Visualization of asymmetric wetting ridges on soft solids with X-ray microscopy

Abstract

One of the most questionable issues in wetting is the force balance that includes the vertical component of liquid surface tension. On soft solids, the vertical component leads to a microscopic protrusion of the contact line, that is, a ‘wetting ridge’. The wetting principle determining the tip geometry of the ridge is at the heart of the issues over the past half century. Here we reveal a universal wetting principle from the ridge tips directly visualized with high spatio-temporal resolution of X-ray microscopy. We find that the cusp of the ridge is bent with an asymmetric tip, whose geometry is invariant during ridge growth or by surface softness. This singular asymmetry is deduced by linking the macroscopic and microscopic contact angles to Young and Neuman laws, respectively. Our finding shows that this dual-scale approach would be contributable to a general framework in elastowetting, and give hints to issues in cell-substrate interaction and elasto-capillary problems.

Liquid Droplets Act as “Compass Needles” for the Stresses in a Deformable Membrane

“…For instance, studies on the partial wetting of liquid drops on soft solids show that Young's law is applicable on length scales much larger than the bulk elastocapillary length γ=E, where γ is the liquid-air surface tension and E is the Young's modulus of the solid. However, on smaller length scales, the contact line reveals a wetting ridge set by a Neumann construction involving surface stresses [20][21][22][23][24][25][26].…”

“…For instance, studies on the partial wetting of liquid drops on soft solids show that Young's law is applicable on length scales much larger than the bulk elastocapillary length γ=E, where γ is the liquid-air surface tension and E is the Young's modulus of the solid. However, on smaller length scales, the contact line reveals a wetting ridge set by a Neumann construction involving surface stresses [20][21][22][23][24][25][26].Partial wetting on deformable substrates may also be studied by employing a highly compliant geometry, such as a droplet on a thin freestanding film [27][28][29][30][31]. These studies have considered clamped films which are held taut and support a uniform and isotropic tension.…”

Equilibrium of droplets on a deformable substrate: Influence of disjoining pressure

“…This free energy should be subtracted from the free energy of the droplet, otherwise the excess free energy of the droplet will be infinite. The excess free energy of the droplet is as follows, (10) where means "as compared with a flat equilibrium film". Therefore Eq.…”

“…There have been a number of experimental studies recently that have considered liquids on deformable substrates [8][9][10][11][12][13][14], where deformation of soft solids was investigated near the apparent contact line, but there exists a gap in theoretically understanding of the problem. This void is primarily due to the stress singularity present at the three phase contact line.…”

Analogies between elastic and capillary interfaces

“…The x-ray image in Fig. 5(a) from Park et al [25] shows a detailed view of the three-phase contact line at the edge of a water drop. The solid is pinched by the action of the liquid-vapor surface tension γ .…”