Effects of Charge

Neighbor Forces Acting on Particle

Charged-Patch Model

Assume that the particle charge is localized to a discreet section of the particle

Electrostatic contribution to attractive force F_E is given by

A_C is the contact area

s is the charge density

Estimate of F_VW

Note:These particles are irregularly-shaped

No silica:

Particle radius = 4mm

W_A = 0.05 J/m²

q/m = 37 + 3 mC/g

r = 1.2 g/cm³

From JKR theory:

Measured value:F_S = 970 nN

2% Silica:

Assume JKR contact radius = 196 nm

r_silica = 30 nm

r_silica = 1.75 g/cm³.

Þhave about 10 silica particles within the contact zone.

Approximate JKR removal force by

= 39 nN.

Measured:F_S’ = 70 nN

Estimate of F_Im:

Þ F_Im = 20 – 40 nN

Estimate of F_E:

Patch charge density limited by dielectric strength of air.

Þ F_E » 30 nN

Key feature to note:If the particle has sufficient irregularity, van der Waals forces, electrostatic image forces, and charged-patch forces all predict about the same size force, which is comparable to experimentally determined detachment force.