Surfing the capillary wave: Wetting dynamics beneath an impacting drop

The initiation of contact between liquid and a dry solid is of great fundamental and practical importance. We experimentally probe the dynamics of wetting that occur when an impacting drop first contacts a dry surface. We show that, initially, wetting is mediated by the formation and growth of nanoscale liquid bridges, binding the liquid to the solid across a thin film of air. As the liquid bridge expands, air accumulates and deforms the liquid-air interface, and a capillary wave forms ahead of the advancing wetting front. This capillary wave regularizes the pressure at the advancing wetting front and explains the anomalously low wetting velocities observed. As the liquid viscosity increases, the wetting front velocity decreases; we propose a phenomenological scaling for the observed decrease of the wetting velocity with liquid viscosity.

Figure 1

High-speed TIR imaging of the initiation of wetting: (a) Collimated, monochromatic light (MLS) totally internally reflects off of the glass-air interface (DP). The angle of incidence is tuned such that, for a glass-liquid interface, light no longer obeys the conditions for total internal reflection and instead transmits through a wet glass. Reflected light exiting the prism is magnified with a long-working-distance microscope objective (MS) and is imaged on our fast camera's imaging sensor (Phantom V711) (HSC) at up to 180 000 frames per second. (b) A typical TIR image of a capillary bridge formed beneath the thin film of air approximately 500 microns from the center of the impact. The height profile of the liquid above the solid surface can be calculated from the recorded intensity. (c) Three-dimensional rendering of the height map for the contact patch shown in (b). The color bar indicates the height above the glass surface.

Figure 2

Initiation and growth of liquid-solid contact: (a) A sequence of TIR images showing the initiation of contact between the glass surface and a 10 cSt liquid drop. At $t=0$, the contact first forms. As time progresses, the contact line moves symmetrically out from the initial point of contact formation. The air ahead of the advancing wetting front fails to drain and instead deforms the liquid-air interface. Consequently, a bright “halo” surrounds the liquid bridge. (b) A schematic representing the $r-z$ plane normal to the impact surface demonstrates how the halo region grows ahead of the advancing contact. As mentioned in the Supplemental Material [29], the conformation of the liquid-air interface (dashed line) cannot be resolved below one micron with the TIR method, limiting our ability to resolve the profile within nanometers of the contact line. (c) The azimuthally averaged height profiles are plotted in a kymograph for 10 cSt liquid. The contact line progresses outward with a nearly constant velocity, and the lateral extent of the halo grows over time, as indicated by the widening of the bright red region. (d) A kymograph of liquid-solid contact initiation beneath a 1 cSt liquid drop shows similar, albeit more rapid, dynamics. (e) A kymograph of liquid-solid contact beneath a 100 cSt liquid drop. Here, the contact line moves with a slower velocity.

Figure 3

Kinematics of the wetting front: (a) Five consecutive height profiles ($dt=5.5\mu \mathrm{s}$) of a wetting front propagating outward from the point of contact initiation. The halo region leading the propagating front excites a capillary wave ahead of it, with a lateral extent ${\ell }_{\mathrm{halo}}$ and vertical dimension $dh$. The front position $r_c$ is defined as the location where the wetting front reaches the height of the film in the far field $h_{\mathrm{film}}$. (b) The volume of air displaced by the advancing wetting front, assuming the air is incompressible, can be used to develop a prediction for $dh, d{h}_p=r{h}_{\mathrm{film}}/{\ell }_{\mathrm{halo}}$. The measured value of $dh, d{h}_m$, is obtained via TIR measurements immediately after contact initiation, and compares favorably with $d{h}_p$, as can be seen by the direct relationship between these quantities. Inset: ${\ell }_{\mathrm{halo}}$ as a function of $t$; colors represent different viscosities. ${\ell }_{\mathrm{halo}}$ grows slowly in time; no systematic dependence of ${\ell }_{\mathrm{halo}}$ is found as $\nu$ is varied. The height of the halo feature $dh$ increases in time, as shown here for $\nu =76$ cSt liquid, as can be seen by the gold points corresponding to the axis on the right-hand side of the plot.

Figure 4

Surfing on a capillary wave: (a) A schematic of the spreading capillary bridge. Fluid is shown in blue, the halo region and thin film of air are shown in white, and the surface is indicated by the black solid line. Viscous dissipation is localized in a boundary layer, indicated by the region trailing the contact line. (b) The average contact line velocity is plotted as a function of liquid viscosity; error bars indicate standard deviation of all contact events. Mean velocity decreases as a nonlinear function of liquid viscosity. Inset: over a small range, the velocity varies inversely with ${\ell }_{\mathrm{halo}}$ for the 5 cSt liquid, consistent with the predicted scaling for a capillary wave.