Rayleigh-Taylor instability under a flat beam

A theoretical and experimental study on the Rayleigh-Taylor instability of a thin liquid film is presented. The experiments were performed by coating the underside of a flat beam with uniform liquid film. The size of the beam is such that a linear arrangement of drops is formed allowing the measurement of the drops growth. The experimental growth of the drops has been compared to the results obtained from a stability analysis performed on the equation that controls the thickness evolution and an excellent agreement is found. In addition, both time and length scales of the phenomenon are established.

Figure 1

Schematic view of the experimental setup used to obtain Rayleigh-Taylor instability under a flat beam.

Figure 2

(Color online) Photography of the drops aligned along the beam.

Figure 3

Drop formation during an experiment with $150\mu \text{m}$ of initial thickness. Time difference between images is $\sim 1200\text{s}$.

Figure 4

(Color online) Two profiles obtained in an experiment with an initial thickness of $150\mu \text{m}$ at (a) $t\sim 0$ and (b) $t\sim 1000\text{s}$.

Figure 5

Distribution of distances between drops (wavelength) corresponding to experiments performed with both initial thicknesses: 150 and $350\mu \text{m}$.

Figure 6

Drop formation during an experiment with $350\mu \text{m}$ of initial thickness. Time difference between images is $\sim 100\text{s}$.

Figure 7

Two profiles obtained in an experiment with an initial thickness of $350\mu \text{m}$ at (a) $t\sim 0$ and (b) $t\sim 350\text{s}$.

Figure 8

Mean amplitude of the drops as a function of time for experiments performed with both initial thicknesses: 150 (empty symbols) and $350\mu \text{m}$. The straight lines show the data mean slope.

Figure 9

Dimensionless form of Fig. 8 obtained by using ${\sigma }_0^{-1}$ and $h_0$ as time and thickness scales, respectively.