Week # 1 Particle Technology Fundamentals

1. Week # 1Particle Technology Fundamentals MARTIN RHODES (2008) Introduction to Particle Technology , 2nd Edition. Publisher John Wiley & Son, Chichester, West Sussex, England.

2. Solids Handling / Particle Technology

3. Sand Granular Fertilizers Polymer Pellets Coal Cohesive free-flowing Powder granular solid Granular Materials Cement Particle ‘diameter’ 1 mm 10mm 100mm 1mm 10mm 100mm Size ranges of various granular materials. Cohesive dp>100mm Dp < 100 mm Considerable attractive or cohesive forces between

5. Photographs of sand (a) Ottawa standard sand (b) Monterey sand

15. Describing the size of a single particle. Some terminolgy about diameters used in microscopy. • Equivalent circle diameter. • Martin’s diameter. • Feret’s diameter. • Shear diameter.

18. Describing the size of a single particle • Regular-shaped particles • The orientation of the particle on the microscope slide will affect the projected image and consequently the measured equivalent sphere diameter. • Sieve measurement: Diameter of a sphere passing through the same sieve aperture. • Sedimentation measurement: Diameter of a sphere having the same sedimentation velocity under the same conditions. Comparison of equivalent sphere diameters.

19. Comparison of equivalent diameters • The volume equivalent sphere diameter is a commonly used equivalent sphere diameter. • Example: Coulter counter size measurement. The diameter of a sphere having the same volume as the particle. • Surface-volume diameter is the diameter of a sphere having the same surface to volume ratio as the particle. (Example) Shape Cuboid Cylinder Cuboid: side lengths of 1, 3, 5. Cylinder: diameter 3 and length 1.

23. Description of populations of particles • Typical differential frequency distribution F: Cumulative distribution, integral of the frequency distribution.

24. Typical cumulative frequency distribution

25. For a given population of particles, the distributions by mass, number and surface can differ dramatically. • All are smooth continuous curves. • Size measurement methods often divide the size spectrum into size ranges, and size distribution becomes a histogram. • Comparison between distributions

26. Total number of particles, N and total surface area S are constant. • Particle shape is independent of size, as is constant. V is the total volume of the particle population and av is the factor relating the linear dimension of particle to its volume.

27. Common methods of displaying size distributions Arithmetic-normal Distribution Log-normal Distribution z: Arithmetic mean of z, sz: standard deviation of log x Arithmetic-normal distribution with an arithmetic mean of 45 and standard deviation of 12.

28. Log-normal distribution plotted on linear coordinates • Log-normal distribution plotted on logarithmic coordinates

30. Methods of particle size measurements: Sieving • Sieving: Dry sieving using woven wire sieves is appropriate for particle size greater than 45 mm. The length of the particle does not hinder it passage through the sieve aperture. • Most common modern sieves are in sizes such that the ratio of adjacent sieve sizes is the fourth root of two (e.g. 45, 53, 63, 75, 90, 107 mm).

31. Methods of particle size measurements: Microscopy • The optical microscope may be used to measure particle size down to 5 mm. • The electron microscope may be used for size analysis below 5 mm. • Coupled with an image analysis system, the optical and electron microscopy can give number distribution of size and shape. • For irregular-shaped particles, the projected area offered to the viewer can vary significantly. Technique (e.g. applying adhesive to the microscope slide) may be used to ensure “random orientation”.

32. For a sphere Stoke’s law Motion of solid particles in a fluid

33. Standard drag curve for motion of a sphere in a fluid

34. Single Particle Terminal Velocity

35. To calculate UT and x • (a) To calculate UT, for a given size x, • (b) To calculate size x, for a given UT, Independent of UT Independent of size x

36. Particles falling under gravity through a fluid Method for estimating terminal velocity for a given size of particle and vice versa

37. Non-spherical particles Drag coefficient CD versus Reynolds number ReP for particles of sphericity ranging from 0.125 to 1.0

41. Where the plotted line intersects the standard drag curve for a sphere (y = 1), Rep = 130. • The diameter can be calculated from: Hence sphere diameter, xv = 619 mm. • For a cube having the same terminal velocity under the same conditions, the same CD vesus Rep relationship applies, only the standard drag curve is that for a cube (y = 0.806)

47. Packed Beds: Ergun Equation Pressure Drop-Flow Relation

48. Hagen-Poiseuille: Tube equivalent diameter: Pressure drop-flow relationship Laminar flow: Darcy (1856) Flow area = eA; wetted perimeter = SBA; SB: Particle surface area per unit volume of the bed. Total particle surface area in the bed = SBAH For packed bed, wetted perimeter = SBAH/H = SBA

49. Carmen-Kozeny eq.: A Sv = 6/x Turbulent flow:

50. General equation for turbulent and laminar flow Ergun eq.