This is a past research activity (my Ph.D. thesis), but it is still a research interest. In fact, I taught a graduate course on "Waves in fluids" in the "Instabilities in Dissipative Systems" doctoral program of the University of Navarra

The results presented here, have been mostly reported in the publications cited ⇒ here ⇐

Introduction

This research was mainly done in two different directions. The first concerned externally forced waves in a Natterer tube. The used tube is cylindrical (diametre = 1 cm, length = 28 cm), and is filled with CO₂ at vapour pressure for room temperature (20 ^oC). In this conditions, the liquid phase fills just one half of the whole volume of the tube. The forcing consists on a sinusoidal mechanical force exerted to the tube along its axis. A very important parameter in this case is the kinematical viscosity which is relatively small. The other direction concerned parametrically excited waves in a viscous fluid (this experiment was performed at Simon Fraser University under the supervision of Prof. J. Bechhoefer).

Collaborators

(in alphabetical order, all levels of collaboration: in the lab, permanent collaboration, temporary collaboration)

• John Bechhoefer

• Jesús Salán (my Ph.D. supervisor, deceased on Apr 18, 2008)

Results

All the results shown here correspond to the experiment with the Natterer tube. For results on the other direction and discussion, along with comparing the two systems, look at my Ph.D. thesis report. The movies in this page are converted from old and defective VHS videos. So, excuse please the visual quality. Also, they are only for visualizing, because in order to measure the stroboscopic effect should be removed (as effectively was in all the measurements). Also, it could be some cut sequences (as a result of the actual VHS quality) which originally were consecutive time sequences, but now they are not, so I present only the representative pieces, which are much smaller (the other available upon request).

In the following movies, you can see the behavior of the fluid at various frequencies and excitation amplitudes near the threshold:

• Without excitation:

• At 15 Hz , 1.1 V

• At 80 Hz , 2.1 V

In the following movies, you can see the behavior of the fluid at fixed frequency (excitation amplitude) varying the other parameter:

• Varying the frequency

In the following movies, you can see the behavior of the fluid at different conditions where the non linear effects are more apparent:

• At 50 Hz , 1.3 V (at 50 Hz the stroboscopic effect is much more noticeable, as a very slow time modulation)

• At 25.3 Hz , 0.6 V one can see very intense nonlinear effects (at 25 Hz the stroboscopic effect is also very noticeable, as a very slow time modulation)

In the following movies, you can see drops appear on the interface:

• At 80 Hz , 2.8 V (many drops travel on the interface, colliding among them and even forming bound states)

• Decreasing excitation amplitude one may observe hysteresis: at 80 Hz , 2.1 V (there is a single drop stable on the interface; compare to the movie above at the same value for the parameters)

• Increasing the excitation amplitude again one may get more drops in the tube: at 80 Hz , 2.3 V

• Also one may get stable drops at smaller by decreasing both the frequency and the amplitude (hysteresis): at 50 Hz , 1.4 V

In the following movies, you can see an interesting effect which results from the interaction of surface waves and sound waves. It occurs around 350 Hz, but the results are very sensitive to temperature:

• At approximately 0.5 V, and varying slightly the frequency you can see (top view) how the steady "soliton" doubles, and each of the "solitons" double again, and so on. At approx. 54 s the soliton train losses stability. At 1:20 appears a very interesting phenomenon.

• Wider side view. At approx. 54 s the soliton train losses stability. At 7:18 the camera turns to see one extremity of the tube (which is empty of liquid). At 7:54 the train losses stability.