On roughness-induced adhesion enhancement

While adhesion reduction due to roughness is not surprising, roughness induced adhesion remained a puzzle until recently. Guduru and coworkers have shown a very convincing mechanism to explain both the increase of strength and of toughness in a sphere with a concentric single scale of waviness. Kesari and coworkers later showed some very elegant convenient asymptotic expansions of Guduru's solution. This enhancement is very high and indeed, using Kesari's solution, it is here shown to depend uniquely on a Johnson parameter for adhesion of a sinusoidal contact. However, counterintuitively, it leads to unbounded enhancement for conditions of large roughness for which the Johnson parameter is very low. Guduru postulated that this enhancement should occur after sufficiently large pressure has been applied to any spherical contact. Also, although the enhancement is limited to the Johnson, Kendall and Roberts (JKR) regime of large soft materials with high adhesion, the DMT limit for the smooth sphere is found otherwise. However, for hard materials, even the Derjaguin, Muller and Toporov (DMT) limit for the smooth solids is very hard to observe, which suggests that adhesion reduction is also not yet well understood. The limitations of the assumption of simply connected area are here further discussed, and a well-known model for hard particles in contact with rough planes due to Rumpf is used to show that, in the range where an unbounded increase is predicted, orders of magnitude reduction is instead expected for rigid solids. We suggest that Guduru's model may be close to an upper bound for adhesion of rough bodies, while the Rumpf-Rabinovich model may be close to a lower bound.