Static Wetting on Soft Solids; Formation of an Asymmetric Wetting Ridge
When a droplet is gently deposited on a smooth surface, Young's or Neumann's law is commonly applied to explain the equilibrium on a solid or a liquid surface. However, on a soft and deformable surface, the laws are in principle invalid because the vertical component of the liquid's surface tension (Î³_{LV}) deforms the surface right below the three-phase (liquid-solid-vapor) contact line and a microscopic structure forms along the rim of the droplet, called as a 'wetting ridge' (Fig. 1(a)). The underlying mechanism of ridge formation is a key to understand wetting behaviors on soft solids, but has not been fully understood with limited observations in conventional visualization techniques. The general wetting principle applicable to solids with a wide range of softness was elucidated by Korean scientists of Pohang University of Science and Technology (POSTECH), South Korea, in a paper published in Nature Communications [1]. They achieved direct real-time visualization of wetting ridges with high spatiotemporal resolution of X-ray microscopy at the Advanced Photon Source at Argonne National Laboratory, USA (Fig. 1(b)). Their results show that the formation of the wetting ridge can be deduced by Young's and Neumann's laws in macroscopic and microscopic scales, respectively.
They found that a wetting ridge is actually asymmetric and its tip is rotated along a liquid-vapor interface inclined at the macroscopic contact angle (Î¸) (Fig. 1(c)), which follows Young's law regardless of the surface elasticity (E). Compared with symmetrical models based on linear elastic theory, the scale of the wetting ridges is determined by the ratio of the vertical force and the surface elasticity, Î³_{LV}sinÎ¸/E, consistent with the models. However, the ridge deviates significantly from the models where capillarity is more dominant than elasticity (Fig. 1(d)) and, more importantly, where the tip geometry is independent of the elasticity (Fig. 1(e)). They also found that the tip geometry is invariant during continuous and slow growth of the ridge with a constant rate (~ 7 nm/s) (Fig. 1(f)). These results indicate liquid-like behavior of the soft solid at the tip. They finally confirmed that Neumann's law should be valid here, after examining all of the possible factors suggested by theoretical models to date.
They suggested the applicability of dual-scale force balance in static wetting on soft solids, which will be a basis for studying dynamic wetting behaviors on soft solids, such as spreading, contact angle hysteresis, and evaporation. Furthermore, it would be potentially important in understanding many biological processes affected by mechanical microenvironments.
References
[1] S. J. Park et al., Nat. Commun. 5, 4369 (2014).
Fig. 1: (a) A wetting ridge (red box) is formed by the surface tension of a water droplet along a contact line. (b) A representative X-ray image of a wetting ridge (red box in (a)). (c) Extraction of three interfaces (dashed square in (b)). The macroscopic (Î¸) and the microscopic (Î¸_{S}, Î¸_{v} and Î¸_{L}) contact angles can be measured at the tip. (d) The asymmetric ridges are compared to three linear elastic (LE) symmetrical models. (Inset) The cusps of the wetting ridges are identically superimposed by Δu_{z}(x) = u_{z}(x) - u_{z}(o). (e) (Top) The plot of angular differences (ΔAngle) with respect to E, based on the average values for 3 kPa. The macroscopic (Î¸, black circle) and the microscopic (Î¸_{S} (blue circle), Î¸_{v} (blue square) and Î¸_{L} (blue triangle)) angles are measured at w< ~ 0.4 Î¼m. The error bars are standard deviations. (Bottom) The little difference of K = sinÎ¸_{S}/Î¥_{LV} (ΔK< 4%), resulted from that of ΔÎ¸_{S} (< Â±1.6Â°), indicates invariant surface stresses Î¥_{SL} and Î¥_{SV}. (f) (Top) The ridge height u_{z}(o) linearly increases (~7 nm/s) until depinning at Δt (observing time) = 181 s. X-shaped symbols are the values obtained after depinning. The abrupt decrease (red arrow) is attributed to an instantaneous elastic recovery. (Bottom) ΔÎ¸_{S} is unchanged during the ridge growth (Î¸_{S} = 56.3 Â± 5.1Â°) even after depinning. Black dashed lines are to guide the eye. |