Influence of capillarity and gravity on confined Faraday waves

Experiments characterizing the influence of gravity and interfacial tension on Faraday instability in immiscible, confined fluid layers are presented. The variation in interfacial tension was obtained by controlling the temperature of a suitable binary fluid pair while the influence of gravity was analyzed through a series of terrestrial and microgravity (parabolic flight) experiments. These experiments confirm the existence of a crossover frequency, on either side of which gravity plays opposing roles. The current experiments also reveal that the neutral stability curves under Earth's gravity drift toward lower frequencies as the temperature of the liquid pair approaches its upper consolutal value, i.e., the temperature of complete miscibility. Such drifts in the low frequency range are shown to occur primarily due to the reduction in density difference between the layers, whereas at very high frequencies they are controlled by the lowering of interfacial tension. In the absence of gravity, the Faraday waves are characterized by larger wave numbers, and, as in terrestrial conditions, the instability thresholds at high frequencies increase with an increase of temperature, i.e., reduction in interfacial tension value. This surprising stabilization originates from the lowering of the critical wavelength that leads to increased viscous dissipation.

Figure 1

Experimental test cell with the liquids.

Figure 2

Critical amplitude required for the onset of Faraday instability in confined, immiscible FC-72/silicone oil system at different temperatures under terrestrial conditions: (a) $38{}^{\circ }\mathrm{C}$, (b) $40{}^{\circ }\mathrm{C}$, (c) $41.5{}^{\circ }\mathrm{C}$, (d) $42{}^{\circ }\mathrm{C}$. The labels A, B, C, etc., represent the various modes and are described in the text.

Figure 3

Interfacial modes of excitation at onset, depicted in Fig. 2. While B alone is harmonic, all other modes are subharmonic.

Figure 4

Interfacial modes of excitation in microgravity conditions for different temperatures and forcing frequencies. (a) 7 Hz, (b) 11 Hz.

Figure 5

Threshold range measured in microgravity conditions in comparison with terrestrial experiments at temperatures (a) $T=38{}^{\circ }\mathrm{C}$, (b) $T=40{}^{\circ }\mathrm{C}$, (c) $T=41.5{}^{\circ }\mathrm{C}$.

Figure 6

Threshold range measured in microgravity conditions for different temperatures. Observe that the critical amplitude typically increases with an increase in temperature.