Asymmetrical dripping

Dripping from a faucet is studied, where by cutting diagonally the tip breaks the cylindrical symmetry. We measured long dripping time series recorded with a laser-beam apparatus and continuous change in drop position using a high-speed camera. It is found that the added degree of freedom produces a transversal oscillation of a pending drop, which couples with a vertical oscillation induced by the breaking off of the previous drop. As a consequence dripping times shorten and dripping patterns regularize. The effect is attributed to the “reduced” contact circle and to decreased frequency of the vertical oscillations of the residue. A very complex flow circulation pattern within the forming drop is observed. It is suggested that geometrical shape vibrations of the pending drop take place by the development of eddies of different amount, more effective in the vicinity of the highest edge of the tip, where they dissipate more slowly. This asymmetrical liquid flow is brought about by the slanting form of the orifice and overlaps with the axial oscillations.

Figure 1

(a) Schematic diagram of the experimental setup. (b) Configuration of the stainless nozzles utilized: Flat $\left(F\right)$ and oblique $\left(O\right)$ shaped.

Figure 2

Photographs showing at $Q\sim 0.1\text{ml}∕\mathrm{s}$ the breakup of a drop falling from $F$ and $O$ nozzles. We can see that the “effective” contact circle for the $O$ tip is smaller than the $F$ one.

Figure 3

Plots of dripping bifurcation diagrams for nozzles with orifice of diameter $d=2\text{mm}$: (a) $F$ nozzle $\left(\vartheta =0°\right)$; and $O$ nozzles with (b) $\vartheta =15°$, (c) $\vartheta =30°$, (d) $\vartheta =45°$.

Figure 4

(Color) Blow-up of the superimposed bifurcation diagrams shown in Fig. 3.

Figure 5

Plots of dripping spectra for nozzles of $d=2\text{mm}$: (a) $\vartheta =0°$; (b) $\vartheta =45°$.

Figure 6

(Color) Enlargement of the superimposed bifurcation diagrams shown in Fig. 5.

Figure 7

Same as in Fig. 5, but for $d=4\text{mm}$.

Figure 8

A sequence of pictures showing the $F$ axial symmetric oscillations of the liquid residue and a falling drop at $Q\sim 0.1\text{ml}∕\mathrm{s}$. One observes also a satellite drop. On each image we report the frame number captured by the high-speed video system, operating at $2000\text{fps}$.

Figure 9

(Color) Vertical position of the center of mass vs time of a forming drop from a $F$ nozzle of diameter $d=2\text{mm}$, for three values of flow rate. The origin of the coordinate system is located at the intersection point of the vertical axis of symmetry with the horizontal plane. The curves were obtained by spline interpolation among the data points.

Figure 10

The analog of Fig. 8 for the oscillations of a forming drop from an $O$ nozzle with $\vartheta =45°$.

Figure 11

Center of mass coordinates (origin at the intersection point of the vertical axis of symmetry with the cut plane) vs time of a drop hanging from an $O$ nozzle $\left(d=2\text{mm}\right)$, at two flow rates: $Q=0.16\text{ml}∕\mathrm{s}$ (a), (c), (e); $Q=0.20\text{ml}∕\mathrm{s}$ (b), (d), (f).