Particle Adhesion to Highly Compliant Substrates:  Anomalous Power-Law Dependence of the Contact Radius on Particle Radius

Abstract

The adhesion-induced contact radius and meniscus height between soda-lime glass particles and three highly compliant polyurethane substrates (Young's modulus between 4 kPa and 0.7 MPa) were measured using scanning electron microscopy as a function of particle radius. Two distinct power-law exponents were found. A value of about 2/3, which is in good agreement with the predictions of the JKR theory (Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc., London Ser. A 1971, 324, 301), was found for larger particles. However, the experimentally obtained exponent for smaller particles was found to be approximately 3/4. The present results are compared with the predictions of the large-scale deformation model of Maugis (Maugis, D. Langmuir 1995, 11, 679) as well as a self-consistent surface-energy model. Although both models contain some interesting features, neither theory can fully account for the observed behavior.

Extension of the Two-Dimensional JKR Theory to the Case with a Large Contact Width

“…2.3. One can see that when m ¼ p=4, the classical JKR solution would predict a 0 ¼ R, i.e., the contact half-width equals the cylinder radius due to the surface energy driven [19]. In fact, the classical plane strain JKR solution is invalid theoretically without the condition of a very small contact width.…”

Adhesion Map of Spheres: Effects of Curved Contact Interface and Surface Interaction Outside Contact Region

“…When two spheres have similar Young's moduli, two J values in general should be used: one for the compressive external load case to ensure a flat contact area, i.e., J A cs = A flat = πa 2 ; the other for the tensile external load case to describe the curved contact surface. However, for a rigid glass particle in contact with the highly compliant polyurethane substrate [22,23], only one J value should be taken into account for the curved contact interface effect. The equation 12by Rimai et al [23] is:…”

“…A direct impact of the contact area flatness is on the calculation of the adhesion energy, which together with the elastic energy of deformation determines the final contact state [19,21]. The experiments by Rimai et al [22,23] show that for some small particles, the 2/3 JKR power-law dependence of contact radius on particle radius is violated and an anomalous 3/4 power-law is found. Rimai et al ruled out the plastic deformation causing the anomalous power-law [22,23].…”

“…The experiments by Rimai et al [22,23] show that for some small particles, the 2/3 JKR power-law dependence of contact radius on particle radius is violated and an anomalous 3/4 power-law is found. Rimai et al ruled out the plastic deformation causing the anomalous power-law [22,23]. Rimai et al ascribed this anomalous powerlaw to the curved contact interface effect [23].…”

“…Rimai et al ruled out the plastic deformation causing the anomalous power-law [22,23]. Rimai et al ascribed this anomalous powerlaw to the curved contact interface effect [23]. From the viewpoint of the LJ force law, the contact region cannot be exactly flat because it is incommensurate with the variation of contact pressure across the area [12].…”