The Breakup of a Liquid Droplet

maximios

Ever wondered what happens to a raindrop during its journey from clouds to the ground? It does not stay intact. It deforms and breaks as it comes down. According to Villermaux and Bossa, the raindrop flattens as it comes down and forms a bag-like structure before it breaks (I strongly recommend watching the supplementary movie on this page for the high-definition video).

Why does a Liquid Droplet Break?

A liquid droplet assumes a spherical shape because of surface tension. The force of surface tension tries to minimize the surface area of a liquid droplet for a given volume. Since a sphere has a minimum surface area (Sₘᵢₙ) for a given volume, the droplet takes a spherical shape. The force of surface tension opposes any shape change from a sphere as the new shape has a surface area greater than Sₘᵢₙ. Hence, to break a droplet into smaller droplets, which involves increasing the surface area, a force greater than the surface tension of the liquid is needed. Where does this force come from? In the case of a falling raindrop, this force arises because of the relative motion between the falling raindrop and the surrounding air. This force can be called as an aerodynamic force. The basic requirement for creating the aerodynamic force for breaking a liquid droplet is the presence of relative motion between the droplet and surrounding gas flow-field. The magnitude of this aerodynamic force depends on the magnitude of the relative velocity between the droplet and the surrounding gas flow-field. For example, the magnitude of the aerodynamic force in the case of a falling raindrop in a quiescent surrounding (air is stationary) is lesser than in the case of the falling raindrop in an ascending stream of air, because the magnitude of the relative velocity is larger in the latter case, and thus the potential for droplet breakup is more in the latter case. But how large should this aerodynamic force be in comparison to the surface tension force to induce droplet breakup? In other words, what should be the minimum value of the ratio of this disrupting aerodynamic force to the surface tension force to induce droplet breakup? This ratio of the disrupting aerodynamic force to the surface tension force is known as the Weber number (We). Experimentally, it was found that the minimum value of the Weber number needed for droplet breakup to happen is We = 11±2. It is not as though the droplet breakup does not happen for We < 11. But, this breakup is not practically useful (it is discussed later). Also, for We < 11, the droplet breakup is not always guaranteed. However, for We > 11, the droplet breakup is always guaranteed. And, this breakup is practically useful too. So, let’s look at how a liquid droplet breaks for We < 11 and We > 11?

How Does a Liquid Droplet Break?

For We < 11, the disrupting aerodynamic force is not strong enough to overcome the surface tension force completely. This makes the droplet oscillate, and sometimes break. This breakup is known as vibrational breakup. In this breakup, the droplet breaks into 2 or 3 droplets whose sizes are comparable to the parent droplet.

But why does a droplet oscillate before it breaks? As long as We > 1, the disrupting aerodynamic force is greater than the surface tension force. Then, instead of breaking/disintegrating, why should a droplet oscillate?

Figure 1 shows a droplet in a stream of air for which 1 11 has received serious attention from several researchers. The droplet can break via any of the breakup modes mentioned above depending on the value of the Weber number. The breakup modes differ in characteristics such as the morphology of breakup, droplet size distribution of the product droplets, breakup times, etc. The physical mechanism behind each of the breakup modes is still under debate. However, numerous experimental and numerical works have revealed valuable information regarding these breakup modes. Such information is useful for designing and developing spray nozzles, injectors, atomizers in practical applications.

References

  1. M A Rodrıguez-Valverde, M A Cabrerizo-Vılchez, and R Hidalgo-Alvarez, The Young–Laplace equation links capillarity with geometrical optics, EUROPEAN JOURNAL OF PHYSICS, 2003.
  2. J. Tan, M. Papadakis, and M. K. Sampath, Computational Study of Large Droplet Breakup in the Vicinity of an Airfoil, Technical report, 2005.
  3. Emmanuel Villermaux and Benjamin Bossa, Single-drop fragmentation determines size distribution of raindrops, Nature Physics, 2009.
  4. Myth of raindrop formation exploded (https://www.newscientist.com/article/dn17487-myth-of-raindrop-formation-exploded/)
  5. Weisstein, Eric W., Osculating Circle, From MathWorld — A Wolfram Web Resource (https://mathworld.wolfram.com/OsculatingCircle.html)
  6. Spheroid (Wikipedia)