Adhesion of Spheres DMT Theory

The pull-off in the DMT theory occurs at zero contact radius and the adhesion force is given by 

In their original paper, DMT used a thermodynamic approach to calculate the contribution of the adhesion energy. They found that the surface forces give an additional contribution of 2jtu adhi to the normal load at zero indentation that decreases to with increasing indentation 6. In a later paper [855], the authors 

The radius of contact at zero external load (Fl = 0) for that variant of the DMT theory is 

A silicon oxide sphere with 20 p,m diameter sits on a silicon oxide surface. Estimate the contact radius at zero external force and calculate the adhesion force.E = 5.4 x lO Pa, v = 0.17,Ys = 50mNm, densityq = 2600kgm . With J i = 10 pm and R2 = oo, the effective particle radius is R = Ri = 10 m. 

The contact radius is estimated using the JKR model. Without external forces, we have 

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