Powder flow What and how to measure. Gabrie Meesters

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1 2 Powder flow What and how to measure Gabrie Meesters

2 Flowability according to Carr Flowability-fluidity Angle of repose : α R Compressibility: C Angle of spatula : α S Cohesiveness: Co 2

3 Angle of repose α s 3

4 Angle of spatula The greater the angle of spatula the less a powder flows. When α s < 40 the powder flows α s 4

5 Compressibility Measure the bulk density: ρ B [kg/m 3 ] Measure the tapped bulk density: ρ T [kg/m 3 ] C = ρ T ρ B ρ T 100 5

6 Cohesiveness : C o Pass powder through 3 superimposed control sieves of different aparture (which covers the sieze distribution of the powder) weigh the powder that remains on each sieve (W a, W b, W c ) C o = (5 W a + 3 W b + W c ) 100 [%] C o = 100 when non of the powder passes through the largest sieve C o = 0 when all powder passes through the finest sieve 6

7 Uniformity If product is coarse and grainy; no need to determine Cohesiveness Beter to determine a uniformity of the powder based on the size distributions U = d 0.6 d(0.1) D(0.6) = particle size of which 60% passes through the sieve D(0.1) = particle size of which 10% passes through the sieve U reflects the gradient of the size distibution and it magnitude The more narrow the size distribution, the closer U come s to 1 7

8 Floodability Angle of fall : α F Angle of difference : α D Dispersibility : D air 8

Angle of Fall α F After measuring the Angle of Repose, α R, a weight is dropped three times from a specific height onto the base of the powder plate on whhich the powder sits.

9 Angle of Fall α F After measuring the Angle of Repose, α R, a weight is dropped three times from a specific height onto the base of the powder plate on whhich the powder sits. The angle of repose changes after dropping the weight. The new angle is called the angle of inclination or the angle of fall α F. The more fluid like a powder is, the lower is α F than α R 9

10 Angle of difference α D α D = α R - α F The larger the angle of difference the more floodable a powder is. Floodable powders do not automatically have a smaller α F but usually have a much smaller α F, thus having a larger α D 10

Dispersibility D air This value directly refers to the tendency of a powder to disperse in the air when it is falling down (so it is NOT the dispersibility in a liquid!).

11 Dispersibility D air This value directly refers to the tendency of a powder to disperse in the air when it is falling down (so it is NOT the dispersibility in a liquid!). Drop a given quantity of powder down a cilinder at once and measure the quantity that lands on the collecting plate beneath the dropping point D air = q Wd 10 [%] With Q= quantity of powder dispersed (~10 g) [g] W d = quantity of powedr recovered [g] 11

12 12 Flowability index

13 13 Floodability index

14 14 Examples

15 15 Caking of powders

16 Powder Flow Testers & Uniaxial Compression Test Several powder flow testers are available: quantitative results qualitative results equipment design (silos, fluidized beds, etc.) quality control, comparison and ranking Uniaxial Compression Test: Flowability index: Consolidation stress: 1 Unconfined yield strength: c Jenike s classification: Step 1 Step 2 Step

Powder flowability Important factors The behavior of powders generally depends on: Their intrinsic properties: size, density, shape, roughness, porosity, etc.

17 Powder flowability Important factors The behavior of powders generally depends on: Their intrinsic properties: size, density, shape, roughness, porosity, etc. The external conditions: Stress level (State of compaction of the powder) Environment conditions (temperature, humidity) What is the effect of: Consolidation time Temperature Humidity on Yield strength? Caking Step 1 Step 2 Step

individual particles Caking Unwanted Agglomeration Slow process amplified by time

Origins: Any factor that can increase attractive forces Many mechanisms

18 What is Powder caking? Definition : Spontaneous and undesired formation of a coherent mass from individual particles Caking Unwanted Agglomeration Slow process amplified by time and variations of environmental conditions (T, RH, P). Origins: Any factor that can increase attractive forces Many mechanisms Consolidation under pressure Water adsorption/absorption Capillary condensation Liquid bridges Dissolution/Crystallization Phase transition Melting & softening Solid phase diffusion Etc. 1 18

19 Powder caking: Important factors Caking is influenced by: Intrinsic parameters: Particle size distribution Hygroscopicity Glass transition, Tg Chemical composition Hardness, deformability Etc. External factors: Relative Humidity (RH) Temperature Consolidation stress Time Case study: Wet caking of deliquescent materials Ex: salt (NaCl), sugar (sucrose), etc. submitted to Relative Humidity variations Deliquescence: formation of an aqueous solution when the RH reaches a certain Deliquescence Relative Humidity (DRH) threshold value 1 19

20 Wet caking of deliquescent materials: NaCl Step 1 : Deliquescence RH > DRH (76%) Aggregates of a few crystals Smoothing of the surface Increase of the amount of the liquid phase Dissolution (partial/total) 1 Source: Univ Compiegne, France 20

21 Wet caking of deliquescent materials: NaCl Step 2 : Drying RH < DRH (76%) Evaporation of water Re-crystallization Formation of a new cluster Re-crystallization 1 Source: Univ Compiegne, France 21

22 Wet caking of deliquescent materials: NaCl Caking : NaCl powder cakes after 1 sorption/desorption cycle Initial state Final state 1 Source: Univ Compiegne, France 22

23 23 Powder Flow

24 24 Silo failure

25 Shear stress Normal stress 26

26 Mohrs circle construction σ α =principle stresses In any system there are two planes at right angles to each orher in which the shear stresses are zero. The normal stresses acting on these planes are called principle stresses The Mohrs circle represents the possible combinations of normal and shear stressesacting on any plane in a boduy of powder unders stress 27

27 28 Jenike Shear Cell

28 29 Jenike Shear Cell

29 Jenike Tester 30

30 31 Shear Plane

31 Failure mechanism of cohesive granular material Phase A Phase B Phase C 32

32 Microscopic Interpretation 33

33 Yield locus procedure 34

34 Effective yield locus 35

35 Yield locus procedure 36

36 Yield locus procedure 37

37 Yield locus procedure 38

38 Effective yield locus 39

39 Time yield locus Is there a realtion with time for the flow behaviour of a powder. In this case; YES 40

40 Wall yield locus 41

41 Wall yield locus δ= effective angle of internal friction Φ w = angle of wall friction 42

42 43 Yield Locus

43 Hopper flow factor (FF) ff = σ c f c = compacting stress in the hopper stress developed in the powder Value of ff depends on: Nature of the powder Nature of the wall materials Slope of the hopper ff=hopper flow factor f c is called the unconfined yield stress. It is the stress that causes the formation of the arch in the bottom of the hopper So if f> f c there will be flow 44

44 Unconfined yield strength ff = σ c f c 45

45 Flow factor (FF) ff = σ c f c 46

46 47 Powder flow function

47 Determination of critical conditions for flow f c f c 48

48 Summary of design of silo outlet Shear cell tests on powder gives you a family of yield loci Mohr s circle stress analysis gives pairs of values of unconfined yield stress τ, and compacting stress σ C and the value of the effective angle of internal friction of the powder δ Pairs of values of τ and σ C give the powder flow function Shear cell tests of the powder and the matririal hopper wall give the angle of wall friction Φ w Φ w and δ are used to obtain hopper flow factor ff Powder flow function and hopper flow factor are combined to give the stress corresponding to critical flow-no flow σ crit σ crit, H(ϴ) (factor determined by the slope of the hopper wall), and bulk density of the powder, ρ b, are used to calculate the minimum diameter of the conical hopper outlet B. H(ϴ)=2.0 + ϴ/60 With ϴ angle of hopper cone 49

49 50 Chart for hopper flofact values for conical channels δ =30

50 51

51 52

52 53 Jenike tester

53 54 Brookfield ring shear testers

54 55 Schulze tester

55 56 Freeman technology

56 57 Anton Paar

57 58 Anton Paar

58 59

Wheat flour flowability as affected by water activity, storage time and consolidation**

Int. Agrophysics, 2005, 19, 119-124 INTERNATIONAL Agrophysics www.ipan.lublin.pl/int-agrophysics Wheat flour flowability as affected by water activity, storage time and consolidation** E. Domian* and K.