The Derjaguin-Muller-Toporov Model

The Derjaguin-Muller-Toporov model (DMT) is an acceptable approximation of cohesive forces for small particles within the limits of weak cohesion. The attraction force is limited by the separation distance between the pair of contacting particles at which the bond is broken. The limit is smaller for the DMT model over similar models and the particles to which it properly applies. The DMT model neglects the contact deflection. It is indirectly taken into account through the attraction force and uses the Hertzian contact model. The attraction force between a pair of contacting particles is given by:

f_{DMT}=-2 \pi \gamma_{sur} {R^*}

where {R^*} is the effective radius. The figure illustrates how the contact deflection is indirectly taken into account through the attraction force between the particles.

DMT model

The Derjaguin-Muller-Toporov model (DMT)

For more reading consider

Muller V. M., V.S. Yuschenko, and B.V. Derjaguin. On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. Journal of Colloid and Interface Science, 77(1):91-101, 1980

Maugis D. Adhesion of spheres: the JKR-DMT transition using a Dugdale model. Journal of Colloid and Interface Science, 150(1):243-269,1992.

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