How surface stress transforms surface profiles and adhesion of rough elastic bodies

Abstract

The surface of soft solids carries a surface stress that tends to flatten surface profiles. For example, surface features on a soft solid, fabricated by moulding against a stiff-patterned substrate, tend to flatten upon removal from the mould. In this work, we derive a transfer function in an explicit form that, given any initial surface profile, shows how to compute the shape of the corresponding flattened profile. We provide analytical results for several applications including flattening of one-dimensional and two-dimensional periodic structures, qualitative changes to the surface roughness spectrum, and how that strongly influences adhesion.

Surface tension and the strain-dependent topography of soft solids

“…to ensure full crosslinking, we detach the grating from the sample. The patterned surface on the PDMS sample relaxes to a new shape, in which surface stresses and bulk elastic stresses balance [2,3,28], Fig. 1c.…”

“…which we call the flattening equation [2,3,28]. Assuming linear response, this process can be applied to any Fourier mode of a non-sinusoidal surface.…”

Experimental characterization of elastocapillary and osmocapillary effects on multi-scale gel surface topography

“…How elastocapillary and osmocapillary effects change the surface topography can be predicted by the linear elastocapillary and osmocapillary theories. 24,40 For the elastocapillary deformation, Hui et al have obtained the explicit relation between the deformed PSD, C ( q ) and the stress-free PSD, C 0 ( q ): 24 Here v is the Poisson's ratio. For the osmocapillary phase separation, we have previously developed an iterative numerical approach to predict the relation between the PSD of the total topography of both the gel and solvent surfaces, C ( q ), the deformed gel topography, C g ( q ), and the stress-free profile C 0 ( q ).…”

A surface flattening method for characterizing the surface stress, drained Poisson's ratio and diffusivity of poroelastic gels

“…1 t  Alternatively, the short-and long-time solutions can be obtained by studying the deformation driven by surface stress for an elastic solid: the instantaneous response of the porous medium behaves like an incompressible elastic solid, while at long times the porous medium behaves as a compressible elastic solid with 8 the drained Poisson's ratio . Hui et al 67 have recently provide an analytical solution to determine the  flattened surface profile for any initial surface profile of a linear elastic half space, provided that surface stress is isotropic and constant. Using our notation, the deformed surface profile is given by , ,…”