Dynamics of Collapse of Air Films in Drop Impact

Jolet de Ruiter, Jung Min Oh, Dirk van den Ende, and Frieder Mugele

Phys. Rev. Lett. 108, 074505 – Published 17 February 2012

Abstract

Liquid drops hitting solid surfaces deform substantially under the influence of the ambient air that needs to be squeezed out before the liquid actually touches the solid. Nanometer- and microsecond-resolved dual wavelength interferometry reveals a complex evolution of the interface between the drop and the gas layer underneath. For intermediate impact speeds ( $We \sim 1 \dots 10$ ) the layer thickness can develop one or two local minima—reproduced in numerical calculations—that eventually lead to the nucleation of solid-liquid contact at a We-dependent radial position, from a film thickness $> 200 nm$ . Solid-liquid contact spreads at a speed involving capillarity, liquid viscosity and inertia.

Received 10 November 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.074505

Authors & Affiliations

Jolet de Ruiter, Jung Min Oh, Dirk van den Ende, and Frieder Mugele

Physics of Complex Fluids, MESA Institute for Nanotechnology, University of Twente, Post Office Box 217, 7500 AE Enschede, The Netherlands

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Vol. 108, Iss. 7 — 17 February 2012

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Images

Figure 1
Droplet cushioning, and spreading of liquid-solid contact at moderate We impact. (a) Interference profile of the air film below a water droplet at (left) 4.1 and (right) 2.3 ms before nucleation of a liquid-solid contact. (b) Spreading of liquid-solid contact at 0.10, 0.21, 0.32, 0.49, 0.75, 1.05 ms after nucleation. $v_{φ}$ : azimuthal spreading velocity. (c) Sketch of deformed drop indicating interference of light reflected from the solid/air and air/liquid interfaces. Inset: schematic dimple with local minima $h_{1}$ and $h_{2}$ . (d) Characteristic radial intensity profile (thin grey line), and the corresponding interface profile (thick black line). Dotted lines indicate positions of local extrema in $h$ .Reuse & Permissions
Figure 2
Time evolution of interface profiles for water drops with increasing impact velocities $v$ (top to bottom: 0.24, 0.41, $0.52 m \cdot s^{- 1}$ ; corresponding We numbers: 0.9, 2.6, 4.2). Time step: $50 μ s$ . Profiles for different $v$ are shifted vertically for clarity. Note the different scales on the abscissa and the ordinate: maximum slope of interface $< 3 °$ . Numbers in parentheses indicate minimum heights in µm of $h_{1}$ and $h_{2}$ . Inset: nucleation of solid-liquid contact at $r_{2}$ and $r_{1}$ for low (left) and high (right) We, respectively.Reuse & Permissions
Figure 3
Temporal evolution of local minima, and their equilibrium and nucleation height. (a) Symbols: $h_{1}$ versus impact velocity $v$ for experiments with water (black triangles), ethanol (red diamonds), and ${CaCl}_{2}$ (grey squares) drops. Solid lines: universal scaling law for $h_{c}$ (colors according to experimental conditions). Dots: numerical values of $h_{1}$ for water; open dots: profiles with one local minimum, solid dots: two local minima. (b) $h_{1}$ and $h_{2}$ vs time for the experiments shown in Fig. 2. From top to bottom: $v = 0.24$ , 0.41, and $0.52 m \cdot s^{- 1}$ . The star indicates which of the two minima nucleates—at a height $h^{*}$ . (c) Histogram showing the value of $h^{*}$ in 128 experiments with various fluid properties (bin size 50 nm).Reuse & Permissions
Figure 4
Spreading of liquid-solid contact. (a) Azimuthal velocity $v_{φ}$ for ${CaCl}_{2}$ droplets with $h_{1} = 0.23$ , 0.57, and $0.74 μ m$ (from top to bottom). (b) $v_{φ}$ versus the inertial scaling for increasing viscosity (top to bottom). (c) $v_{φ}$ , nondimensionalised by the inertial scaling, versus $μ_{l}^{- 1 / 2}$ for experiments with seven fluids having viscosities ranging from $1 \dots 10^{2} mPa \cdot s$ . (The error in the determination of $v_{φ}$ is typically 5%. All variables given in SI units.)Reuse & Permissions

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