Mixing generated by Faraday instability between miscible liquids

The mixing between two miscible liquids subject to vertical vibrations is studied by way of experiments and a two-dimensional numerical model. The experimental setup consisted of a rectangular cell in which the lighter fluid was placed above the denser one. The diffuse interface was then visualized by a high-speed camera. After an initial period of diffusion growth, the interface becomes unstable with a defined wavelength, which depends on the amplitude and frequency of the acceleration. The waviness of the interfacial region disappears once the mixing of the two fluids takes place. The mixing is characterized by a mixing layer thickness (MLT) which measures the thickness of the mixed region between the two pure fluid domains. We find that the MLT shows an exponential growth with time due to an initial fingering that appears at the interface and then a growth with a defined slope after the mixing takes place. The MLT also increases with amplitude of driving motion. Experimentally determined MLTs are always greater than those determined by computations since the latter assume a jump discontinuity between the fluids prior to shaking, whereas in an experiment an initial diffusive region establishes itself prior to shaking and this is destabilizing. In addition, it is found from computations that mixing is best for low gravity levels at earlier times and high gravity levels at longer times. Explanations are advanced for each of these observations.