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Characteristic rupture height of the mediating air film beneath an impacting drop on atomically smooth mica

Ramin Kaviani and John M. Kolinski*

  • EMSI Laboratory, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

  • *john.kolinski@epfl.ch

Phys. Rev. Fluids 8, 103602 – Published 31 October, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.103602

Abstract

Before a droplet can contact a surface during impact, it must first displace the air beneath it. Over a wide range of impact velocities, the droplet first squeezes the air into a thin film, enhancing its resistance to drainage; this slows the progress of the liquid toward the surface. Indeed, below a critical impact velocity, the air film remains intact, and the droplet rebounds off of the air film without making contact. For impact velocities exceeding this critical impact velocity, the droplet always makes contact. The initiation of contact formation requires a topological transition, whereby the initially connected gas domain is ruptured and a liquid capillary bridge forms, binding the droplet to the surface. Here we probe this transition in detail around the critical impact velocity using calibrated total internal reflection microscopy to monitor the air film thickness and profile at high speed during the impact process. Two air film rupture modalities are observed: nucleated contacts, which are isolated and do not correspond to the global minimum air film thickness, and spontaneous contacts, which occur always on a ring centered upon the impact axis where the air film reaches its global minimum. Our measurements show that for impact velocities exceeding the critical velocity for contact initiation, the air film ruptures at a nearly identical height hmin20 nm, for two fluids: silicone oil and a water-glycerol mixture. The height and time duration of the air film prior to contact are presented for over 180 droplet impact experiments. Impact events of water solution droplets show statistics for contact nucleation different from those for the silicone oil; this suggests that another mechanism may dominate contact nucleation during impact of the solution. Nevertheless, a critical impact velocity above which contact always occurs is identifiable for both liquids.

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  47. To estimate the Reynolds number in the gas phase, we use the slow variation of the air film thickness during rebound, as plotted in Fig. 2. The inertial pressure of the droplet p=ρU2/2500 Pa confirms that the air compression is negligible for U1 m/s. The lateral velocity of the gas can be estimated by considering the changes in h and applying incompressibility locally. By inspection, h decreases by about 25 nm in 2 ms. Thus, a crude estimate of dh/dt is 12.5 µm/s; this change in height must be balanced by a flux of gas laterally along the air film. From incompressibility, ·u=0; thus, for an axisymmetric flow where uθ=0, 1rrurr+uzz=0. Here we assume that the radial direction is given by x and the direction normal to the surface by y and that there is no flow in the azimuthal direction by symmetry. A representative scale of x is 100 µm or more; a representative scale for y is 100 nm or less. Applying these scales, the lateral velocity of the gas is estimated as ux=dxdyuy=104107ḣ=103×12.5µm/s=12.5mm/s. To complete the estimation of Re, we use the air film thickness 100 nm as the length scale, the air density of 1 kg/m3, and the air viscosity of approximately 2×105 Pas, resulting in Re6.25×105; thus, viscous stresses dominate in the air film. Estimating the Reynolds number in the liquid phase is more straightforward. The liquid droplet moves toward the surface at the same velocity as the air film in the vertical direction, estimated at 12.5 µm/s, over a similar lateral scale of 100 µm. The liquid's kinematic viscosity is 20 cSt or 2×105 m2/s, resulting in a similar Re6.25×105. Thus, viscous stresses dominate in both the liquid and the gas during the rebound process.

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