Derjaguin and the DMT Theory: A Farewell to DMT?

Abstract

<jats:title>Abstract</jats:title><jats:p>There is a widespread belief that in the 1970s, two conflicting theories of the adhesion of a spherical particle to a substrate were published: the JKR and DMT theories. And that the dispute was resolved when Tabor introduced a parameter <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>, such that for small <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>, DMT was correct, while for large <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>, JKR was correct. We point out that there never were two theories of contact: the dispute was about the magnitude of the pull-off force (with an implication that since the DMT value was obtained by a <jats:italic>thermodynamic</jats:italic> method, it must be correct). And what Tabor actually said was simply that for large <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>, the neglect of surface forces in the JKR theory was acceptable, and that he distrusted the neglect of deformation by the large surface forces immediately outside the Hertzian contact in the DMT theory. We point out the errors in both the DMT/MDT thermodynamic method and the MDT force method (preferred by MDT) but also argue that once Derjaguin and his collaborators (MYD) established that Hertzian geometry does not occur, no theory based on that geometry should be taken seriously. Derjaguin’s well-merited fame rests on more important contributions.</jats:p>