Mutual Adaptation of a Faraday Instability Pattern with its Flexible Boundaries in Floating Fluid Drops

Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This is implemented by triggering this instability in floating fluid drops. An interaction of Faraday waves with the shape of the drop is observed, the radiation pressure of the waves exerting a force on the surface tension held boundaries. Two regimes are observed. In the first one there is a coadaptation of the wave pattern with the shape of the domain so that a steady configuration is reached. In the second one the radiation pressure dominates and no steady regime is reached. The drop stretches and ultimately breaks into smaller domains that have a complex dynamics including spontaneous propagation.

Figure 1

(a) Vertical section of an isopropanol drop floating on perfluorated oil in absence of oscillations. (b)–(d) A drop of volume $V_2=1.00\pm 0.02\mathrm{ml}$ forced at $f_0=130\mathrm{Hz}$ for three amplitudes of forcing. (b) Faraday waves of weak amplitude, ${\gamma }_m/g=3.28$, (c) steady elongated state, ${\gamma }_m/g=3.93$ and (d) highly perturbed state ${\gamma }_m/g=6.48$. (e) A drop of volume $V_2=10.0\pm 0.1\mathrm{ml}$ square when forced at $f_0=160\mathrm{Hz}$ with ${\gamma }_m/g=4.90$. The bars are 1 cm long.

Figure 2

The case of an ethanol drop of volume $V_2^{\prime }=1.00\pm 0.02\mathrm{ml}$ deposited on silicon oil. (a) Sketch of the vertical section of the floating drop in the absence of oscillations. (b) It is circular at rest with area and thickness $A_2^{\prime }=459\pm 5{\mathrm{mm}}^2$ and $h_2^{\prime }=2.2\mathrm{mm}$ respectively. (c)–(e) Three successive images showing the temporal evolution of the drop when forced at $f_0=130\mathrm{Hz}$ with ${\gamma }_m/g=7.00$. The bar is 1 cm long.

Figure 3

Phase diagram of the different regimes observed in the case of an isopropanol drop of volume $V_2=1.00\pm 0.02\mathrm{ml}$ deposited on perfluorated oil. The drop area at rest is $A_2=530\pm 10{\mathrm{mm}}^2$, its average thickness $h_2=1.9\mathrm{mm}$. Circular ($C$), deformed ($D$), elongated ($E$), highly perturbed (HP), and Faraday ($F$) instability in oil.

Figure 4

(a) Evolution of the aspect ratio of an elongated isopropanol drop on perfluorated oil as a function of the forcing amplitude for different frequencies. The lines are the fits by Eq. (4). (b), (c) Photographs of two drops in an elongated state at $f_0=130\mathrm{Hz}$ for ${\gamma }_m/g=3.97$ and $R=0.42$ (b) and ${\gamma }_m/g=4.62$ and $R=0.28$ (c) and the predicted shapes by the corresponding solutions [Eq. (3)]. The bar is 1 cm long.

Figure 5

(a) The surface of the experimental cell after the fragmentation of a drop of ethanol on silicon oil for $f_0=80\mathrm{Hz}$ and ${\gamma }_m/g=5.06$. (b)–(d) The shape of some of the resulting steady fragments. Each one corresponds to a different fragment size. The bars are 1 cm long.