Ligament-Mediated Spray Formation

The spray formed when a fast gas stream blows over a liquid volume presents a wide distribution of fragment sizes. The process involves a succession of changes of the liquid topology, the last being the elongation and capillary breakup of ligaments torn off from the liquid surface. The coalescence of the liquid volumes constitutive of a ligament at the very moment it detaches from the liquid bulk produces larger drops. This aggregation process has its counterpart on the shape of the size distribution associated with the ligament breakup, found to be very well represented by gamma distributions. The exponential shape of the overall distribution in the spray coincides with the large excursion wing of these elementary distributions, underlying the crucial role played by the ligament dynamics in building up the broad statistics of sprays.

Figure 1

Top: Instantaneous view of the destabilization of a water jet by a coaxial fast air stream showing the development of an axisymmetric shear instability, the digitations at the wave crests, and the ligament formation. The initial diameter of the liquid jet is 8 mm, its velocity $0.6\mathrm{m}/\mathrm{s}$, and the velocity of the air stream is $35\mathrm{m}/\mathrm{s}$. Bottom: Resulting dispersion of droplets in the spray.

Figure 2

Double flash exposure of a ligament just before and after breakup. The duration of a flash is $5\mu \mathrm{s}$, and the interval between the two flashes is 1.6 ms. The resulting droplets are highlighted by a white rim.

Figure 3

Left: Time resolved series of the elongation and breakup of a ligament in the wind showing the coalescence between the blobs constitutive of the ligament as it breaks. The time interval between the pictures is 1.34 ms. Right: An isolated ligament just before breakup covered with blobs of various sizes $d$ matching its local thickness. The evolution of the size distribution $n(d,t)$ is governed by Eq. (2).

Figure 4

Droplet size distribution after ligament breakup $p_B(d)$ for an air velocity of (a) $29\mathrm{m}/\mathrm{s}$ and (b) $50\mathrm{m}/\mathrm{s}$. Lines: fit by gamma distributions. (c) Dependence of the order $\nu$ on the ratio of the average droplet size $⟨d⟩$ to the ligament thickness at breakup $\xi$. (d) Distribution of droplet sizes in the spray $p(d)$. The slight increase of the exponential slopes with air velocity (inset) reflects the variation of the gamma orders $\nu$ on $⟨d⟩/\xi$.