Rain can freefall at speeds of up to 25 miles per hour. If the droplets land in a puddle or pond, they can form a crown-like splash that, with enough force, can dislodge any surface particles and launch them into the air.

Now MIT scientists have taken high-speed videos of droplets splashing into a deep pool, to track how the fluid evolves, above and below the water line, frame by millisecond frame. Their work could help to predict how spashing droplets, such as from rainstorms and irrigation systems, may impact watery surfaces and aerosolize surface particles, such as pollen on puddles or pesticides in agricultural runoff.

The team carried out experiments in which they dispensed water droplets of various sizes and from various heights into a pool of water. Using high-speed imaging, they measured how the liquid pool deformed as the impacting droplet hit the pool’s surface.

Across all their experiments, they observed a common splash evolution: As a droplet hit the pool, it pushed down below the surface to form a “crater,” or cavity. At nearly the same time, a wall of liquid rose above the surface, forming a crown. Interestingly, the team observed that small, secondary droplets were ejected from the crown before the crown reached its maximum height. This entire evolution happens in a fraction of a second.

Scientists have caught snapshots of droplet splashes in the past, such as the famous “Milk Drop Coronet” — a photo of a drop of milk in mid-splash, taken by the late MIT professor Harold “Doc” Edgerton, who invented a photographic technique to capture quickly moving objects.

The new work represents the first time scientists have used such high-speed images to model the entire splash dynamics of a droplet in a deep pool, combining what happens both above and below the surface. The team has used the imaging to gather new data central to build a mathematical model that predicts how a droplet’s shape will morph and merge as it hits a pool’s surface. They plan to use the model as a baseline to explore to what extent a splashing droplet might drag up and launch particles from the water pool.

“Impacts of drops on liquid layers are ubiquitous,” says study author Lydia Bourouiba, a professor in the MIT departments of Civil and Environmental Engineering and Mechanical Engineering, and a core member of the Institute for Medical Engineering and Science (IMES). “Such impacts can produce myriads of secondary droplets that could act as carriers for pathogens, particles, or microbes that are on the surface of impacted pools or contaminated water bodies. This work is key in enabling prediction of droplet size distributions, and potentially also what such drops can carry with them.”

Bourouiba and her mentees have published their results in the Journal of Fluid Mechanics. MIT co-authors include former graduate student Raj Dandekar PhD ’22, postdoc (Eric) Naijian Shen, and student mentee Boris Naar.

Above and below

At MIT, Bourouiba heads up the Fluid Dynamics of Disease Transmission Laboratory, part of the Fluids and Health Network, where she and her team explore the fundamental physics of fluids and droplets in a range of environmental, energy, and health contexts, including disease transmission. For their new study, the team looked to better understand how droplets impact a deep pool — a seemingly simple phenomenon that nevertheless has been tricky to precisely capture and characterize.

Bourouiba notes that there have been recent breakthroughs in modeling the evolution of a splashing droplet below a pool’s surface. As a droplet hits a pool of water, it breaks through the surface and drags air down through the pool to create a short-lived crater. Until now, scientists have focused on the evolution of this underwater cavity, mainly for applications in energy harvesting. What happens above the water, and how a droplet’s crown-like shape evolves with the cavity below, remained less understood.

“The descriptions and understanding of what happens below the surface, and above, have remained very much divorced,” says Bourouiba, who believes such an understanding can help to predict how droplets launch and spread chemicals, particles, and microbes into the air.

Splash in 3D

To study the coupled dynamics between a droplet’s cavity and crown, the team set up an experiment to dispense water droplets into a deep pool. For the purposes of their study, the researchers considered a deep pool to be a body of water that is deep enough that a splashing droplet would remain far away from the pool’s bottom. In these terms, they found that a pool with a depth of at least 20 centimeters was sufficient for their experiments.

They varied each droplet’s size, with an average diameter of about 5 millimeters. They also dispensed droplets from various heights, causing the droplets to hit the pool’s surface at different speeds, which on average was about 5 meters per second. The overall dynamics, Bourouiba says, should be similar to what occurs on the surface of a puddle or pond during an average rainstorm.

“This is capturing the speed at which raindrops fall,” she says. “These wouldn’t be very small, misty drops. This would be rainstorm drops for which one needs an umbrella.”

Using high-speed imaging techniques inspired by Edgerton’s pioneering photography, the team captured videos of pool-splashing droplets, at rates of up to 12,500 frames per second. They then applied in-house imaging processing methods to extract key measurements from the image sequences, such as the changing width and depth of the underwater cavity, and the evolving diameter and height of the rising crown. The researchers also captured especially tricky measurements, of the crown’s wall thickness profile and inner flow — the cylinder that rises out of the pool, just before it forms a rim and points that are characteristic of a crown.

“This cylinder-like wall of rising liquid, and how it evolves in time and space, is at the heart of everything,” Bourouiba says. “It’s what connects the fluid from the pool to what will go into the rim and then be ejected into the air through smaller, secondary droplets.”

The researchers worked the image data into a set of “evolution equations,” or a mathematical model that relates the various properties of an impacting droplet, such as the width of its cavity and the thickness and speed profiles of its crown wall, and how these properties change over time, given a droplet’s starting size and impact speed.

“We now have a closed-form mathematical expression that people can use to see how all these quantities of a splashing droplet change over space and time,” says co-author Shen, who plans, with Bourouiba, to apply the new model to the behavior of secondary droplets and understanding how a splash end-up dispersing particles such as pathogens and pesticides. “This opens up the possibility to study all these problems of splash in 3D, with self-contained closed-formed equations, which was not possible before.”

This research was supported, in part, by the Department of Agriculture-National Institute of Food and Agriculture Specialty Crop Research Initiative; the Richard and Susan Smith Family Foundation; the National Science Foundation; the Centers for Disease Control and Prevention-National Institute for Occupational Safety and Health; Inditex; and the National Institute of Allergy and Infectious Diseases of the National Institutes of Health.