che572 chapter 4 interparticle forces.pdf

8/19/2019 CHE572 Chapter 4 Interparticle Forces.pdf

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CHAPTER 4

INTERPARTICLE FORCES4.1 Introduction

• The knowledge of interparticle forces: in sizeenlargement process (granulation, agglomeration,tabletting), fine particle processes (fluidization, particletransport).

• Size enlargement process: smaller particles are puttogether to form larger masses but the original particlescan still be identified.

• Why increase the mean size: to reduce dust hazard,reduce caking and lumping formation, improve flowproperties etc.

• Example of applications: pharmaceutical formulation –defined active ingredient, catalyst support – controlsurface to volume ratio.

4.2 Interparticle bonding.

• The most important forces causing the structuring of amixture are:o due to moistureo due to electrostatic chargeo due to Van der Waal forces



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4.2.1 Bonding due to moisture

• Moisture retention in powder = f(nature of the solids,ambient humidity, temperature, pressure)

• Moisture will be present as :(i) adsorbed vapour if the humidity is below a critical

value(ii) liquid bridges for higher humidities.

• The binding force = f(actual humidity) for both cases.

4.2.1.1 Adsorbed layer bonding

• The bonding is caused by the overlapping of theadsorbed layers of neighbouring particles and itsstrength is proportional to tensile strength of the

adsorbed film and the area of contact.

• In a simple case of two dissimilar spheres, the contactarea and the bond strength can be calculated.

R1 R2

δ y



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+

−=

1m

m R

2

y4S 2

δ π

• Boding surface between a flat surface and a spherewould be twice as large as that between two equi-sizedspheres.

• Important variable of bonding: particle shape and surfaceroughness.

• In most cases, the surfaces of the contacting particleswill not be perfectly smooth and surface roughness willreduce the area of contact and hence the bond strength.

4.2.1.2 Liquid bridge bonding

• When the relative humidity reaches a critical point, liquidbridges form between particles and this is a nature of

cohesive particles.

• A liquid bridge will only be stable if its tendency toevaporate equals the tendency of water vapour tocondense on it.

• As humidity increases, the area of particle surfacecovered by the bridge increases and the independenceof neighbouring liquid bridges becomes a function ofporosity and of absolute particle size.

4.2.2 Electrostatic bonding



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• Two solids in rubbing contact will charge each otherelectrostatically.

• Electrons are transferred until at equilibrium, a contactpotential difference is established.

• Depending on the sign of the charge particles will tend tobond to the mixer wall or to other dissimilar particles.

• Generally, electrostatic effects are unwelcome as theyare not only unpredictable but they could give thepotential for a dangerous electrostatic charge.

4.2.3 Van der Waal force bonding

• Attractive forces exist between neutral atoms or

molecules which are separated by a distance which islarge compared to their own dimension.

• These force known as Van der Waal forces and theydecrease with the distance apart according to a powerlaw.

• The extension of Van der Waals theory of attractive forcefor bulk powder was carried out by Lifshitz (1955)

• Particles do not have to touch in order that attractionoccurs but it can be seen from equation 4.1 and 4.2 thatthe magnitude of the force decreases with the square ofthe distance between the surfaces.



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• For attraction force between flat surface and a sphere,

R Z 8

hF 2

o

wvdw π

= (4.1)

• Equation (4.1) was then modified for the attraction forcetwo sphericals:

+

=21

212o

wvdw R R

R R

Z 8

hF

π (4.2)

where h w = Lifshitz – VDW constantZo = distance between two solidsR = radius of sphere

• The range of attraction is smaller than for electrostaticbonding and for a similar packing density, the effectivearea of contact will also be smaller.

4.3 Interaction of the bonding forces

• In powder mixing, the humidity of the atmosphere plays acrucial role in determining the relative importance of theforces.



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• Adsorbed and liquid bridge bonding forces can dominateother possible bonding forces and also influence theirmagnitude.

• On theoretical basis, Rumpf (1962) plotted thetheoretical tensile strength of agglomerates as a functionof particle size (Fig. 11.2 – pg 271 from handout).

• The effect of adsorbed moisture on the Van der Waals

forces is to increase their value as the adsorbed layersmay be considered as part of particle and a decrease inthe interparticulate distance will occur.

• Rumpf suggests that the effect of such adsorbed layerscan increase the contribution of Van der Waals forces tothe cohesive strength of bulk powders by a factor of 100.

• Electrostatic forces will decay rapidly as humidity causesair to be more conductive and therefore favour dischargefrom the particles.

• Adsorbed moisture also reduces the magnitude ofmechanical forces such as friction and interlocking, asthe adsorbed film act as lubricant, decrease friction andreduces the chances of stable interlocking.

• As the particle size of fine component decreases to thesub-micron range, the relative importance of the bondingforces will change again.

che572 chapter 4 interparticle forces.pdf

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