Below is a video I took on falling water droplets from a tap at my home. Observe how a large drop detaches itself from the tap and falls down, not as a single drop, but as a series of droplets with certain degree of periodicity associated with it. The video was shot at around 960 frames per second.
Why does this happen ? A simple answer is : to minimize surface energy. Interestingly, the transition of a large drop to smaller droplets is mediated via formation of a liquid tread, which further breaks up into smaller droplets. This tread (not evident in my video) takes the form of an instability, and facilitates the process of minimizing the free energy. The nature of this breakup depends on parameters such as surface tension, viscosity, density and geometry of the liquid thread. The initial conditions, such as the opening of the tap and pressure of the flow, too play a critical role in determining the droplet formation.
Actually, the problem of falling droplets has a rich history, which dates back to the times of Leonardo da Vinci (who else 
), who made innumerable observations on the fluid flow (see some comments from his notebook here). There are many other people who have contributed towards our understanding of this problem. In the current literature, this instability problem is generally know as Plateau-Rayleigh instability, name after the two who played a vital role in quantifying this phenomenon and generalizing it to fluid jets.
In recent times, thanks to high speed photography, our visualization and hence deeper understanding of this instability problem has enormously increased. This understanding is fantastically communicated in a public lecture titled “The life and death of a drop” (see embedded video below) given by Sidney Nagel. This video has some spectacular movies captured by high speed camera ( > 10,000 frames per second) and looks at the falling droplet problem from the viewpoint of basic physics.
Why is this interesting problem ? Apart from the aesthetic and curiosity, the problem of fluid jets and their evolution is of great relevance in understanding fundamental processes of fluid dynamics, including astrophysical situations. Also, the problem of fluid droplets, their instability and splashing is of huge relevance in applications such as ink jet printing, wall painting, water reservoir management, blood flow analysis and many other problems in physiology and biomedicine.
What strikes me about the falling droplets is its simplicity and universality. It reminds me of a poem by Emily Dickinson:
Simplicity
How happy is the little stone
That rambles in the road alone,
And doesn’t care about careers,
And exigencies never fears;
Whose coat of elemental brown
A passing universe put on;
And independent as the sun,
Associates or glows alone,
Fulfilling absolute decree
In casual simplicity.
