Figure 2. Effect of surface elasticity on wetting ridge formation.

(a) Representative X-ray images of wetting ridges on a silicone gel (E≈3 kPa) and a PDMS film (≈16 kPa). Scale bars, 5 μm. (b) The surface profiles clearly show a strong E-dependence of the vertical displacement u_z(x). The asymmetric and bent cusps are compared with three LE symmetrical models by Style et al.8 (solid lines), Limat12 (dashed lines) and de Gennes and Shanahan10,11,20 (dash-dotted lines). For E≈3 kPa, the model by Shanahan is invalid in the observed region here. The detailed fitting descriptions are in Supplementary Fig. 2. (Inset) The cusps are identically superimposed by Δu_z(x)=u_z(x)−u_z(0) at w<<l_e. (c) (Top) The angular differences (ΔAngle) are plotted with E, based on the average values for 3 kPa, for the macroscopic (θ, black circle) and the microscopic (θ_S (blue circle), θ_V (blue square) and θ_L (blue triangle)) angles measured at w< ~0.4 μm. The error bars are s.d. from five sets of image data for 3 kPa, one set for 10 kPa and three sets for 16 kPa. (Bottom) K is obtained with θ_S and γ_LV, that is, K=sinθ_S/γ_LV. The little difference of K (ΔK<4%), resulted from that of Δθ_S (< ±1.6°), indicates invariant surface stresses Υ_SL and Υ_SV at the tips.