detector Hydrodynamic chromatography x d Depends upon detector Fraunhofer diffraction (laser) 2000 Equiv laser diameter By volume Mie theory light scattering (laser) Equiv laser diameter By volume Photon correlations spectroscopy Equiv laser diameter By number Scanning infrared laser 3 00 Chord length By number Aerodynamic sizing nozzle flow x d By number Mesh obscurtion method 5 25 x A By number Laser Doppler phase shift 0,000 Equiv laser diameter Mean only Time of transition Equiv laser diameter By number Surface area to volume ratio Permeametry Hindered settling Gas diffusion Gas adsorption Adsorption from solution Flow microcalorimetry Calculated x SV By number mean

5 HANDOUT 3.5 ELECTRONIC PARTICLE COUNTER The electronic particle counters can measure particle sizes ranging from 0.4 to 200 micrometers. This method requires the particles to be placed in a stirred electrolyte solution. The resistance to the flow of electrical current through a small aperture is calibrated to the change in resistance depending upon the particle size (Figure ). Figure. Basic components of the Coulter Counter. As the particles pass through the aperture opening, they bend the current flux lines around the particles, thus causing a longer length for the current to pass and thus a higher resistance to the current (Figure 2). Voltage and current are measured to quantify the resistance using Ohm s Law: V = IR. APERTURE OPENING WITHOUT PARTICLE APERTURE OPENING WITH PARTICLE Figure 2. Particles in the aperture bend the electrical current flux lines.

6 HANDOUT 3.6 EXAMPLE 3- A sample of M&M s with peanuts are weighed as listed in Table 3-. Using an average density of.23 grams per cubic centimeter, the average candy diameter (assuming spherical shape) is calculated. Plot the frequency distribution and the cumulative frequency distribution of the average diameter of the candies. Using the formulas in Eqs.(3-3) and (3-4) the frequency and cumulative frequency distributions are calculated. The particle sizes are added up in x increments of 0.05 cm. The size ranges start with.45 to.50 cm. All M&Ms of size less than.50 are counted in the first increment, all M&Ms with size between.5 and.55 are in the second increment, and so on. The values for n j are determined by counting the number of M&Ms that fall in a given size increment and are assigned to the average size in the increment. Table 3-. Mass and diameter distribution of M&M s. Grams Dia, cm Size < Avg size No. fdx f F For example, there are 7 M&Ms in the size increment range of.5 to.55 cm and are assigned to the average size of.525 cm. fdx is determined by 7/2= , f is /0.05 = F is determined by cumulative summing the values fdx. The results of the summation are plotted in Figure 3-4. Frequency Distribution Frequency Distribution of M&Ms Diameter, cm Figure 3-4. Plot of frequency and cumulative frequency distributions for M&M s f F

7 HANDOUT 3.7 MODE HARMONIC MEAN ARITHMETIC MEAN f MEDIAN QUADRATIC MEAN CUBIC MEAN f x Figure 3.5. Comparison of mean size distributions where the various means are defined by: gx ( ) = gxdf ( ) 0 g(x) = x NAME OF MEAN ARITHMETIC MEAN, x a x 2 QUADRATIC MEAN, x q x 3 CUBIC MEAN, x c log x GEOMETRIC MEAN, x g /x HARMONIC MEAN, x h

8 HANDOUT 3.8 Sieve analysis of a sample of particles. Mass, number, and area fractions are calculated. Sieve analysis of a sample of particles. Mass, number and area fractions are calculated. Note Note 2 VOLUME AREA TRAY SIEVE AVG SIEVE MASS ON VOLUME V NUMBER NUMBER A AREA SIZE, MASS, TRAY, MM SIZE, MM g FRAC MM^3 FRAC MM^3 FRAC MM^2 MM^2 FRAC pan TOTAL MASS Comparison of the fractional distributions of the particle size distributions Fraction Mass & Volume Frac Number Frac Area Frac Avg Particle Size, mm

9 HANDOUT Expl curve Stokes Intermediate Newton Law Cd Re Figure 3.9. Drag coefficient for spheres versus Reynolds number. The three approximate curves from left 35 / to right are CD = 24 / Re p(stoke s Law range for Rep<), C D = 8. 5 / R ep (Intermediate range for <Rep<000), and C D = 044. (Newton s Law range 000<Rep<00,000).

10 HANDOUT 3.0 Table 3-3 Sphericity of Some Common Materials (McCabe & Smith, 5 th ed, pg928; Perry s Handbook 6 th ed, pg 5-54). PARTICLE MATERIAL SPHERICITY Sphere.0 Cube 0.8 Short Cylinder (Length=Diameter) 0.87 Berl saddles 0.3 Raschig rings 0.3 Coal dust, natural (up to 3/8 inch) 0.65 Glass, crushed 0.65 Mica flakes 0.28 Sand Average for various types Flint sand, jagged Sand, rounded Wilcox sand, jagged Most crushed materials 0.6 to 0.8

11 HANDOUT 3..E+0.E+09.E+08.E+07.E+06 Plot to determine drag coefficients of irregularly shaped particles at terminal velocity. The particles are randomly oriented relative to the flow direction. Shape is accounted for by the sphericity. SPHERICITY CdRep^2.E+05.E+04.E+03.E+02.E+0.E+00.E-0.E+00.E+0.E+02.E+03.E+04 Rep Where Cd R 2 4 ep = 3 N GA 3 ρd pu R = d p ρ( ρ p ρ ) g ep N GA = 2 µ µ D p is the equivalent diameter of a sphere with the same volume as the particles, x v.

12 HANDOUT 3.2 ut* 00 0 Sphericity = Sphericity for Disks only dp* Date taken from Kunii & Levenspiel Fluidization Engineering, 2ed Butterworth, Boston, 99, page 8 Where ut* = ut µ and d p 2 g ( ρ ρ ) s ρ g g / 3 / 3 ( ρ ρ ) g ρ g s g * = d p 2 µ