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Theoretical Derivation of Interparticle Forces

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Book cover The Dynamics of Fine Powders

Part of the book series: Elsevier Handling and Processing of Solids Series ((HPSS))

Abstract

The so-called interparticle forces comprise capillary forces, electrostatic forces and Van der Waals forces.

The analysis in this chapter is a further elaboration and explanation of the paper by Cottaar and Rietema (1986).

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Abbreviations

A:

Hamaker constant (J)

Cij :

Constant in Lennard-Jones potential for substances i and j (J m6)

d:

Particle diameter, or diameter of the spring wire (m)

D:

Equivalent diameter of contacting particles (m)

e:

Free space between windings of spring (—)

E:

Elasticity modulus of powder (N m -2)

Em :

Elasticity modulus of spring material (N m -2)

Epc :

Elasticity modulus of particle contact (N m -2)

Es :

Elasticity modulus of spiral spring (N m -2)

F:

Force between particles (N)

Fc :

Cohesion force (N)

G:

Gas adsorption function (—)

h:

Flattening of particles (m)

k:

Boltzmann constant (J K -x)

K:

=(l-v2)/Y(N -;1m2)

L:

Distance between particle centre and surface of the plane (m)

n:

Molecule density (m -3)

Na :

Density of adsorbed gas molecules (m -2)

N:

oa Maximum density of adsorbed gas molecules (m -2)

r:

Distance between molecules (m)

rij :

Molecule parameter (see eqn (4.5)) (m)

R:

Radius of particle, or radius of spiral spring (m)

s:

Parameter indicated in Fig. 4.4 (m)

T:

Temperature (K)

Um :

Total molecular potential of system (J)

Uc :

(y)Binding energy between two planes (J)

V:

Volume of particle (m3)

Vij:

Intermodular potential for substances i and;(J)

Y:

Young’s modulus of elasticity (N m -2)

z:

Smallest distance between the surfaces of the particle and the plane (m)

α:

Ratio of constants for molecular solid-solid interaction and gas adsorption (—)

δ:

Fraction of adsorbed gas density (—)

εc :

Dimensionless interaction parameter (—)

ζ:

Dimensionless distance (—)

ŋ:

Dimensionless flattening (—)

θC :

Dimensionless density of adsorbed gas molecules (—)

v:

Poisson’s ratio (—)

ρd :

Density of solid particles (kg m -3)

σc :

Cohesion constant (N m -2)

σn :

Normal stress (N m -2)

τ:

Ratio of adsorption energy to thermal energy (—)

Ø:

Dimensionless external force applied to the particle-plane system (—)

x:

Dimensionless interaction energy (—)

ψ:

Dimensionless elastic deformation energy (—)

ω:

= ζ-ŋ (—)

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Author information

Authors and Affiliations

  1. Europlaan 16, 5691, En Son, The Netherlands

    K. Rietema

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  1. K. Rietema
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© 1991 Elsevier Science Publishers Ltd

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Rietema, K. (1991). Theoretical Derivation of Interparticle Forces. In: The Dynamics of Fine Powders. Elsevier Handling and Processing of Solids Series. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3672-3_4

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  • DOI: https://doi.org/10.1007/978-94-011-3672-3_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-85166-594-5

  • Online ISBN: 978-94-011-3672-3

  • eBook Packages: Springer Book Archive

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