Rebound suppression of a droplet impacting on an oscillating horizontal surface

The behavior of a droplet impinging onto a solid substrate can be influenced significantly by the horizontal motion of the substrate. The coupled interactions between the moving wall and the impacting droplet may result in various outcomes, which may be different from the usual normal droplet impact on a stationary wall. In this paper, we present a method to suppress drop rebound on hydrophobic surfaces via transverse wall oscillations, normal to the impact direction. The numerical investigation shows that the suppression of droplet rebound has a direct relationship with the oscillation phase, amplitude, and frequency. For a particular range of oscillation frequencies and amplitudes, a lateral shifting of the droplet position is observed along the oscillating direction. While large oscillation amplitude favors the process of droplet deposition, a high frequency promotes droplet rebound from the oscillating wall. A linear trend in the transition region between deposition and rebound is observed from a scaled phase diagram of the oscillation amplitude versus frequency. We provide a systematic investigation of drop deposition and elucidate the mechanism of rebound suppression through the temporal evolution of the nonaxial kinetic energy and the velocity flow field.

Figure 1

Schematic of a liquid droplet impacting on a horizontally oscillating solid surface.

Figure 2

Schematic of a liquid drop on a solid surface with a contact angle. The diffused interface is shown by dashed lines.

Figure 3

Comparison of maximum spread factor from the present study with prediction equations for a single droplet impacting on a neutral wetting surface.

Figure 4

Experimental validation of time evolution of spread factor $D^{*}$ and droplet height $H^{*}$ for $\mathrm{We}=12.8$ at the contact angles: (a) $\theta ={31}^{\circ }$ and (b) $\theta ={107}^{\circ }$.

Figure 5

(a) Profiles of the different wave forms for the oscillating substrate and (b) temporal evolution of the normalized contact width for different wave forms for velocity amplitude $U_A=0.15$ and frequency $\overline{\omega }=1.0$.

Figure 6

Velocity field inside the droplet for two nonsinusoidal wave forms at $T^{*}=2.0$ for $U_A=0.15$ and $\overline{\omega }=1.0$: (a) triangle and (b) square.

Figure 7

Interface profiles of the impacting droplet for (a) sine, (b) triangle, and (c) square wave forms of the oscillating substrate with $U_A=0.15$ and $\overline{\omega }=1.0$ at $T^{*}=4.0$.

Figure 8

Temporal evolution of the normalized contact width for different phase angles ($\psi$) at $\overline{\omega }=1.0$ for two oscillation amplitudes: (a) $U_A=0.125$ and (b) $U_A=0.15$.

Figure 9

Temporal evolution of the normalized contact width for different phase angles ($\psi$) with oscillation frequency (a) $\overline{\omega }=0.5$ and (b) $\overline{\omega }=1.5$ at $U_A=0.1$.

Figure 10

Temporal evolution of impacting droplet (a) $T^{*}=2.74$, (b) $T^{*}=4.11$, (c) $T^{*}=6.17$, and (d) $T^{*}=8.91$ for $U_A=0.05$ (top row) and $U_A=0.15$ (bottom row) on a surface with $\overline{\omega }=1.0$.

Figure 11

Temporal evolution of impacting droplet at (a) $T^{*}=3.08$, (b) $T^{*}=5.14$, (c) $T^{*}=6.85$, and (d) $T^{*}=10.28$ for $\overline{\omega }=0.5$ (top row) and $\overline{\omega }=1.5$ (bottom row) on a surface with $U_A=0.10$.

Figure 12

Temporal evolution of the normalized contact width for different wall oscillation (a) amplitudes and (b) frequencies.

Figure 13

Temporal evolution of the normalized shift in the $X$ center of mass of the impacting droplet for different wall oscillation (a) amplitudes and (b) frequencies.

Figure 14

Temporal evolution of the AR of the contact area for different wall oscillation (a) amplitudes and (b) frequencies.

Figure 15

Temporal evolution of the nonaxial distribution of the kinetic energy ($\eta$) for different wall oscillation (a) amplitudes and (b) frequencies.

Figure 16

Phase diagram for droplet rebound suppression: (a) oscillation amplitude versus frequency $\overline{\omega }-U_A$, (b) scaled diagram $\overline{\omega }-(\overline{\omega }/U_A)$ for the droplet rebound and deposition regimes. The $\circ$ and $◃$ symbols represent rebound and deposition regimes, respectively.

Figure 17

Instantaneous velocity field inside the droplet along the symmetry plane at (i) $T^{*}=4.104$, (ii) $T^{*}=5.814$, and (iii) $T^{*}=8.892$ for (a) the nonoscillating and (b) the oscillating cases with $U_A=0.15$ and $\overline{\omega }=1.0$.

Figure 18

Temporal evolution of the ratio of kinetic energy of the droplet along the principal axes between oscillating and nonoscillating walls.

Figure 19

Temporal evolution of the surface energy of the impinging drops on oscillating and nonoscillating surfaces. The energy is nondimensionalized by $\sigma R_o^2$.