che5700 陶瓷粉末處理 batching and mixing batch feed always involves mixing, objective: - high...

Che5700 陶瓷粉末處理

Batching and Mixing Batch feed always involves mixing, objective: -

high uniformity, high reliability (more judgment (experience) rather science; no proper equations to describe particle flow)

Before mixing: action of feeding; next few graphs showing some common equipments, goal: good powder flowability.

Most ideal state of mixing: random homogeneous mixture RHM

•What is the mixer meant to do? • produce a good mix• What do you mean by “good” then?• the mixer need to have the right quality (appearance, particle concentration)• well mixed, on a microscopic scale• the products should be free of long-range difference of concentrations• the mixture needs to be random• well mixed on certain scale of scrutiny• product must undergo a certain rate of reaction

Purpose of Mixing

Bulk Solid Transport


One way to avoid funnel flow: reduce friction from walls

Mass flow – first in, first out, good results; Funnel flow – first in, last out (rat holing); not

desirable

Properties of Mass of Particles


Pressure is not the same in all directions: one applied pressure will create some pressures in other directions, but always smaller; related to particle shape and packing; define K’ = normal pressure/applied pressureShear applied at surface will be transmitted through a static mass of particlesDensity of mass will varyBefore flow, mass of particles will increase its volume first (dilation)When angular solids are piled up on a flat surface, there will be an angle of repose; (free flowing solids: this angle is between 15 and 30o)

Angle of Friction

Angle of storage tank and angle of friction of particle whether particle can free flow, i.e. mass flow or funnel flow;

Arching: state when particle can not flow at all

Common experience: flow of powder decrease if size of flow unit > 15% of opening size

Cohesive & Noncohesive Solids

Non-cohesive solids (free flowing; cohesionless): K’ 0.35 – 0.6Cohesiveness: often sensitive to moisture


Angle of friction: influenced by particle size, shape, or even water content, it often increase cohesive force between particles increase angle of friction more difficult to free flow

Abrasion: another possible problem with ceramic particles during transportation

Powder Mixing


More art than science; Can never achieve perfect mixing like that in fluid phase; Complete mixing: often refers to specific structure, not

attainable from a random process; Characterization of mixture: I.e. degree of

homogeneity - (1) a statistical problem; (2) sample size (scale of scrutiny) consideration – need to be “proper”, too large or too small: little value; e.g. sintering after mixing – then consider diffusion distance during sintering, choose appropriate size for sampling ， can be considered as single sample within that size.

lack of scale-up principle: due to poor understanding of particle behaviour during motion;

Scale of Segregation

•The length, area or volume of the largest region of each component in the mixture is referred to “scale of segregation” of that component• In a liquid solution: minimum scale of segregation – size of largest molecules• In a particle system: largest particle size

• Completely random vs completely dispersed• Degree of segregation larger in the former case

Sampling size: e.g. adding carotene into powder milk (1/1000), how should we sampling?

Degree of Mixedness

rnrqprrn

nxp

!)!(

!)( nrx /

)2

)(exp(

2

1)()(

2

2

px

dx

xdpxF

p,q true fractions; x measured fraction


Use statistical numbers as index of degree of mixing, to discuss uniformity of sample, to compare different mixing equipment and operation conditions.

Statistically, bimodal distribution for mixtures, often use Gaussian or Poisson distribution as examples

E.g. A, B equivalent , except color different, then

Mixing Indices


2/10

2

]1

)([

N

CCis

N

2/111 ))1(

(n

CCr

ro

o sM

loglog

loglog

2/1

11 )]1([ CCo

* Sampling analysis: Standard deviation s (s2 = variance) ; where o = standard deviation of original segregated mixture; r = standard deviation of ultimate completely random mixture; s = standard deviation of current sample; N = number of analyzed samples; n = particle number in sample

More Indices


For example:Rose – M = 1 – s/o; (unmixed 0 mixed 1- 1/n1/2)Lacey – M = (o

2 – s2)/(o2 - r

2) (from 0 1)Kramer – M = (o – s)/(o - r) (from 0 1)Hixon-Tenney-Harvey index: if x > p D1 = (1-x)/(1-p) x < p D2 = x/p x = p D3 = 1 average degree of mixing Da = (N1 D1 + N2 D2 + N3

D3)/N ( x = value of some component in sample, p= expected

value)

2/1211221 )]

)()(([

s

ww

r M

fCfCCC

•For different material and different size, use this equnation to calculate RHM 的 variance;•C1, C2 = fractional concentration of each component•Ms = mass of samplefw sum of product of the weight fraction f of particles in each size class and the mean particle weight W in the class (could it be f * w; not fw)

Mixing Analysis


Previous mixing index to evaluate mixing process or effect of parameters, try to minimize error in sampling and analysis.

Macro-scale mixing: by chemical analysis, phase analysis, etc.; Micro-scale mixing: observation by microscopy technique

E.g. use M index: to study time effect, determine optimal condition; indicating de-mixing behavior; mixing – by relative movement of particles: convection, shear, diffusion (three mechanisms). Different equipment provide different mechanisms.

Inverse of mixing segregation (percolation of fines, trajectory segregation, rise of coarse upon vibration)

Mixing yeast into dough: an example

source: Unit operations in food processing5 kg yeast mix into 95Kg dough after 5 min, 100 gm sample, yeast analysis: 0, 16.5, 3.2, 2.2, 12.6, 9.6, 0.2, 4.6, 0.5, 8.5;After 10 min, 3.4, 8.3, 7.2, 6.0, 4.3, 5.2, 5.7, 2.6, 4.3, 2.0; M = (so^2 – s^2)/(so^2 – sr^2) so^2 = 0.048; sr^2 ~0; s5^2 = 0.003, s10^2 = 0.00038 M5 = 0.93; M10 = 0.99

Important Parameters


Mixing effect affected by: type of equipment energy input flowability and composition of sampe (size, shape,

density, surface characteristics)

For complete description of mixing, one need: sample variance (intensity of segregation) scale of segregation (to micro-scale) long range structure

Microscale and Macroscale Mixedness

• Microscale analysis provide information on microscale mixedness• Macroscale mixedness can be analyzed by many technqiues (chemical or physical)• Sampling and analysis error should be kept to a minimum• uncertainty in the standard deviation (s) become low when a large number of samples are taken

Taken from JS Reed, 2nd ed.

• Taken from JS Reed, 1995• Commercial mixers: usually with two or more mixing elements to produce: high shear mixing in a local region & low shear bulk mixing

One example of two mixing elements

To avoid vortex, we may add baffles

Turbulence and cavitation – for diffusion (micro-scale mixing)

Mechanism in Horizontal Drum Mixer


•Path of circulation: particle move with rotating cylinder, mixing only if change in path of particles•Radial mixing: due to mixing in the gravity direction (drop to a void); velocity gradient important;•Radial de-mixing: core formation, small and heavy particles gradually go to bottom•Axial mixing: diffusion mode•Axial de-mixing: band formation, effect from mixer walls;

Change drum mixer into cone shape, beneficial to mixing; (taken from JS Reed, 1995) cement mixer!

Rate Process


•dM/dt = A (1-M) – B (where is segregation potential; M = 1 - 2) unmixing process

In principle: B – effect from equipment; - effect from particle characteristics

Equipment used in mixing of viscous paste (Taken from JS Reed, 1995); (a) helical mixer; (c) double planetary mixer

Sigma blade mixer

取自 JS Reed, 1995

Extent of reaction depend on degree of mixing and uniformity

Types of Mixers

J. Bridgewater, Particuology, 10(4), 397-427, 2012

Mixing mechanism: convection, diffusion, shear

Aeration Blending


Or named fluidized blending, for mixing of different particles. Some advantages:

can obtain uniform mixtures, even different in density can be precisely controlled, energy cost/unit weight

sample lower easy to operate and maintain large capacity fast and easy loading; many different methods for

feeding (e.g. pneumatic, mechanical, gravity) Can use other gases, in addition to air

Dispersion of Powder into Liquid


Steps involved: adhesion (a b), immersion (b c) and spreading (c d);

Work involved with each step (equilibrium consideration):Wa = SL – (LV + SV) = -LV (cos +1) negative for any Wi = 4SL - 4LV =-4LV cos < 90o, negative valueWs = (SL + LV) - SV = -LV (cos -1) positive value, at=0o, this number is zeroIn summary: work must be done to obtain spreading

Contact Angle


cos = (SV - SL) /LV

Wetting implies contact angle < 90o

Macroscale Mixing and Microscale Mixing


Mixing of viscous slurry with a single impeller: difficult to achieve both ** macrocsale mixing high pumping capacity ** microscale mixing turbulence

Look at two parameters, Re & P (power requirement) ** Re = N s (dia.)2/ …. turbulence ** P/Re = CD N2 (dia.)3 …. Pumping capacity CD: drag coefficient; For high viscosity, same power, but need large Re (microscale mixing) need small size propeller, or increase velocity; yet for small propeller, non-uniformity occur (macroscale mixing)

Mixing and EMI Performance

* ABS + Ni powder or fiber mixing (Barbender mixer or dry mixing) composite for EMI measurements

0 5 10 15 20 25 30

0

10

20

30

40

50

60

Ave

rag

e E

MI S

E (

dB

)

Nickel vol. %

Brabender/powder Dry mixing/powder Dry mixing/filament

Dry mixing produced better shielding effect than Barbender mixer (in terms of low threshold value)

(a) Barbender mixer (powder; 20%); (b) dry mixing (powder 7%); (c) dry mixing (filament, 7%)

Barbender mixer produced perfect mixing, not necessary good for EMI purposes; dry mixing produced macro-scale uniformity, not micro-scale uniformity

Correlation between percent measureable (electrical resistance) of composite of various samples

0 5 10 15 20 25 30

0

20

40

60

80

100

PM

(%

)

Nickel vol. %

Brabender/powder Dry mixing/powder Dry mixing/filament

Electrical resistance measurement by 4 point probe

che5700 陶瓷粉末處理 batching and mixing batch feed always involves mixing, objective: - high...

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