Dynamic Behavior of a Drop on a Vertically Oscillating Surface - Selected Topics of Computational and Experimental Fluid Mechanics - page 465

Fig. 2 Harmonic phase in a drop with 60 µ lat28Hz a expansion b contraction

µ

Fig. 3 Height of a 60 1

drop at subject to a
frequency of 28Hz

periodically with respect to the central axis, at the same frequency of the external
force (Fig. 2 ).
The height of the dropwas determined as a function of time (Fig. 3 ). The frequency
of the drop is the same as the forcing frequency so the response can be considered
linear.

4.2 Geometric Phase

In this phase polygonal patterns appear. Two different volumes were studied: one of
60 µ l to analyze the heights as a function of time, and another of 200 µ l to obtain

better images.
It has been observed that as the frequency increases above the harmonic phase,
the polygons increase the number of sides. Figure 4 shows two instants of a drop
of 200

l subject to a frequency of 43Hz. A two dimensional pentagonal stationary
wave is formed. The motion of the five nodes and antinodes is such that vertex and
sides switch periodically in a caleidocycle.
As the frequency is slightly increased (46Hz) the figure becomes an hexagon as
can be seen in Fig. 5 . The behavior is also a caleidocycle.

µ