Dynamic Behavior of a Drop on a Vertically Oscillating Surface - Selected Topics of Computational and Experimental Fluid Mechanics - page 469

Fig. 10 Height of the peaks as a function of frequency
5 Conclusions and Future Work
It can be concluded that, as observed by previous authors, the dynamical behavior
of a drop subject to vertical oscillations can be classified in three phases:
(a) harmonic: the drop deforms as a whole in periodic expansions and contractions,
(b) geometric: a two dimensional stationary wave is produced showing polygonal
patterns,
(c) chaotic: the pattern is completely irregular and changes with time. There is a
critical value at which atomization starts; the drop breaks into droplets.
A periodic or quasiperiodic behavior of the heights has been observed depend-
ing on the phase. However, a more detailed analysis of the frequency spectrum is
required.
So far there is some information that the final state depends on the trajectory.
For example, after the chaotic phase, a geometric phase can be attained following
two different procedures. Future work will make a detailed study of the changes as
a function of frequency to determine critical values for each phase. Hysteresis will
also be searched for. These experiments will give information about the nonlinear
behavior of the phenomenon, and will probably provide elements for a numerical
simulation.
In particular, the spectrum of the signal in the chaotic phase should be analyzed.
So far, a main frequency can be determined but the signal is not sinusoidal.