Friction of Fine Particles

Coulomb s friction theory for particles was based on the idea that the traction force divided by the plate area was given by an adhesion pressure K plus a friction term JA where p was the friction coefficient, i.e. 

The problem with this equation is threefold. First, the friction coefficient calculated from Equation (9.14) in the experiment of Fig. 9.15(a) does not match that measured in Fig. 9.14(b). 0.5mm sand grains give p = 0.45 whereas two large quartz blocks give p = 0.3. Second, the friction of sand grains increased as the particles got smaller, rising to 0.6 for wet sand 0.01 mm in diameter. Finally, the friction of fine powders is not constant as the normal pressure is increased but falls substantially at high loads, in conflict with Equation (9.14). 

These discrepancies are explained by the JKR theory as first defined by Barquins, Maugis and colleagues. Although Equation (9.14) is the simplest expression which takes into account both the external load and the molecular adhesion, it cannot be correct for elastically deforming bodies because there is then an extra term arising from the interaction of the applied load and the adhesive forces. From the JKR expression for a particle on a flat surface. Fig. 9.16, the effective load pressing the particle into the surface is 

The results on crossed polymer fibers obtained by Briscoe and Kremnitzer shown in Fig. 9.16 gave good agreement with Equation (9.16). The friction force increased more rapidly than Coulomb s law predicted at low loads but approached Coulomb s law at high loads. The value of the work of adhesion W from these friction experiments was near 0.1 Jm , close to the value determined in direct adhesion experiments on the same fibers. 

The logical conclusion from these arguments is that the friction coefficient of powders must vary substantially with both particle diameter and applied pressure. This fits the experience of soil mechanics where it is known that finer grains give higher friction. 

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