Effect of surface tension on the relaxation of a viscoelastic half‐space perturbed by a point load

Abstract

We study the effect of surface tension on the flattening of a surface perturbed by a point load subsequent to its removal. The surface bounds an infinite isotropic linear viscoelastic incompressible half space. The point load is initially applied for a sufficiently long time so that the half space is fully relaxed before the load removal. An exact solution is obtained assuming small deformation. We then specialize our theory to the case of a standard viscoelastic solid. There is an initial reduction of the surface displacement immediately after load removal that is found to be directly proportional to the ratio of applied load to surface tension. This is followed by a temporal decay of the surface profile that depends only on the relaxation time and the long and short time moduli of the viscoelastic solid. Our work also provides the Green's function for a suddenly applied point load on the surface of a viscoelastic half space. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 274–280

Singular dynamics in the failure of soft adhesive contacts

“…As evident from these plots, higher frame rates enable us to capture shorter-time dynamics, while lower frame rates capture a much larger field of view. In Figure 2(b), we see that at large r the surface displacement falls away as 1/r, as would be expected for a purely elastic deformation of an elastic half-space [43]. For small r, on the other hand, we observe that the recoiling peak rounds off rather than ending in a sharp point.…”

“…Complete recovery to a flat surface takes about 1 second. We find that the profiles and power law exponents we observe in the self-similar regime are fundamentally different than the relaxation after breakup of either simple liquids or viscoelastic materials [43,49,54]. Instead, by applying a simple scaling argument, we show that our observations are consistent with the recoil being driven by surface stresses and slowed by Darcy flow of the gel's viscous free fluid phase through its crosslinked elastic network.…”

“…In this regime, which can be as large as tens of µm or even mm, soft solids begin to act like liquids that can't flow: for example, undergoing capillary instabilities [20][21][22][23], forming adhesive contacts that quantitatively resemble capillary bridges [24][25][26][27], and blurring the line between adhesion and wetting [28][29][30][31][32][33][34][35]. Other effects have also been found to be important for understanding gel mechanics, including poroelasticity [36][37][38][39][40][41], arising from the dissipative flow of the internal fluid phase of a gel through its elastic network, and viscoelasticity, which in gels includes accounting for the power-law frequency-dependence of the storage and loss moduli typical of these materials at high frequencies [42][43][44][45][46].…”

“…With a few notable exceptions (e.g. [41,43,44]), most low-and high-strain studies exploring the effects of solid capillarity have focused on static or quasi-static deformations. However, soft solids are often subjected to extreme deformations and fast dynamics, especially in the context of adhesive detachment [43,44,47].…”

“…[41,43,44]), most low-and high-strain studies exploring the effects of solid capillarity have focused on static or quasi-static deformations. However, soft solids are often subjected to extreme deformations and fast dynamics, especially in the context of adhesive detachment [43,44,47]. Meanwhile, there exists a rich literature studying dynamic capillary instabilities and breakup in liquids [48][49][50][51][52][53][54], but it is not yet known whether similar singularities occur in capillarydominated solids.…”