SECTORES DE LA COCINA

In the following experiment the camera resolution was again of small width, 512×48 pixels while the frame rate was smaller at 125f ps. We chosep= 1.04 which corresponds to 8.400 and 8.303Hz in water and sunflower oil respec- tively. At different sweep rates the amplitude is gradually increased and again decreased. Also, the intervals slightly varied to determine if this was a fac- tor, but we did not find significant influence, as long as all regimes are passed through. As we know the excitation as a function of the camera time when can relate it to the wave height. As mentioned before there is some fluctuation on the forcing signal. A result is plotted in figure 4.17 for the slowest sweep rate of 0.5·10−3gs−1 for the interval 0.01 ≤f ≤0.30 in water. Most notably are a few jets at the transition from a solid-body to a standing wave state. The results are combined in figures 4.18 and 4.18 where the transitions locations are denoted. The direction of the sweeps is from bottom to top and this is how one should read the plots. For every rate there are three runs for water and two for sunflower oil.

Figure 4.18: Transition locations in water plotted as function of the sweep rate and the excitation. The graph should be read as follows. As the frequency is constant for every run, we start at a small excitation at a certain sweep rate, say 1.3·10−3gs−1. As the excitation increases we move up in a straight line. Atf = 0.15 the wave transitions into a jetting state. Atf = 0.3 (solid red line) the sweep direction is reversed, i.e. the excitation is now decreasing, but in the plot we keep moving upward. When the excitation returns to approximately

f = 0.2 the fluid transitions in the standing wave state and in the solid body state atf = 0.05. At a small excitation, f = 0.01 in this case, the run ends. The experiment was performed three times for every sweep rate.

as irregularities survive much linger in a low viscous fluid. For both fluids there is overlap of the regimes for faster rates. In some instance the jetting state is only reached when the excitation amplitude is already decreasing. For water at small rates there also seems to be overlap but these are merely a few jets formed in the transition from a solid-body to a standing wave state, like in figure 4.17. Apparently, jets are always created in water for the transition from solid-body state. For sunflower oil this is only the case at faster rates where there is clear separation of the transition mechanism around 3·10−3gs−1. At lower rates the system transitions smoothly into a standing wave from the solid-body state. Water has a similar division for smaller rates than 1.5·10−3gs−1. For both fluids this transition is at lower excitation for lower sweep rates, although it seems that this transition in oil has not yet reached it asymptote. Even more slower sweep rates are not possible at this system’s settings.

Figure 4.19: Transition locations in sunflower oil plotted as function of the sweep rate and the excitation. Atf = 0.37 (solid red line) the sweep direction is reversed. The experiment was performed twice for every sweep rate.

the graphs, when the forcing decreases) are well defined and show little depen- dence on the sweep rate, except the latter case in oil. In that case the transition is at higher excitation for lower sweep rates as one would expect since the system has more time to react the the decreasing excitation. The system transition the the solid-body state eventually, but this evolution is slow compared to faster sweep rates. For water the trend is slightly in the opposite direction for small rates. For the jetting to standing wave transition there is apparently not much time needed to adapt. In the experiment with 4.87·10−3gs−1 and varying fre- quencies (figure 4.16) this was not the case. Evidently, the system behaves very differently when varying the parameters discarded in this experiment.

We observe that the system has enough time to adapt to the forcing at small sweep rates. Hence, we confirm the presence of hysteresis in our setup. Let us denote the size of the hysteresis by ∆f, which is calculated by subtracting the excitation of the transitions for increasing and decreasing forcing. In figure 4.20 the hysteresis for both transitions is plotted as function of the sweep rate. For transitions of the solid body and standing wave states the minimum difference in excitation amplitude are approximately 0.09 for water and 0.05 for oil. The hysteresis in this transition depends on the sweep rate. For oil the trend is steeper which means that waves in oil react slower to a change in excitation. If we look at figure 4.19 we observe that especially the transition for increasing forcing is depended on the sweep rate. It is unknown why this is different in

Figure 4.20: The difference in forcing (∆f) for both transitions in water and sunflower oil plotted as function of the sweep rate. The points are obtained from the average of the transitions locations in figures 4.18-4.19 and then taking the difference. A positive value means the transition occurred for higher values of f when increasing the amplitude. For instance the solid-body to standing wave transition for sunflower for 0.5·10−3gs−1 is atf = 0.20 when the forcing increases and atf = 0.15 when decreasing, yielding ∆f = 0.05.

water. We would expect a constant value for the hysteresis at very small sweep rates as the change of the excitation will be very slow compared to the dynamics of the fluid. Apparently, the sweep rate is not small enough, although the trend is flattening at the left of the graph. At the smallest sweep rate considered here, the hysteresis is approximately twice as large for water. In section 2.2.9 we based that the energy required for the initial wetting on the movement of the contact line. We found that it should be proportional to the surface tension. The value for water is appropriately twice the value for oil.

In this transition we observed a few number of jets, in water for all sweep rates and for larger rates in oil. We explain this as follows. The contact line force can keep the system in a solid-body state for a long time and when it breaks loose the friction decreases with increasing amplitude, temporally leading to practically unbounded growth, resulting in jets before a standing wave stabilizes. Both results supports the hypothesis that the hysteresis in this transition is mainly due to the initial wetting motion. More investigation in the transition, like the influence of meniscus waves is required to be conclusive. One should also vary the values for surface tension and contact angle hysteresis in experiment.

The transitions of the standing wave and jetting states show an irregular trend for the hysteresis. At the smallest sweep rate, the values are 0.01 and 0.02 for water and oil respectively, but vary in both directions. In section 2.3 we argued that the hysteresis should be positive (∆f >0) but we are inconclusive about the exact mechanism.

A final note is on the smoothness of the jets. The ones created from a solid-body state are better reproducible and show less asymmetric motion as for standing wave transitions to jets. This can be expected as there are more irregularities is standing wave. Jets created in a jetting state are completely exposed to this effect.